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terrytao.wordpress.com

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao

MathAI / ML

’10’15’20’25
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1,168 from 22 Feb 2007 to 31 Oct 2026
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weekly (121 in the last year)
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2026 111

  1. Report of the Summit on Math Research in the Age of AI
  2. Collaborative retreat: New developments in the theory of zeta functions
  3. AI, Mathematics, Education, and a public goods problem
  4. On the diameter and distribution of Sidon sets
  5. 247A, Notes 3: Singular integral operators
  6. The quasi-Riemann hypothesis
  7. More additional blog posts and articles
  8. Disadvantages of Designating Mathematicians for AI Output Releases
  9. oai-math-revised: a community hub for revising OpenAI’s math write-ups
  10. IAS applications for membership in the school of mathematics
  11. Simple and critical zeros of the Riemann zeta-function
  12. Mathematics is a subject for the young
  13. An experimental AI-math challenge: using tenth discriminant bounds to explore arguments ruling out Siegel zeroes
  14. A sketch of the proof of non-existence of Siegel zeroes
  15. The Bourgain Project
  16. Will it be a golden age or a dark age for mathematics (and science)?
  17. Starting a new journal
  18. Some of my recent talks and interviews
  19. SAIR Open Math OS released
  20. How to Formalize All of Mathematics
  21. Why are we even doing all this?
  22. Simons Foundation Launches $15M Effort To Help Mathematicians Navigate AI Era
  23. Call for stories: human–AI collaboration in recent mathematics
  24. First Proof, Third Batch webinar
  25. 2026 AMS Committee on Education Workshop Report
  26. This is normal bad work
  27. Additional recent pieces on math and AI
  28. Illustration beyond Proof
  29. Math 2.0
  30. What mathematicians should know about the Lean Theorem Prover: questions of reliability and AI
  31. What should we tell our students?
  32. AHM Statement on OpenAI’s October 6 Release of Mathematical Documents
  33. The barriers of perception
  34. Hexagon
  35. Changes to the Erdős problems web site
  36. Postdoc position on formal verification and algorithm discovery for numerical analysis
  37. The Future of Mathematics
  38. On classical solutions and singularity formation in incompressible fluids
  39. What does the advent of powerful AI models mean for mathematicians like me?
  40. AIM: an invitation to explore mathematics together
  41. 247A, Notes 2: The Hardy–Littlewood maximal function and applications
  42. arXiv updates its rate limiting policy
  43. Two reports
  44. How AI does, and does not, change the way I do math
  45. Joint Statement about Mathathon
  46. Cognitive Sanctuaries or: Manifesto of the Department Chair
  47. A value-based approach to mathematics
  48. ICIAM Statement on Mathematics and Artificial Intelligence
  49. Recommendations of the Summit on PhD Math Education in the Age of AI
  50. We’re gonna need a lot more mathematicians
  51. Headlines and inside stories: understanding and trust in AI for mathematics, science, and engineering
  52. Why I agreed to join AGMAI
  53. Open problems, open mathematics
  54. Announcing the Advisory Group on Mathematics and Artificial Intelligence
  55. 247A, Notes 1: Rearrangement-invariant spaces
  56. Why Do We Need Human Mathematicians Anymore?
  57. If math is more than proof, we need to better celebrate the rest of it
  58. SAIR’s Open Math Model initiative
  59. A CERN for AI-assisted science?
  60. Why I didn’t sign the Fields medallists’ letter
  61. Becoming a benchmark
  62. SAIR competition – Lean Kernel Challenge
  63. Proofs, Prompts and Posts
  64. Let the Diners Into the Kitchen
  65. Open letter from Fellows of the Royal Society on AI existential risk
  66. Fast math/slow math
  67. The technical debt of AI-generated mathematics
  68. Why I do mathematical research
  69. “Deep theorems were scarce and difficult and so became an effective mechanism to identify deep thought. AI has broken this system.”
  70. Happy, those able to know the causes of things
  71. Wimbledon, the U.S. Open, and the future of mathematics
  72. After Math
  73. Crowdsourcing a list of general resources on the purpose, value, and nature of mathematics
  74. The status of the Hodge conjecture
  75. On the Hodge conjecture
  76. A Severe Misalignment of AI in Mathematics
  77. On the existence of non-sofic groups
  78. SAIR competition: Andrews-Curtis challenge
  79. Stable singularity of the Euler equations on R^3
  80. Crowdsourcing a list of general resources on AI and mathematics
  81. Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations
  82. Rotating needles in space: the road to the Kakeya conjecture, and why it matters
  83. Mathematical Discourse
  84. Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
  85. Palomar – a registry of Lean verified mathematics
  86. A digestion of the proof of Sendov’s conjecture
  87. A partial digestion of the HRT counterexample
  88. A digestion of the Jacobian conjecture counterexample
  89. Two more apps: visualizing the zeta process and the motions of the heavens
  90. Visualizing the Gilbreath expectation sequence
  91. Call for long programs, workshops, and summer schools at IPAM
  92. A paper diagram visualizer
  93. A random variable visualizer
  94. Old and new apps, via modern coding agents
  95. Gilbreath’s conjecture: a Cramér random model and a deterministic analysis
  96. A digestion of unit distance constructions
  97. Third SAIR competition: inverse Galois challenge
  98. On the proposed rule changes to the administration of federal grants
  99. Modular Arithmetic Challenge
  100. Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond
  101. Products of consecutive integers with unusual anatomy
  102. Mathematical methods and human thought in the age of AI
  103. Local Bernstein theory, and lower bounds for Lebesgue constants
  104. Mathematics Distillation Challenge – Equational Theories
  105. SLMath Deputy Director Search
  106. Six Math Essentials
  107. IPAM industrial short course in generative AI algorithms – deadline for applications closing soon
  108. A crowdsourced repository for optimization constants?
  109. Rogers’ theorem on sieving
  110. The integrated explicit analytic number theory network
  111. Polynomial towers and inverse Gowers theory for bounded-exponent groups

2025 29

  1. The maximal length of the Erdős–Herzog–Piranian lemniscate in high degree
  2. The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale
  3. The story of Erdős problem #1026
  4. Quantitative correlations and some problems on prime factors of consecutive integers
  5. Growth rates of sequences governed by the squarefree properties of its translates
  6. Call for industry sponsors for IPAM’s RIPS program
  7. Climbing the cosmic distance ladder: another sample chapter
  8. Sum-difference exponents for boundedly many slopes, and rational complexity
  9. New Nikodym set constructions over finite fields
  10. Mathematical exploration and discovery at scale
  11. Smooth numbers and max-entropy
  12. A crowdsourced project to link up erdosproblems.com to the OEIS
  13. SLMath announces new research programs
  14. Rough numbers between consecutive primes
  15. Salem Prize now accepting nominations for 2025
  16. Decomposing a factorial into large factors (second version)
  17. On the number of exceptional intervals to the prime number theorem in short intervals
  18. A Lean companion to “Analysis I”
  19. Some variants of the periodic tiling conjecture
  20. A tool to verify estimates, II: a flexible proof assistant
  21. Orders of infinity
  22. A proof of concept tool to verify estimates
  23. Stonean spaces, projective objects, the Riesz representation theorem, and (possibly) condensed mathematics
  24. A suspicious conference
  25. Decomposing a factorial into large factors
  26. The three-dimensional Kakeya conjecture, after Wang and Zahl
  27. Closing the “green gap”: from the mathematics of the landscape function to lower electricity costs for households
  28. Cosmic Distance Ladder videos with Grant Sanderson (3blue1brown): commentary and corrections
  29. New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach

2024 26

  1. Quaternions and spherical trigonometry
  2. On the distribution of eigenvalues of GUE and its minors at fixed index
  3. AI for Math fund
  4. On several irrationality problems for Ahmes series
  5. Higher uniformity of arithmetic functions in short intervals II. Almost all intervals
  6. The elephant in the room
  7. Climbing the cosmic distance ladder: launching an instagram
  8. The equational theories project: a brief tour
  9. A pilot project in universal algebra to explore new ways to collaborate and use machine assistance?
  10. Pointwise convergence of bilinear polynomial averages over the primes
  11. A possible approach to finite time blowup for the Euler equations
  12. Planar point sets with forbidden four-point patterns and few distinct distances
  13. Erdos problem #385, the parity problem, and Siegel zeroes
  14. A result of Bui–Pratt–Zaharescu, and Erdös problem #437
  15. What are the odds, II: the Venezuelan presidential election
  16. Dense sets of natural numbers with unusually large least common multiples
  17. A computation-outsourced discussion of zero density theorems for the Riemann zeta function
  18. Salem prize now accepting nominations for 2024
  19. An abridged proof of Marton’s conjecture
  20. On product representations of squares
  21. Erratum for “An inverse theorem for the Gowers U^{s+1}[N]-norm”
  22. Notes on the B+B+t theorem
  23. Two announcements: AI for Math resources, and erdosproblems.com
  24. Marton’s conjecture in abelian groups with bounded torsion
  25. AI Mathematical Olympiad – Progress Prize Competition now open
  26. Talks at the JMM

