The Curious Engineer

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Stories by Keith McNulty on Medium

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MathScience

’26
Posts
282 from 30 Aug 2026 to 23 Oct 2026
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monthly (10 in the last year)
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personal blog
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2026 10

  1. The Hotel That Never Runs Out Of Rooms
  2. The Line That Would Not Behave
  3. The Fairest Dice in the House
  4. How Abstract Algebra Can Explain Chemistry, Music and So Much More
  5. A Lovely Little Number Theory Result About The Sum Of Cubes
  6. The Critical Importance of Planning Your Mathematical Attack
  7. The Facinating and Checkered History of the Logistic Function
  8. What Was School Math Like in Ancient Egypt
  9. A Gentle Introduction to One of the Toughest Disciplines in Math
  10. The Vicious Sibling Rivalry that Led to a Brand New Branch of Mathematics

Undated 272

  1. The freestyle libre 2 thanks 5aa5810c9b5a
  2. Firstly my aim here is to illustrate some personal analysis and not to claim a scientific standard ce6350e9a787
  3. I will respectfully disagree 976f31d4d418
  4. Hi matthew 5ec6c2db16d3
  5. I bought them direct from the manufacturer 408248e9c54d
  6. Id rather not mention the brand in the main article as i don t want to to appear like i am 29f1cb1cba5
  7. Where possible i used food labeling 2a7f8b11bac5
  8. Carbs and fat metabolise into energy via the digestive system cced7de5e622
  9. Thanks brandon b5b2ac853c9f
  10. You can choose whether to share my response with your wife or not but i did mention longer term 28a5bdbb8686
  11. Remember that wine or any alcohol is very high in calories 75525f8cc185
  12. Sure i used the freestyle libre 2 3121ca702a84
  13. Thanks and apologies corrected 9fb714c43a9
  14. The day they nuked charleston e0b3a460fe2d
  15. Hello there f667819ca783
  16. The letter which took 220 years to arrive 2b1442a938b1
  17. Then it would be great of you could write and contribute such a generalized piece paying af430e09595c
  18. Just a quick correction d85b7a783809
  19. I hope so d178f52ba778
  20. Https en wikipedia org wiki multivariate statistics e535994a7480
  21. Generally you need to know at least one root to manually factorize a cubic using a pencil and paper a1581cdc8037
  22. Talking frogs or talking toads f5a21b4c3488
  23. The conditions positive integer and m n are both in the title 2cff2bc3f01b
  24. Thinking forwards and backwards in math 80e080076d5d
  25. In a lottery an entrant chooses a number or a set of numbers as they wish numbers are then drawn 236d7028e513
  26. It would be helpful if you could post your approach to the solution to the extent that it differs eb8060d742ac
  27. A beautiful classical mechanics problem with a surprising solution ac41cfe55164
  28. The era of the data engineer is upon us 51674b6dc8b7
  29. What is the 2023rd derivative of this function 418777b9e4a0
  30. A cambridge math problem with a surprise twist ff59d5cfd2d1
  31. My most hated word in data science fbc7f076df18
  32. A challenging integration problem 83029a8720ad
  33. Why choose between r and python 890b678bee16
  34. A tough cambridge university probability problem 22f43e6b34a
  35. A cambridge mathematics entrance question which requires no knowledge aedb7c862780
  36. What is the area of this shape d7ec2e675fa7
  37. Graph theory and the great london stink of 1858 f1f3f31d8d63
  38. A short history of our favorite chocolate candy bars 5adba5446482
  39. A primer on statistical power and power analysis bdce41e97475
  40. Note that 420 is divisible by 7 and n n 1 n 1 is the product of three consecutive integers 59ef965c69ea
  41. How to work with absolute value math functions a30a64da7078
  42. Thanks so much for spotting this c04cab47c0ec
  43. How statistics is used to manage dam capacity 3341d19d8739
  44. The power of generalization in math 4a604b84390c
  45. Yes thanks so much for spotting and for letting me know c2a723f4e484
  46. An introduction to one of the most beautiful and useful structures in mathematics bde2236d9d80
  47. Zero a short history of the representation of nothingness ea3e405475a6
  48. A critically important skill in analytical problem solving 60718a83d26d
  49. The beautiful simplicity of demoivres theorem 51a575a5ba09
  50. Can a polynomial be indivisible like a prime number 4a07c38be801
  51. Hi lee the proof of a803a4c3a0ed
  52. The mathematical skills of generalization and abstraction 3233cf8683f3
  53. Some beautiful uses of eulers formula 8c6715d9d428
  54. The beautiful rotational surface area formula a74edb5f9f8f