2023 26

  1. A generalized Cauchy-Schwarz inequality via the Gibbs variational formula
  2. A slightly longer Lean 4 proof tour
  3. Formalizing the proof of PFR in Lean4 using Blueprint: a short tour
  4. On a conjecture of Marton
  5. A Maclaurin type inequality
  6. Bounding sums or integrals of non-negative quantities
  7. Undecidability of translational monotilings
  8. Monotone non-decreasing sequences of the Euler totient function
  9. Yoneda’s lemma as an identification of form and function: the case study of polynomials
  10. A lower bound on the mean value of the Erdős-Hooley delta function
  11. The convergence of an alternating series of Erdős, assuming the Hardy–Littlewood prime tuples conjecture
  12. Adjoint Brascamp-Lieb inequalities
  13. Sumsets and entropy revisited
  14. Salem Prize now accepting nominations
  15. Sums of GUE matrices and concentration of hives from correlation decay of eigengaps
  16. AI Anthology
  17. An upper bound on the mean value of the Erdős-Hooley delta function
  18. Inequalities, convergence, and continuity as “special deals”
  19. AI to Assist Mathematical Reasoning: A Workshop
  20. PCAST Working Group on Generative AI Invites Public Input
  21. Elias M. Stein Prize for New Perspectives in Analysis
  22. A Host–Kra F^omega_2-system of order 5 that is not Abramov of order 5, and non-measurability of the inverse theorem for the U^6(F^n_2) norm; The structure of totally disconnected Host–Kra–Ziegler factors, and the inverse theorem for the U^k Gowers uniformity norms on finite abelian groups of bounded
  23. Mathematics for Humanity initiative – application deadline extended to June 1
  24. Would it be possible to create a tool to automatically diagram papers?
  25. Infinite partial sumsets in the primes
  26. Illustrating the Impact of the Mathematical Sciences

2022 27

  1. Special relativity and Middle-Earth
  2. An improvement to Bennett’s inequality for the Poisson distribution
  3. Postdoctoral Research Positions in Mathematics and AI at the Sydney Mathematics Research Institute
  4. A counterexample to the periodic tiling conjecture
  5. Trying out Mathstodon
  6. UCLA Math Undergraduate Merit Scholarship for 2023
  7. Upcoming workshop on “Machine assisted proofs” at IPAM
  8. A Bayesian probability worksheet
  9. What are the odds?
  10. A counterexample to the periodic tiling conjecture
  11. Using the Smith normal form to manipulate lattice subgroups and closed torus subgroups
  12. Request for comments from the ICM Structure Committee
  13. ICM and IMU award ceremony begins tomorrow
  14. Registration for the virtual ICM is now open
  15. Notes on inverse theorem entropy
  16. Partially specified mathematical objects, ambient parameters, and asymptotic notation
  17. Higher uniformity of arithmetic functions in short intervals I. All intervals
  18. Nominations for 2023 Doob prize now open
  19. Web page for the Short Communication Satellite (SCS) of the 2022 virtual ICM now live
  20. Short communication satellite event for the 2022 virtual ICM?
  21. 2022 ICM satellite coordination group
  22. Measurable tilings by abelian group actions
  23. Resources for displaced mathematicians
  24. The International Congress of Mathematicians (ICM 2022) will now be fully virtual. How best to utilise this format?
  25. Satz vom Nullprodukt
  26. Perfectly packing a square by squares of nearly harmonic sidelength
  27. Masterclass on mathematical thinking

2021 22

  1. The inverse theorem for the U^3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
  2. The structure of arbitrary Conze-Lesigne systems
  3. A math rave
  4. Venn and Euler type diagrams for vector spaces and abelian groups
  5. Nines of safety: a proposed unit of measurement of risk
  6. The Hardy–Littlewood–Chowla conjecture in the presence of a Siegel zero
  7. More analysis questions from a high school student
  8. Undecidable translational tilings with only two tiles, or one nonabelian tile
  9. Varieties of general type with many vanishing plurigenera, and optimal sine and sawtooth inequalities
  10. The Gowers uniformity norm of order 1+
  11. Quantitative bounds for Gowers uniformity of the Mobius and von Mangoldt functions
  12. Singmaster’s conjecture in the interior of Pascal’s triangle
  13. Goursat and Furstenberg-Weiss type lemmas
  14. Is there a non-analytic function with all differences analytic?
  15. Boosting the van der Corput inequality using the tensor power trick
  16. The inclusion-exclusion principle for commuting projections
  17. Job advertisement: Director of UCLA Endowed Olga Radko Math Circle (ORMC)
  18. 246B, Notes 4: The Riemann zeta function and the prime number theorem
  19. A statement from mathematics department faculty at Stanford and MIT
  20. 246B, Notes 3: Elliptic functions and modular forms
  21. 246B, Notes 2: Some connections with the Fourier transform
  22. The effective potential of an M-matrix

2020 38

  1. 246B, Notes 1: Zeroes, poles, and factorisation of meromorphic functions
  2. Course announcement: 246B, complex analysis
  3. Sendov’s conjecture for sufficiently high degree polynomials
  4. Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle
  5. Holomorphic images of disks
  6. A correction to “An arithmetic regularity lemma, an associated counting lemma, and applications”
  7. Climbing the cosmic distance ladder (book announcement)
  8. The structure of translational tilings in Z^d
  9. Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration
  10. An uncountable Mackey-Zimmer theorem
  11. Exploring the toolkit of Jean Bourgain
  12. Course announcement: Math 246A, complex analysis
  13. Vaughan Jones
  14. Zarankiewicz’s problem for semilinear hypergraphs
  15. Fractional free convolution powers
  16. The Ionescu-Wainger multiplier theorem and the adeles
  17. Pointwise ergodic theorems for non-conventional bilinear polynomial averages
  18. Higher uniformity of bounded multiplicative functions in short intervals on average
  19. The sunflower lemma via Shannon entropy
  20. Homogenization of iterated singular integrals with applications to random quasiconformal maps
  21. 247B, Notes 4: almost everywhere convergence of Fourier series
  22. 247B, Notes 3: pseudodifferential operators
  23. 247B, Notes 2: Decoupling theory
  24. John Conway
  25. Mathematics Seminars List
  26. 247B, Notes 1: Restriction theory
  27. Polymath proposal: clearinghouse for crowdsourcing COVID-19 data and data cleaning requests
  28. 2019-2020 Novel Coronavirus outbreak: mathematics of epidemics, and what it can and cannot tell us (Nicolas Jewell)
  29. Abel prize awarded to Furstenberg and Margulis
  30. Course announcement: Math 247B, Classical Fourier Analysis
  31. Analysis and applications: The mathematical work of Elias Stein
  32. Options for giving math talks and lectures online
  33. Cut norms and degree lowering
  34. Illustrating the impact of the mathematical sciences
  35. Some slides from Basel
  36. Louis Nirenberg
  37. Equidistribution of Syracuse random variables and density of Collatz preimages
  38. Some recent papers

2019 35

  1. Elgindi’s approximation of the Biot-Savart law
  2. 254A, Notes 10 – mean values of nonpretentious multiplicative functions
  3. Maryam Mirzakhani New Frontiers Prize
  4. Eigenvectors from Eigenvalues: a survey of a basic identity in linear algebra
  5. An uncountable Moore-Schmidt theorem
  6. 254A, Notes 9 – second moment and entropy methods
  7. Almost all Collatz orbits attain almost bounded values
  8. 254A announcement: Analytic prime number theory
  9. Large prime gaps and probabilistic models
  10. Quantitative bounds for critically bounded solutions to the Navier-Stokes equations
  11. Eigenvectors from eigenvalues
  12. Sharp bounds for multilinear curved Kakeya, restriction and oscillatory integral estimates away from the endpoint
  13. Twisted convolution and the sensitivity conjecture
  14. Symmetric functions in a fractional number of variables, and the multilinear Kakeya conjecture
  15. Living Proof: Stories of Resilience Along the Mathematical Journey
  16. Abstracting induction on scales arguments
  17. Ruling out polynomial bijections over the rationals via Bombieri-Lang?
  18. Searching for singularities in the Navier–Stokes equations
  19. The spherical Cayley-Menger determinant and the radius of the Earth
  20. A function field analogue of Riemann zeta statistics
  21. The alternative hypothesis for unitary matrices
  22. Submissions for the Breakthrough Junior Challenge now open
  23. Local trigonometric polynomial approximations to the Riemann zeta function
  24. Effective approximation of heat flow evolution of the Riemann xi function, and a new upper bound for the de Bruijn-Newman constant
  25. Nominations for 2020 Doob Prize now open
  26. Value patterns of multiplicative functions and related sequences
  27. Conversions between standard polynomial bases
  28. Uhlenbeck’s theorem on connections with small curvature
  29. Prismatic cohomology
  30. Two announcements
  31. On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows
  32. Two events
  33. Request for comments from the ICM Structure Committee
  34. Word maps close to the identity
  35. 255B, Notes 2: Onsager’s conjecture

2018 44

  1. Jean Bourgain
  2. Polymath15, eleventh thread: Writing up the results, and exploring negative t
  3. Elias Stein
  4. 255B, Notes 1: The Lagrangian formulation of the Euler equations
  5. 254A, Supplemental: Weak solutions from the perspective of nonstandard analysis (optional)
  6. Fourier uniformity of bounded multiplicative functions in short intervals on average
  7. Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion
  8. The nonlinearity of the Fefferman-Stein decomposition
  9. 254A, Notes 3: Local well-posedness for the Euler equations
  10. 254A, Notes 2: Weak solutions of the Navier-Stokes equations
  11. 254A, Notes 1: Local well-posedness of the Navier-Stokes equations
  12. On the recently removed paper from the New York Journal of Mathematics
  13. The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures
  14. Polymath15, tenth thread: numerics update
  15. 254A, Notes 0: Physical derivation of the incompressible Euler and Navier-Stokes equations
  16. Trying to understand the Galois correspondence
  17. QED version 2.0: an interactive text in first-order logic
  18. Birkar, Figalli, Scholze, Venkatesh
  19. Gamifying propositional logic: QED, an interactive textbook
  20. A corollary of the ergodic theorem
  21. 1% quasimorphisms and group cohomology
  22. Heat flow and zeroes of polynomials II: zeroes on a circle
  23. Commutators close to the identity – an update
  24. 246C notes 4: Brownian motion, conformal invariance, and SLE
  25. Polymath15, ninth thread: going below 0.22?
  26. 246C notes 3: Univalent functions, the Loewner equation, and the Bieberbach conjecture
  27. Polymath15, eighth thread: going below 0.28
  28. Polymath16 now launched: simplifying the lower bound argument for the Hadwiger-Nelson problem
  29. 246C notes 2: Circle packings, conformal maps, and quasiconformal maps
  30. Commutators close to the identity
  31. 246C notes 1: Meromorphic functions on Riemann surfaces, and the Riemann-Roch theorem
  32. Polymath15, seventh thread: going below 0.48
  33. Polymath15, sixth thread: the test problem and beyond
  34. Course announcement: 246C, complex analysis
  35. Polymath15, fifth thread: finishing off the test problem?
  36. Polymath15, fourth thread: closing in on the test problem
  37. Long gaps in sieved sets
  38. Polymath15, third thread: computing and approximating H_t
  39. Polymath15, second thread: generalising the Riemann-Siegel approximate functional equation
  40. Polymath15, first thread: computing H_t, asymptotics, and dynamics of zeroes
  41. Polymath proposal: upper bounding the de Bruijn-Newman constant
  42. Lehmer pairs and GUE
  43. The De Bruijn-Newman constant is non-negative
  44. Homogeneous length functions on groups

2017 38

  1. Correlations of the von Mangoldt and higher divisor functions II. Divisor correlations in short ranges
  2. Metrics of linear growth – the solution
  3. Bi-invariant metrics of linear growth on the free group, II
  4. Bi-invariant metrics of linear growth on the free group
  5. Embedding the Boussinesq equations in the incompressible Euler equations on a manifold
  6. An inverse theorem for an inequality of Kneser
  7. Continuous approximations to arithmetic functions
  8. IPAM program in quantitative linear algebra, Mar 19-Jun 15 2018
  9. UCLA Math Undergraduate Merit Scholarship for 2018
  10. The logarithmically averaged and non-logarithmically averaged Chowla conjectures
  11. Heat flow and zeroes of polynomials
  12. Odd order cases of the logarithmically averaged Chowla conjecture
  13. An update to “On the sign patterns of entrywise positivity preservers in fixed dimension”
  14. Inverting the Schur complement, and large-dimensional Gelfand-Tsetlin patterns
  15. Szemeredi’s proof of Szemeredi’s theorem
  16. Continuous analogues of the Schur and skew Schur polynomials
  17. Dodgson condensation from Schur complementation
  18. An addendum to “amplification, arbitrage, and the tensor power trick”
  19. On the sign patterns of entrywise positivity preservers in fixed dimension
  20. The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
  21. Schur convexity and positive definiteness of the even degree complete homogeneous symmetric polynomials
  22. On the universality of the incompressible Euler equation on compact manifolds
  23. Maryam Mirzakhani
  24. On the universality of potential well dynamics
  25. What are some useful, but little-known, features of the tools used in professional mathematics?
  26. Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges
  27. PCMI lecture notes on random matrix theory
  28. Quantitative continuity estimates
  29. Generalisations of the limit functional
  30. New bounds for Szemerédi’s theorem, III: A polylogarithmic bound for r_4(N)
  31. Notes on nilcharacters and their symbols
  32. Counting objects up to isomorphism: groupoid cardinality
  33. Yves Meyer wins the 2017 Abel Prize
  34. Furstenberg limits of the Liouville function
  35. Special cases of Shannon entropy
  36. A bound on partitioning clusters
  37. Open thread for mathematicians on the immigration executive order
  38. Some remarks on the lonely runner conjecture

2016 37

  1. AMS open math notes
  2. Finite time blowup for a supercritical defocusing nonlinear Schrodinger system
  3. Call for nominations for the 2018 Chern Medal
  4. An integration approach to the Toeplitz square peg problem
  5. Another problem about power series
  6. 246A, Notes 5: conformal mapping
  7. A problem involving power series
  8. Math 246A, Notes 4: singularities of holomorphic functions
  9. Math 246A, Notes 3: Cauchy’s theorem and its consequences
  10. 246A, Notes 2: complex integration
  11. 246A, Notes 1: complex differentiation
  12. 246A, Notes 0: the complex numbers
  13. Course announcement: 246A, complex analysis
  14. Heuristic computation of correlations of higher order divisor functions
  15. Heuristic computation of correlations of the divisor function
  16. An erratum to “Global regularity of wave maps. II. Small energy in two dimensions”
  17. Notes on the “slice rank” of tensors
  18. Notes on the Bombieri asymptotic sieve
  19. Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation
  20. It ought to be common knowledge that Donald Trump is not fit for the presidency of the United States of America
  21. How to assign partial credit on an exam of true-false questions?
  22. A symmetric formulation of the Croot-Lev-Pach-Ellenberg-Gijswijt capset bound
  23. Equivalence of the logarithmically averaged Chowla and Sarnak conjectures
  24. Visualising random variables
  25. Notes on the Nash embedding theorem
  26. L-functions and modular forms database now out of beta
  27. IMU Graduate Breakout Fellowships – Call for Nominations
  28. A quick application of the closed graph theorem
  29. Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors; polynomial patterns in primes
  30. Biases between consecutive primes
  31. Sumfree sets in groups
  32. Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity
  33. Nominations for 2017 Breakthrough and New Horizons Prizes now open
  34. Discrete Analysis site now live
  35. Finite time blowup for a supercritical defocusing nonlinear wave system
  36. Finite time blowup for an Euler-type equation in vorticity stream form
  37. IPAM begins search for new director