  55. An amazing mathematical theory discovered by a teenager df4683c6f60f
  56. The hotel that never runs out of rooms e0e2d78d7e73
  57. The line that would not behave 5ec712c37b63
  58. The uncomfortable origins of regression 3795423e78a0
  59. Thanks so much for point this out i applied a small correction to the proof to fix this ab0f53726113
  60. Why the natural numbers are so fundamental to mathematics 822edc7e2624
  61. What are hyperreal numbers c563908c7cc5
  62. Its not optional for the definition of any field including the real numbers 0274fc0fe918
  63. Interestingly i rewatched this tonight f6a15cb24a28
  64. You really need to use more analogies 9d7d848908a3
  65. Seeing a view to a kill at second last made me stop reading 3d13f3d736d8
  66. Very true fcdf0536135d
  67. That movie was called special bulletin i wrote about it here https link medium com 0g8lkg79amb 3c3e919e075b
  68. Can you solve this very challenging trigonometry question 44372ddff651
  69. Https vimeo com 305272247 8f056161a654
  70. Test your r and statistics knowledge with this cambridge exam question 42f44f562dd3
  71. A high school math problem which is a lot easier than it looks 2c1c2757db4a
  72. When math functions have amazing babies together 7889a5090fba
  73. Is your mental math good enough 323fc58e4110
  74. I dont think so dec06c94aba
  75. A beautiful problem in classical mechanics ad36b79ed9b7
  76. Five common analytics fails 46d897c3f24c
  77. Russell thanks for posting this db5668633f0b
  78. Thanks jens 69a18fe1ce24
  79. How to scrape the web in r d77b11fca40d
  80. Thank you so much for pointing this out 51ecd3602a6b
  81. A completely mad problem in elementary statistics 65f5ad7fa77f
  82. What matters on a speed date 6305f3c9a0a9
  83. Interestingly i believe there are actually at least three ways of solving this problem 697d0f222445
  84. Yes and the curve shows that there is only one such m so its pretty trivial 841c1fbe250d
  85. So glad to hear e52c1acbb863
  86. Typhoid mary and the birth of people networks 7a7fed39b6f7
  87. Absolutely true the r code is just an afterthought to encourage students to embrace programming 5da36f3524b5
  88. I wouldnt describe it as questionable as that implies that there is some basis to believe it 484aed1e2fe0
  89. It may be more used in the uk where i am based 5705ec14ccdd
  90. What smoking did for data science e577dc973b08
  91. Https brilliant org wiki small angle approximation c18a5b4edd94
  92. I agree with your last statement aa90c73efb1
  93. Ten time saving r hacks d01f093beebd
  94. Amazing math applications movement inside a sphere a69811058f59
  95. Could one of you please show me how to derive the maclaurin expansion of sinx without knowing that e82efcde50ae
  96. Two fascinating properties of the fibonacci sequence 2cc4a895b904
  97. A fun introduction to modular arithmetic cb98ce2d9e1c
  98. How to solve equilibrium problems involving two connected bodies c19b63612ec0
  99. Possibly the most useful beast in the history of all mathematics af6053895568
  100. A simple proof of a 400 year old theorem about numbers 986f44d01f3b
  101. Solving a delightful problem about unit fractions c1761d667ed6
  102. I have edited to explain this in more detail 4dd869a44f6b
  103. Apologies for not being transparent enough with my early workings i have made edits to make more f464e263d565
  104. An incredibly satisfying statistics and trigonometry problem 9b1cdc1411fa
  105. The fundamental theorem of algebra d6491104493c
  106. The beautiful abstract structures known as finite groups e945954538f0
  107. How 1 was invented in 16th century italy 71e62bcb3a30
  108. This means you are using an old version of 4 this pipe symbol became native in r version 4 1 0 bc64dadbe477
  109. An interesting cambridge university mathematics entrance question 195753d25d71
  110. Finite degree polynomials are never undefined as they are continuous across all real values of x 930174ee2fb6
  111. A more efficient option in my opinion is to note that sqrt 3 2 cos 30 cos 2x15 2cos 2 15 7943bf45c9d9
  112. The complex mathematics of a pool shot d41c83e98a06
  113. Badges and certificates wont make you a good data scientist bef3da3a469d
  114. Four brain traps you should avoid 1e06abc51b05
  115. Calculus is not always the answer 29b8db8e835a
  116. Building a model heres the first question you should ask 43d308da6e9a
  117. The 1980s guide to surviving nuclear war 5505af643f63
  118. Great article which is approachable bu non mathematicians and introduces useful methods and a 364ebc212b77
  119. The method of postulating what we want has many advantages they are the same as the advantages 13bfa0004534
  120. Cool calculus extending the product rule to the n th derivative a8a77c598d50