2015 52

  1. A new polymath proposal: explaining identities for irreducible polynomials
  2. The two-dimensional case of the Bourgain-Demeter-Guth proof of the Vinogradov main conjecture
  3. Decoupling and the Bourgain-Demeter-Guth proof of the Vinogradov main conjecture
  4. A conjectural local Fourier-uniformity of the Liouville function
  5. A cheap version of Halasz’s inequality
  6. 275A, Notes 5: Variants of the central limit theorem
  7. Chains of large gaps between primes
  8. Klaus Roth
  9. Analytic number theory program at MSRI: Jan-May 2017 (second announcement)
  10. 275A, Notes 4: The central limit theorem
  11. A small remark on the Elliott conjecture
  12. 275A, Notes 3: The weak and strong law of large numbers
  13. 275A, Notes 2: Product measures and independence
  14. Sweeping a matrix rotates its graph
  15. 275A, Notes 1: Integration and expectation
  16. 275A, Notes 0: Foundations of probability theory
  17. Entropy and rare events
  18. The logarithmically averaged Chowla and Elliott conjectures for two-point correlations; the Erdos discrepancy problem
  19. The Erdos discrepancy problem via the Elliott conjecture
  20. Sign patterns of the Mobius and Liouville functions
  21. Heath-Brown’s theorem on prime twins and Siegel zeroes
  22. A wave equation approach to automorphic forms in analytic number theory
  23. Equidistribution for multidimensional polynomial phases
  24. Analytic Number Theory program at MSRI: Jan-May 2017
  25. Deducing the inverse theorem for the multidimensional Gowers norms from the one-dimensional version
  26. Deducing a weak ergodic inverse theorem from a combinatorial inverse theorem
  27. An inverse theorem for the continuous Gowers uniformity norm
  28. A nonstandard analysis proof of Szemeredi’s theorem
  29. Cycles of a random permutation, and irreducible factors of a random polynomial
  30. Inverse theorems for sets and measures of polynomial growth
  31. Gaps between primes
  32. Nested approximate subgroups
  33. A differentiation identity
  34. Cancellation for the multilinear Hilbert transform
  35. Failure of the L^1 pointwise and maximal ergodic theorems for the free group
  36. A remark on the lonely runner conjecture
  37. The standard branch of the matrix logarithm
  38. Embedding the SQG equation in a modified Euler equation
  39. Newton iteration and the Siegel linearisation theorem
  40. The ergodic theorem and Gowers-Host-Kra seminorms without separability or amenability
  41. Random matrices: tail bounds for gaps between eigenvalues
  42. 254A, Notes 8: The Hardy-Littlewood circle method and Vinogradov’s theorem
  43. An averaged form of Chowla’s conjecture
  44. 254A, Supplement 7: Normalised limit profiles of the log-magnitude of the Riemann zeta function (optional)
  45. 254A, Supplement 6: A cheap version of the theorems of Halasz and Matomaki-Radziwiłł (optional)
  46. 254A, Notes 7: Linnik’s theorem on primes in arithmetic progressions
  47. 254A, Notes 6: Large values of Dirichlet polynomials, zero density estimates, and primes in short intervals
  48. 254A, Notes 5: Bounding exponential sums and the zeta function
  49. 254A, Supplement 5: The linear sieve and Chen’s theorem (optional)
  50. 254A, Notes 4: Some sieve theory
  51. 254A, Notes 3: The large sieve and the Bombieri-Vinogradov theorem
  52. 254A, Supplement 4: Probabilistic models and heuristics for the primes (optional)

2014 52

  1. The Erdos-Ulam problem, varieties of general type, and the Bombieri-Lang conjecture
  2. Long gaps between primes
  3. 254A, Supplement 3: The Gamma function and the functional equation (optional)
  4. 254A, Notes 2: Complex-analytic multiplicative number theory
  5. 254A, Supplement 2: A little bit of complex and Fourier analysis
  6. Random matrices have simple spectrum
  7. 254A, Supplement 1: A little bit of algebraic number theory (optional)
  8. 254A, Notes 1: Elementary multiplicative number theory
  9. A general parity problem obstruction
  10. 254A announcement: Analytic prime number theory
  11. Discretised wave equations
  12. The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture
  13. A Banach algebra proof of the prime number theorem
  14. Additive limits
  15. A trivial generalisation of Cayley’s theorem
  16. The “bounded gaps between primes” Polymath project – a retrospective
  17. Derived multiplicative functions
  18. Narrow progressions in the primes
  19. Large gaps between consecutive prime numbers
  20. (Matilde Lalin) Attending conferences with small children
  21. Khot, Osher, Griffiths
  22. Avila, Bhargava, Hairer, Mirzakhani
  23. Variants of the Selberg sieve, and bounded intervals containing many primes
  24. Real analysis relative to a finite measure space
  25. The parity problem obstruction for the binary Goldbach problem with bounded error
  26. Hilbert’s fifth problem and approximate groups
  27. The subspace theorem approach to Siegel’s theorem on integral points on curves via nonstandard analysis
  28. Algebraic probability spaces
  29. Lebesgue measure as the invariant factor of Loeb measure
  30. An abstract ergodic theorem, and the Mackey-Zimmer theorem
  31. Polymath8: wrapping up
  32. When is correlation transitive?
  33. Polymath 8b, XI: Finishing up the paper
  34. Kolmogorov’s power law for turbulence
  35. Dwork’s proof of rationality of the zeta function over finite fields
  36. Stickiness, graininess, planiness, and a sum-product approach to the Kakeya problem
  37. The Bombieri-Stepanov proof of the Hasse-Weil bound
  38. A proof of Roth’s theorem
  39. Polymath8b, X: writing the paper, and chasing down loose ends
  40. The Monge-Cayley-Salmon theorem via classical differential geometry
  41. Metric entropy analogues of sum set theory
  42. Conserved quantities for the surface quasi-geostrophic equation
  43. Noether’s theorem, and the conservation laws for the Euler equations
  44. Conserved quantities for the Euler equations
  45. Polymath8b, IX: Large quadratic programs
  46. Polymath8b, VIII: Time to start writing up the results?
  47. “New equidistribution estimates of Zhang type, and bounded gaps between primes” – and a retrospective
  48. Finite time blowup for an averaged three-dimensional Navier-Stokes equation
  49. Polymath8b, VII: Using the generalised Elliott-Halberstam hypothesis to enlarge the sieve support yet further
  50. Polymath8b, VI: A low dimensional variational problem
  51. Polymath8b, V: Stretching the sieve support further
  52. A sporadic image resizing bug in WordPress LaTeX

2013 53

  1. Polymath8b, IV: Enlarging the sieve support, more efficient numerics, and explicit asymptotics
  2. Mertens’ theorems
  3. Polymath8b, III: Numerical optimisation of the variational problem, and a search for new sieves
  4. Ultraproducts as a Bridge Between Discrete and Continuous Analysis
  5. Polymath8b, II: Optimising the variational problem and the sieve
  6. Polymath8b: Bounded intervals with many primes, after Maynard
  7. Polymath8: Writing the first paper, V, and a look ahead
  8. Qualitative probability theory, types, and the group chunk and group configuration theorems
  9. Real stable polynomials and the Kadison-Singer problem
  10. Expansion in finite simple groups of Lie type
  11. A spectral theory proof of the algebraic regularity lemma
  12. Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
  13. Polymath8: Writing the paper, IV
  14. Polymath8: Writing the paper, III
  15. The Poisson-Dirichlet process, and large prime factors of a random number
  16. Expansion in finite simple groups of Lie type
  17. Notes on simple groups of Lie type
  18. Polymath8: Writing the paper, II
  19. Polymath8: Writing the paper
  20. An improved Type I estimate
  21. Computing convolutions of measures
  22. The Riemann hypothesis in various settings
  23. A cheap version of the Kabatjanskii-Levenstein bound for almost orthogonal vectors
  24. Local universality of zeroes of random polynomials
  25. A physical space proof of the bilinear Strichartz and local smoothing estimates for the Schrodinger equation
  26. The distribution of primes in doubly densely divisible moduli
  27. Bounded gaps between primes (Polymath8) – a progress report
  28. The distribution of primes in densely divisible moduli
  29. Bounding short exponential sums on smooth moduli via Weyl differencing
  30. A truncated elementary Selberg sieve of Pintz
  31. Estimation of the Type III sums
  32. A multi-dimensional Szemer\’edi theorem for the primes via a correspondence principle
  33. Estimation of the Type I and Type II sums
  34. Further analysis of the truncated GPY sieve
  35. A combinatorial subset sum problem associated with bounded prime gaps
  36. The elementary Selberg sieve and bounded prime gaps
  37. Online reading seminar for Zhang’s “bounded gaps between primes”
  38. The prime tuples conjecture, sieve theory, and the work of Goldston-Pintz-Yildirim, Motohashi-Pintz, and Zhang
  39. A Fourier-analytic proof of Frobenius’ theorem
  40. Multiple recurrence and convergence results associated to F_p^omega-actions
  41. (Ingrid Daubechies) Planning for the World Digital Mathematical Library
  42. Quasirandom groups and a cheap version of the Brauer-Fowler theorem
  43. Notes on the classification of complex Lie algebras
  44. The theorems of Frobenius and Suzuki on finite groups
  45. An informal version of the Furstenberg correspondence principle
  46. Rectification and the Lefschetz principle
  47. A Fourier-free proof of the Furstenberg-Sarkozy theorem
  48. Supercommutative gaussian integration, and the gaussian unitary ensemble
  49. The pseudoconformal and conformal transformations
  50. The Harish-Chandra-Itzykson-Zuber integral formula
  51. Some notes on Bakry-Emery theory
  52. Small doubling in groups
  53. Matrix identities as derivatives of determinant identities

2012 52

  1. A mathematical formalisation of dimensional analysis
  2. An introduction to special relativity for a high school math circle
  3. Mixing for progressions in non-abelian groups
  4. The spectral proof of the Szemeredi regularity lemma
  5. Lars Hormander
  6. Multiple recurrence in quasirandom groups
  7. The closed graph theorem in various categories
  8. Spending symmetry
  9. UCLA Math Undergraduate Merit Scholarship for 2013
  10. Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets
  11. A direct proof of the stationarity of the Dyson sine process under Dyson Brownian motion
  12. van Kampen’s theorem via covering spaces
  13. Walsh’s ergodic theorem, metastability, and external Cauchy convergence
  14. Garth Gaudry
  15. The Chowla conjecture and the Sarnak conjecture
  16. Some notes on Weyl quantisation
  17. Einstein’s derivation of E=mc^2 revisited
  18. A partial converse to Bezout’s theorem
  19. The probabilistic heuristic justification of the ABC conjecture
  20. Definable subsets over (nonstandard) finite fields, and almost quantifier elimination
  21. A trivial remark about schemes
  22. The Lang-Weil bound
  23. On sets defining few ordinary lines
  24. Bill Thurston
  25. Call for nominations: National Academy of Sciences Award for Scientific Reviewing
  26. Mini-polymath4 discussion thread
  27. Mini-polymath4 begins in three hours
  28. Forum of Mathematics, Pi and Forum of Mathematics, Sigma
  29. Updates on the two polymath projects
  30. Random matrices: Universality of local spectral statistics of non-Hermitian matrices
  31. Two polymath projects
  32. Heuristic limitations of the circle method
  33. Cayley graphs and the algebra of groups
  34. New bounds for Szemeredi’s theorem, Ia: Progressions of length 4 in finite field geometries revisited
  35. Lewis Carroll logic puzzles
  36. New version of algebra game
  37. Gamifying algebra?
  38. A cheap version of nonstandard analysis
  39. Hilbert’s fifth problem and related topics
  40. Some ingredients in Szemerédi’s proof of Szemerédi’s theorem
  41. 254A, addendum: Some notes on nilprogressions
  42. The asymptotic distribution of a single eigenvalue gap of a Wigner matrix
  43. 254B, Notes 7: Sieving and expanders
  44. 254B, Notes 6: Non-concentration in subgroups
  45. A statement on the cost of knowledge declaration
  46. 254B, Notes 5: Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
  47. Random matrices: The Universality phenomenon for Wigner ensembles
  48. Every odd integer larger than 1 is the sum of at most five primes
  49. The cost of knowledge
  50. Random matrices: Sharp concentration of eigenvalues
  51. 254B, Notes 4: The Bourgain-Gamburd expansion machine
  52. Continued fractions, Bohr sets, and the Littlewood conjecture

2011 86

  1. Montgomery’s uncertainty principle
  2. A variant of Kemperman’s theorem
  3. A nilpotent Freiman dimension lemma
  4. The spectral theorem and its converses for unbounded symmetric operators
  5. 254B, Notes 3: Quasirandom groups, expansion, and Selberg’s 3/16 theorem
  6. Random matrices: The Four Moment Theorem for Wigner ensembles
  7. 254B, Notes 2: Cayley graphs and Kazhdan’s property (T)
  8. 254B, Notes 1: Basic theory of expander graphs
  9. A central limit theorem for the determinant of a Wigner matrix
  10. Course announcement: 254B, expansion in groups of Lie type
  11. The number of cycles in a random permutation
  12. The Katai-Bourgain-Sarnak-Ziegler orthogonality criterion
  13. Some notes on the Coven-Meyerowitz conjecture
  14. 254A, Notes 9: Applications of the structural theory of approximate groups
  15. UCLA Math Undergraduate Merit Scholarship for 2012
  16. 254A, Notes 8: The microstructure of approximate groups
  17. Associativity of the Baker-Campbell-Hausdorff formula
  18. 254A, Notes 7: Models of ultra approximate groups
  19. The structure of approximate groups
  20. 254A, Notes 6: Ultraproducts as a bridge between hard analysis and soft analysis
  21. 254A, Notes 5: The structure of locally compact groups, and Hilbert’s fifth problem
  22. The Jordan-Schur theorem
  23. 254A, Notes 4: Building metrics on groups, and the Gleason-Yamabe theorem
  24. 254A, Notes 3: Haar measure and the Peter-Weyl theorem
  25. The Brunn-Minkowski inequality for nilpotent groups
  26. “Introduction to measure theory” now published
  27. The inverse function theorem for everywhere differentiable maps
  28. 254A, Notes 2: Building Lie structure from representations and metrics
  29. 254A, Notes 1: Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula
  30. 254A, Notes 0: Hilbert’s fifth problem and related topics
  31. The Collatz conjecture, Littlewood-Offord theory, and powers of 2 and 3
  32. Hilbert’s seventh problem, and powers of 2 and 3
  33. Notes on local groups
  34. The Hilbert-Smith conjecture
  35. A geometric proof of the impossibility of angle trisection by straightedge and compass
  36. A correction to “Localisation and compactness properties of the Navier-Stokes global regularity problem”
  37. Localisation and compactness properties of the Navier-Stokes global regularity problem
  38. Counting the number of solutions to the Erdös-Straus equation on unit fractions
  39. Erdos’ divisor bound
  40. Mini-polymath3 discussion thread
  41. Mini-polymath3 begins in 24 hours
  42. Pappus’s theorem and elliptic curves
  43. Gleason’s lemma
  44. On the number of solutions to 4/p = 1/n_1 + 1/n_2 + 1/n_3
  45. Polynomial bounds via nonstandard analysis
  46. Compactness and contradiction
  47. Mini-polymath 3 time and date
  48. Two small facts about Lie groups
  49. The C^{1,1} Baker-Campbell-Hausdorff formula
  50. Hilbert’s fifth problem and Gleason metrics
  51. Brouwer’s fixed point and invariance of domain theorems, and Hilbert’s fifth problem
  52. Mini-polymath 3: 2011 IMO question
  53. Central extensions of Lie groups, and cocycle averaging
  54. The Furstenberg multiple recurrence theorem and finite extensions
  55. van Dantzig’s theorem
  56. Locally compact groups with faithful finite-dimensional representations
  57. The Cotlar-Stein lemma
  58. Locally compact topological vector spaces
  59. Stein’s spherical maximal theorem
  60. Epistemic logic, temporal epistemic logic, and the blue-eyed islander puzzle lower bound
  61. The Birkhoff-Kakutani theorem
  62. Stein’s maximal principle
  63. Ado’s theorem
  64. Effective limiting absorption principles, and applications
  65. Stein’s interpolation theorem
  66. The limiting absorption principle
  67. A proof of the Fredholm alternative
  68. The blue-eyed islanders puzzle – repost
  69. Higher order Fourier analysis
  70. An erratum to “Strongly dense free subgroups of semisimple Lie groups”
  71. Bezout’s inequality
  72. An incidence theorem in higher dimensions
  73. Random matrices: Universality of eigenvectors
  74. The shallow water wave equation and tsunami propagation
  75. Hamidoune’s Freiman-Kneser theorem for nonabelian groups
  76. Exceptional isogenies between the classical Lie groups
  77. Rohlin’s problem on strongly mixing systems
  78. Lines in the Euclidean group SE(2)
  79. Topics in random matrix theory
  80. The Szemeredi-Trotter theorem via the polynomial ham sandwich theorem
  81. The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices
  82. Universality
  83. An introduction to measure theory
  84. The Peter-Weyl theorem, and non-abelian Fourier analysis on compact groups
  85. A note on approximate subgroups of GL_n(C) and uniformly nonamenable groups
  86. The inverse conjecture for the Gowers norm over finite fields in low characteristic

2010 90

  1. The Bourgain-Guth argument for proving restriction theorems
  2. Outliers in the spectrum of iid matrices with bounded rank perturbations
  3. “An epsilon of room”, Vol. I, now published
  4. The mesoscopic structure of GUE eigenvalues
  5. Large values of the Gowers-Host-Kra seminorms
  6. Concentration compactness via nonstandard analysis
  7. Nonstandard analysis as a completion of standard analysis
  8. The Guth-Katz bound on the Erdős distance problem
  9. UCLA Math Undergraduate Merit Scholarship for 2011
  10. Asymptotic decay for a one-dimensional nonlinear wave equation
  11. The “no self-defeating object” argument, and the vagueness paradox
  12. 245A, Notes 6: Outer measures, pre-measures, and product measures
  13. The Dyson and Airy kernels of GUE via semiclassical analysis
  14. 245A: Problem solving strategies
  15. Strongly dense free subgroups of semisimple algebraic groups
  16. The “no self-defeating object” argument, revisited
  17. 245A, Notes 5: Differentiation theorems
  18. The Cosmic Distance Ladder (version 4.1)
  19. Covering a non-closed interval by disjoint closed intervals
  20. 245A, Notes 4: Modes of convergence
  21. Polymath3 now active
  22. 245A, Notes 3: Integration on abstract measure spaces, and the convergence theorems
  23. An inverse theorem for the Gowers U^{s+1}[N] norm
  24. Deterministic methods to find primes
  25. 245A, Notes 2: The Lebesgue integral
  26. A second draft of a non-technical article on universality
  27. 245A, Notes 1: Lebesgue measure
  28. A first draft of a non-technical article on universality
  29. 245A, prologue: The problem of measure
  30. Course announcement: 245A, Real analysis
  31. Spielman, Meyer, Nirenberg
  32. Lindenstrauss, Ngo, Smirnov, Villani
  33. On hiatus II
  34. The Golden-Thompson inequality
  35. Cayley graphs and the geometry of groups
  36. Mini-polymath2 discussion thread
  37. Finitary consequences of the invariant subspace problem
  38. Mini-polymath2 start time
  39. The uncertainty principle
  40. Organising mini-polymath2
  41. Future mini-polymath project: 2010 IMO Q6?
  42. The Euler-Arnold equation
  43. 254B, Lecture Notes 7: The transference principle, and linear equations in primes
  44. An inverse theorem for the Gowers norm U^{s+1}[N] (announcement)
  45. 254B, Notes 6: The inverse conjecture for the Gowers norm II. The integer case
  46. 254B, Notes 5: The inverse conjecture for the Gowers norm I. The finite field case
  47. Higher order Hilbert spaces
  48. Random matrices: Localization of the eigenvalues and the necessity of four moments
  49. Approximate subgroups of linear groups
  50. 254B, Lecture Notes 4: Equidistribution of polynomials over finite fields
  51. Suzuki groups as expanders
  52. Some links
  53. Suggestions for games that promote mathematical thinking?
  54. 254B, Notes 3: Linear patterns
  55. DHJ Polymath paper accepted
  56. Write in your own voice
  57. Is there a countable certificate for connectedness?
  58. The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation
  59. 254B, Notes 2: Roth’s theorem
  60. Amplitude-frequency dynamics for semilinear dispersive equations
  61. 254B, Notes 1: Equidistribution of polynomial sequences in tori
  62. Scale-oblivious metric fragmentation and the nonlinear Dvoretzky theorem
  63. A computational perspective on set theory
  64. 254A, Notes 8: The circular law
  65. A type diagram for function spaces
  66. Course announcement: 254B, Higher order Fourier analysis
  67. 254A, Notes 7: The least singular value
  68. The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi
  69. 254A, Notes 6: Gaussian ensembles
  70. Quasilinear well-posedness
  71. A proof of Gromov’s theorem
  72. Yet another proof of Szemerédi’s theorem
  73. An arithmetic regularity lemma, an associated counting lemma, and applications
  74. Buzzing
  75. 254A, Notes 5: Free probability
  76. An epsilon of room: pages from year three of a mathematical blog
  77. Density Hales-Jewett and Moser numbers
  78. 254A, Notes 4: The semi-circular law
  79. Ultralimit analysis, and quantitative algebraic geometry
  80. Linear approximate groups
  81. Some notes on group extensions
  82. 254A, Notes 3b: Brownian motion and Dyson Brownian motion
  83. “Density Hales-Jewett and Moser numbers” – nearing the final draft
  84. 254A, Notes 3a: Eigenvalues and sums of Hermitian matrices
  85. 254A, Notes 3: The operator norm of a random matrix
  86. Mean field games
  87. 254A, Notes 2: The central limit theorem
  88. 254A, Notes 1: Concentration of measure
  89. 254A, Notes 0a: Stirling’s formula
  90. 254A, Notes 0: A review of probability theory

2009 139

  1. Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems
  2. A demonstration of the non-commutativity of the English language
  3. The free nilpotent group
  4. The double Duhamel trick and the in/out decomposition
  5. Approximate bases, sunflowers, and nonstandard analysis
  6. Random covariance matrices: Universality of local statistics of eigenvalues
  7. Random Martingales and localization of maximal inequalities
  8. Non-commutative Freiman theorems, and model theory
  9. Reading seminar 6: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  10. Course announcement: 254A – random matrices
  11. An inverse theorem for the Gowers U^4 norm
  12. From Bose-Einstein condensates to the nonlinear Schrodinger equation
  13. Reading seminar 5: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  14. UCLA Math Seeks Exceptional Student for Undergraduate Merit Scholarship
  15. Nonstandard analogues of energy and density increment arguments
  16. An elementary non-commutative Freiman theorem
  17. Reading seminar 4: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  18. The “no self-defeating object” argument
  19. Displaying maths online, II
  20. Reading seminar 3: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  21. Displaying mathematics on the Web
  22. An entropy Plünnecke-Ruzsa inequality
  23. Applications-oriented periodic table
  24. A finitary version of Gromov’s polynomial growth theorem
  25. Reading seminar 2: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  26. A new proof of the density Hales-Jewett theorem
  27. Math Overflow
  28. Grothendieck’s definition of a group
  29. Reading seminar: “Stable group theory and approximate subgroups”, by Ehud Hrushovski
  30. Global wellposedness for the Maxwell-Klein-Gordon equation below the energy norm
  31. A variation norm Carleson theorem
  32. Israel Gelfand
  33. Mazur’s swindle
  34. At the AustMS conference
  35. Two quick updates
  36. The prime number theorem in arithmetic progressions, and dueling conspiracies
  37. A speech for the American Academy of Arts and Sciences
  38. Structure and randomness in the prime numbers (IMO Festschrift submission)
  39. Two more Clay-Mahler lectures
  40. The cosmic distance ladder
  41. More Mahler lectures
  42. A remark on partial sums involving the Möbius function
  43. Mathematical research and the internet
  44. Determinantal processes
  45. The least quadratic nonresidue, and the square root barrier
  46. Random matrices: Universality of local eigenvalue statistics up to the edge
  47. The AKS primality test
  48. Mathematics/Statistics blogs wiki page
  49. What do mathematicians need to know about blogging?
  50. Polymath4 (“Finding Primes”) now officially active
  51. Global regularity of wave maps VII. Control of delocalised or dispersed solutions
  52. Moser’s entropy compression argument
  53. P=NP, relativisation, and multiple choice exams
  54. New polymath blog, and comment ratings
  55. “Poincaré’s legacies” now published
  56. IMO 2009 Q6 mini-polymath project: impressions, reflections, analysis
  57. IMO 2009 Q6 mini-polymath project cont.
  58. IMO 2009 Q6 as a mini-polymath project
  59. Structure and randomness in the prime numbers
  60. Feynman’s lectures online
  61. Selberg’s limit theorem for the Riemann zeta function on the critical line
  62. DHJ: Writing the second paper III.
  63. Benford’s law, Zipf’s law, and the Pareto distribution
  64. Operator splitting for the KdV equation
  65. Bulk universality for Wigner hermitian matrices with subexponential decay
  66. Sumset and inverse sumset theorems for Shannon entropy
  67. Freiman’s theorem for solvable groups
  68. An equivalence between inverse sumset theorems and inverse conjectures for the U^3 norm
  69. Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
  70. Global regularity of wave maps VI. Abstract theory of minimal-energy blowup solutions
  71. DHJ: Still writing the second paper
  72. The Szemerédi-Trotter theorem and the cell decomposition
  73. Talagrand’s concentration inequality
  74. Random matrices: universality of local eigenvalue statistics
  75. Google Wave
  76. Reflections on compressed sensing
  77. DHJ: Writing the second paper
  78. 245C, Notes 5: Hausdorff dimension (optional)
  79. The two-ends reduction for the Kakeya maximal conjecture
  80. Recent progress on the Kakeya conjecture
  81. Szemeredi’s regularity lemma via the correspondence principle
  82. At the Fefferman conference
  83. The federal budget, rescaled
  84. 245C, Notes 4: Sobolev spaces
  85. Presidential address at the National Academy of Sciences
  86. WordPress blocked again by great firewall of China?
  87. Szemeredi’s regularity lemma via random partitions
  88. An inverse theorem for the bilinear L^2 Strichartz estimate for the wave equation
  89. 245C, Notes 3: Distributions
  90. Tricki now live
  91. Some notes on amenability
  92. The completeness and compactness theorems of first-order logic
  93. 245C, Notes 2: The Fourier transform
  94. Polymath1 and three new proofs of the density Hales-Jewett theorem
  95. DHJ(k): 1200-1299 (Density Hales-Jewett type numbers)
  96. 245C, Notes 1: Interpolation of L^p spaces
  97. Mikhail Gromov wins 2009 Abel prize
  98. (Frank Morgan) New AMS blog
  99. Sailing into the wind, or faster than the wind
  100. 245B, Notes 13: Compactification and metrisation (optional)
  101. 245B final; 245C course announcement
  102. DHJ(3): 1100-1199 (Density Hales-Jewett type numbers)
  103. The Kakeya set and maximal conjectures for algebraic varieties over finite fields
  104. The power of convex relaxation: near-optimal matrix completion
  105. Infinite fields, finite fields, and the Ax-Grothendieck theorem
  106. DHJ(3): 900-999 (Density Hales-Jewett type numbers)
  107. Random matrices: The distribution of the smallest singular values
  108. 245B, Notes 12: Continuous functions on locally compact Hausdorff spaces
  109. Tricks Wiki: Give yourself an epsilon of room
  110. 245B, Notes 11: The strong and weak topologies
  111. Hardy’s uncertainty principle
  112. A sharp inverse Littlewood-Offord theorem
  113. Bounds for the first few density Hales-Jewett numbers, and related quantities
  114. A reading seminar on density Hales-Jewett
  115. WordPress LaTeX bug collection drive
  116. 245B, Notes 10: Compactness in topological spaces
  117. Analysis & PDE conferences page
  118. Proposed stimulus amendment eliminates $1.4 billion in NSF funding
  119. Upper and lower bounds for the density Hales-Jewett problem
  120. 245B, Notes 9: The Baire category theorem and its Banach space consequences
  121. A massively collaborative mathematical project
  122. 245B, Notes 8: A quick review of point set topology
  123. Poincaré’s legacies: pages from year two of a mathematical blog
  124. 245B, Notes 7: Well-ordered sets, ordinals, and Zorn’s lemma (optional)
  125. 245B, Notes 6: Duality and the Hahn-Banach theorem
  126. 245B: Sample midterm questions
  127. The high exponent limit $p \to \infty$ for the one-dimensional nonlinear wave equation
  128. An explicitly solvable nonlinear wave equation
  129. An inverse theorem for the uniformity seminorms associated with the action of F^infty_p
  130. 245B, notes 5: Hilbert spaces
  131. Distinguished Lecture Series III: Gregory Margulis, “Homogeneous dynamics and number theory III.”
  132. Distinguished Lecture Series II: Gregory Margulis, “Homogeneous dynamics and number theory II.”
  133. Distinguished Lecture Series I: Gregory Margulis, “Homogeneous dynamics and number theory I.”
  134. 245B notes 4: The Stone and Loomis-Sikorski representation theorems (optional)
  135. 245B, notes 3: L^p spaces
  136. 245B, notes 2: Amenability, the ping-pong lemma, and the Banach-Tarski paradox (optional)
  137. 245B, notes 1: Signed measures and the Radon-Nikodym-Lebesgue theorem
  138. 245B, notes 0a. An alternate approach to the Carathéodory extension theorem
  139. 245B, notes 0: A quick review of measure and integration theory

2008 118

  1. A remark on the Kakeya needle problem
  2. Tricks Wiki: Use basic examples to calibrate exponents
  3. Cohomology for dynamical systems
  4. Math 245B: Real analysis (course announcement)
  5. On multiple choice questions in mathematics
  6. An airport-inspired puzzle
  7. The uniform uncertainty principle and compressed sensing
  8. Upgrading old Java applets?
  9. The Kakeya conjecture and the Ham Sandwich theorem
  10. Structure and Randomness: pages from year one of mathematical blog
  11. Marker lecture IV: “Sieving for almost primes and expanders”
  12. Marker lecture III: “Small gaps between primes”
  13. Marker lectures II, “Linear equations in primes”
  14. Some notes on “non-classical” polynomials in finite characteristic
  15. A counterexample to a strong polynomial Freiman-Ruzsa conjecture
  16. Concentration compactness and the profile decomposition
  17. The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
  18. When are eigenvalues stable?
  19. Distinguished Lecture Series III: Elias Stein, “Algebras of operators”
  20. Distinguished Lecture Series II: Elias Stein, “The Cauchy integral in C^n”
  21. Distinguished Lecture Series I: Elias Stein, “Singular Integrals and Several Complex Variables: Some New Perspectives”
  22. Powell’s endorsement
  23. From the Littlewood-Offord problem to the Circular Law: universality of the spectral distribution of random matrices
  24. Non-measurable sets via non-standard analysis
  25. Small samples, and the margin of error
  26. Finite subsets of groups with no finite models
  27. The Lucas-Lehmer test for Mersenne primes
  28. Princeton Companion to Mathematics
  29. What is a gauge?
  30. The divisor bound
  31. On hiatus
  32. Oded Schramm
  33. The correspondence principle and finitary ergodic theory
  34. Tricks Wiki article: The tensor power trick
  35. Weakly turbulent solutions for the cubic defocusing nonlinear Schrödinger equation
  36. On time management
  37. Global regularity of wave maps V. Large data local wellposedness in the energy class
  38. Random matrices: Universality of ESDs and the circular law
  39. Tate’s proof of the functional equation
  40. Global existence and uniqueness results for weak solutions of the focusing mass-critical non-linear Schrödinger equation
  41. (Timothy Chow) Out-of-print math books
  42. Classification of Almost Quarter-Pinched Manifolds
  43. The Mobius function is strongly orthogonal to nilsequences
  44. Hassell’s proof of scarring for the Bunimovich stadium
  45. The Black-Scholes equation
  46. Global regularity of wave maps IV. Absence of stationary or self-similar solutions in the energy class
  47. The strong law of large numbers
  48. The sum-product phenomenon in arbitrary rings
  49. The van der Corput trick, and equidistribution on nilmanifolds
  50. 285G, Lecture 19: The structure of Ricci flow at the singular time, surgery, and the Poincaré conjecture
  51. 285G, Lecture 18: The structure of high-curvature regions of Ricci flow
  52. 285G, Lecture 17: The structure of κ-solutions
  53. Global regularity of wave maps III. Large energy from R^{1+2} to hyperbolic spaces
  54. 285G, Lecture 16: Classification of asymptotic gradient shrinking solitons
  55. 285G, Lecture 15: Geometric limits of Ricci flows, and asymptotic gradient shrinking solitons
  56. Random matrices: A general approach for the least singular value problem
  57. 285G, Lecture 14: Stationary points of Perelman entropy or reduced volume are gradient shrinking solitons
  58. Outside in
  59. 285G, Lecture 13: Li-Yau-Hamilton Harnack inequalities and κ-solutions
  60. 285G, Lecture 12: High curvature regions of Ricci flow and κ-solutions
  61. Mathematics in Australia
  62. 285G, Lecture 11: κ-noncollapsing via Perelman reduced volume
  63. A global compact attractor for high-dimensional defocusing non-linear Schrödinger equations with potential
  64. 285G, Lecture 10: Variation of L-geodesics, and monotonicity of Perelman reduced volume
  65. 285G, Lecture 9: Comparison geometry, the high-dimensional limit, and Perelman reduced volume
  66. Pearls before breakfast, II
  67. 285G, Lecture 8: Ricci flow as a gradient flow, log-Sobolev inequalities, and Perelman entropy
  68. 285G, Lecture 7: Rescaling of Ricci flows and κ-noncollapsing
  69. A draft version of the blog book
  70. 285G, Lecture 6: Finite time extinction of the third homotopy group, II
  71. On the permanent of a random Bernoulli matrix
  72. 285G, Lecture 5: Finite time extinction of the third homotopy group, I
  73. 285G, Lecture 4: Finite time extinction of the second homotopy group
  74. Please help support mathematics at the University of Southern Queensland
  75. 285G, Lecture 3: The maximum principle, and the pinching phenomenon
  76. 285G, Lecture 2: The Ricci flow approach to the Poincaré conjecture
  77. 285G, Lecture 1: Flows on Riemannian manifolds
  78. 285G, Lecture 0: Riemannian manifolds and curvature
  79. Dvir’s proof of the finite field Kakeya conjecture
  80. The Dantzig selector: Statistical estimation when p is much larger than n
  81. Lewis lectures
  82. 254A, Lecture 17: A Ratner-type theorem for SL_2(R) orbits
  83. PCM article: Ricci flow
  84. 254A, Lecture 16: A Ratner-type theorem for nilmanifolds
  85. PCM article: Hamiltonians
  86. 254A, Lecture 15: The Furstenberg-Zimmer structure theorem and the Furstenberg recurrence theorem
  87. PCM article: Function spaces
  88. 254A, Lecture 14: Weakly mixing extensions
  89. 254A, Lecture 13: Compact extensions
  90. A remark on primality testing and the binary expansion
  91. 254A, Lecture 12: Weakly mixing systems
  92. Why are solitons stable?
  93. (Luca Trevisan) Checking the Quasirandomness of Graphs and Hypergraphs
  94. Kleiner’s proof of Gromov’s theorem
  95. Good on ya, mate
  96. 254A, Lecture 11: Compact systems
  97. 254A, Lecture 10: The Furstenberg correspondence principle
  98. Structure and randomness in the prime numbers
  99. Compressed Sensing
  100. The blue-eyed islanders puzzle
  101. 254A, Lecture 9: Ergodicity
  102. 254A, Lecture 8: The mean ergodic theorem
  103. 254A, Lecture 7: Structural theory of topological dynamical systems
  104. Book version of the blog
  105. 254A, Lecture 6: Isometric systems and isometric extensions
  106. 254A, Lecture 5: Other topological recurrence results
  107. On the testability and repair of hereditary hypergraph properties
  108. 254A, Lecture 4: Multiple recurrence
  109. The asymptotic behaviour of large data solutions to NLS
  110. Distinguished Lecture Series III: Avi Wigderson, “Algebraic computation”
  111. 254A, Lecture 3: Minimal dynamical systems, recurrence, and the Stone-Čech compactification
  112. Distinguished Lecture Series II: Avi Wigderson, “Expander graphs – constructions and applications”
  113. 254A, Lecture 2: Three categories of dynamical systems
  114. Distinguished Lecture Series I: Avi Wigderson, “The power and weakness of randomness in computation”
  115. 254A, Lecture 1: Overview
  116. AMS lecture: Structure and randomness in the prime numbers
  117. PCM article: Generalised solutions
  118. PCM article: Distributions

2007 93

  1. Einstein’s derivation of E=mc^2
  2. PCM article: Differential forms
  3. PCM article: Phase space
  4. Multi-linear multipliers associated to simplexes of arbitrary length
  5. 254A: Topics in Ergodic Theory
  6. Sciencedebate 2008
  7. The Walsh model for M_2^* Carleson
  8. Milliman Lecture III: Sum-product estimates, expanders, and exponential sums
  9. Milliman Lecture II: Additive combinatorics and random matrices
  10. Milliman Lecture I: Additive combinatorics and the primes
  11. The Hahn-Banach theorem, Menger’s theorem, and Helly’s theorem
  12. Hilbert’s nullstellensatz
  13. The distribution of polynomials over finite fields, with applications to the Gowers norms
  14. PCM article: Compactness and compactification
  15. Distinguished Lecture Series III: Charles Fefferman, “Interpolation of functions on R^n”
  16. Distinguished Lecture Series II: Charles Fefferman, “Interpolation of functions on R^n”
  17. Distinguished Lecture Series I: Charles Fefferman, “Interpolation of functions on R^n”
  18. Analysis & PDE
  19. An update on the inverse conjecture for the Gowers norm over finite fields
  20. On the property testing of hereditary graph and hypergraph properties
  21. John’s blowup theorem for the nonlinear wave equation
  22. FOCS slides: structure and randomness in combinatorics
  23. PCM article: The Fourier transform
  24. Snap preview?
  25. The Jordan normal form and the Euclidean algorithm
  26. A quantitative formulation of the global regularity problem for the periodic Navier-Stokes equation
  27. Unipotent elements of the Lorentz group, and conic sections
  28. PCM article: The Schrodinger equation
  29. Ratner’s theorems
  30. The quantitative behaviour of polynomial orbits on nilmanifolds
  31. Another advice page, and an open thread
  32. The crossing number inequality
  33. Pythagoras’ theorem
  34. PCM article: Harmonic analysis
  35. Amplification, arbitrage, and the tensor power trick
  36. PCM “deleted scene”: Wave maps
  37. Printer-friendly CSS, and nonfirstorderisability
  38. Random matrices: the circular law
  39. “Math Doesn’t Suck”, and the Chayes-McKellar-Winn theorem
  40. (Gil Kalai) The entropy/influence conjecture
  41. Atle Selberg
  42. (Alexandre Borovik) Mathematics under arrest
  43. (Emmanuel Kowalski) The large sieve inequalities
  44. 2006 ICM: Étienne Ghys, “Knots and dynamics”
  45. Structure and randomness in combinatorics
  46. Dyadic models
  47. The cubic nonlinear Schrödinger equation in two dimensions with radial data
  48. Darwin’s finches and introgressive hybridisation
  49. Some new pages
  50. A visit to the Royal Society
  51. Norm convergence of multiple ergodic averages for commuting transformations
  52. Scholarpedia article: Szemerédi’s theorem
  53. Open question: deterministic UUP matrices
  54. Ultrafilters, nonstandard analysis, and epsilon management
  55. A quantitative form of the Besicovitch projection theorem via multiscale analysis
  56. The Lebesgue differentiation theorem and the Szemeredi regularity lemma
  57. STOC talk: The condition number of a randomly perturbed matrix
  58. Advice on mathematical careers, and mathematical writing
  59. Open question: The parity problem in sieve theory
  60. The cosmic distance ladder
  61. Open question: effective Skolem-Mahler-Lech theorem
  62. Soft analysis, hard analysis, and the finite convergence principle
  63. Distinguished Lecture Series III: Shing-Tung Yau, “Application of the Geometric Structures to Solve Problems in Algebraic Geometry and Topology”
  64. Distinguished Lecture Series II: Shing-Tung Yau, “The Basic Tools to Construct Geometric Structures”
  65. Distinguished Lecture Series I: Shing-Tung Yau, “What is a Geometric Structure”
  66. Open question: boundedness of the trilinear Hilbert transform
  67. Distinguished Lecture Series III: Shou-wu Zhang, “Triple L-series and effective Mordell conjecture”
  68. Distinguished Lecture Series II: Shou-wu Zhang, “Gross-Zagier formula and Birch and Swinnerton-Dyer conjecture ”
  69. Distinguished Lecture Series I: Shou-wu Zhang, “Overview of rational points on curves”
  70. Fields Medalist Symposium
  71. Resonant decompositions and the I-method for the cubic nonlinear Schrodinger equation on R^2
  72. (Gil Kalai) The weak epsilon-net problem
  73. Open question: What is a quantum honeycomb?
  74. Ostrowski lecture: The uniform uncertainty principle and compressed sensing
  75. Compressed sensing and single-pixel cameras
  76. Pearls before breakfast
  77. Simons Lecture III: Structure and randomness in PDE
  78. Simons Lecture II: Structure and randomness in ergodic theory and graph theory
  79. Simons Lecture I: Structure and randomness in Fourier analysis and number theory
  80. Open question: triangle and diamond densities in large dense graphs
  81. Open question: scarring for the Bunimovich stadium
  82. Paul Cohen
  83. Freiman’s theorem in finite fields via extremal set theory
  84. Why global regularity for Navier-Stokes is hard
  85. Article in the New York Times, and maths education
  86. On the condition number of a randomly perturbed matrix
  87. (Ben Green) The Polynomial Freiman-Ruzsa conjecture
  88. Open question: the Mahler conjecture on convex bodies
  89. Open question: noncommutative Freiman theorem
  90. Quantum mechanics and Tomb Raider
  91. Open question: best bounds for cap sets
  92. Uchiyama’s constructive proof of the Fefferman-Stein decomposition
  93. Setting things up…