  121. A lovely introduction to bivariate probability distribution ca66943dd432
  122. I suspect they took your deconstruction to chatgpt 7e1fdce71bb8
  123. Nice demoivres theorem is also a great way to derive some of these closed form expressions for 7c2c0fc304f9
  124. Death to spreadsheets 16ef9a249cc9
  125. How to find accurate expression for trigonometric sums 6ceb4af51ab3
  126. So you think you can do group theory 8a554f1b58ef
  127. Studying math is more important than ever 47369f787c40
  128. This is a good proof of this fact and is how i would have demonstrated it 57db46fc9347
  129. In 1984 we saw our worst nightmare on our tv screen fd7fa928cfde
  130. Decision makers need more math 0ffc214040d5
  131. Is this the most terrifying number 4d9cf758d8da
  132. Yes a quintic would need to be irreducible unfactorizable in order for it to be insolvable 5eb7fcbc7d0b
  133. If you imagine you are standing on a number line at the number 1 and it takes one step to move 0d8a0925290a
  134. Data scientists dont misuse these words 6f1cc6fb9cfd
  135. I must excuse myself for the pain i have caused you and your kind 8ed71239c888
  136. That is true if you are working in the reals but if you are working in the hyperreals you would ac6c00a0d809
  137. Yes this part of the article is cantors diagonal argument 6ced1f935d54
  138. Yes thats true c1d776d935e7
  139. The small but mighty property of the rational numbers 506c5e625bf8
  140. Just for the joy of experiencing theory matching computation f0f67fec6503
  141. A somewhat mindblowing way to express pi f03cc9d429af
  142. What does elegance mean in math 127fe4b7fedf
  143. Yes this is exactly what i have done just formally 148c1f192cfb
  144. The origins of algorithmic mathematics in ancient babylon f0b7421f9786
  145. How algebra helped us track and index the world e83eec606226
  146. This seems to be a solution to the i th power of i not the i th root of i fa6e19de4a72
  147. Please feel free to show your derivation of this 14722465792e
  148. What is the i th root of i a05d34ac17fd
  149. A lovely geometrical way to understand integration by parts 10faa7f9a25b
  150. The mathematics of pulley systems a5f3134ccb22
  151. The triumphant and tragic story of the study of polynomial roots a29db6c82e9e
  152. This is a great observation and in fact both results follow from a much more powerful result 08ee42e8797e
  153. A delightful and surprising appearance of eulers number f99edc66d45c
  154. The beautiful paradox of gabriels horn 0a8be2e0dcd1
  155. The vicious sibling rivalry that led to a brand new branch of mathematics 2de131bd6af1
  156. Learn four math techniques from this one problem 811eee1a5646
  157. E is also transcendental maybe a proof of that for your next article fc18e63c780c
  158. 18x5 90 so cos 5x 0 ab4ae28caf51
  159. If you can find a way to use officer to edit existing documents to replace the data in their charts f55ca1d9af10
  160. Test your understanding of probability with this teaser 9b7ef5eb45ee
  161. You are 100 correct rob and i have just been lazy with my writing 5d794f40fc2a
  162. The induction step involves deriving the k 1 expression from the k expression 2c999d9f8a4d
  163. A beautiful example of proof by induction be6fdde340c8
  164. The lost art of curve sketching 37edcab895b4
  165. I think that your argument assumes that roots are integers but any real number can be a root 3380310504d2
  166. How to create hans roslings famous animated bubble chart 2b8529b1b717
  167. I 100 agree about the importance of a good diagram in mechanics 5c162a27d1a4
  168. The monster group was effectively proposed as a group that can be generated from previously 835da15c17b6
  169. Why data scientists and engineers quit their jobs a93b6e9f93bb
  170. Dont always trust hints 011cb756fda4
  171. See the text just before the python code 2121d38e9e94
  172. Archie this is a nice question and quite satisfying to solve 8a0ceda23942
  173. Five fascinating facts about pi fa27f64443ce
  174. Although the number of digits in a transcendental number is countable the number of transcendental 43322c3f810f
  175. On the likelihood of societal collapse e6a6569aee06
  176. Not 100 sure what you are getting at 2cdd23578f19
  177. My top tip for tackling tough math problems 674007ab719e
  178. The best sci fi series of all time 8926a4f0ecd5
  179. The math challenge i love to set for myself 3c9eed358f3e
  180. How algebra can solve ancient greek geometry problems 29822e86a434
  181. Andrew many thanks for highlighting this 91efb9bda9fa
  182. One of the most elegant and practical applications of abstract algebra 0e6c8853ab0f
  183. How can xⁿ 1 have n solutions f8cf58eeb442
  184. The definition relates to non degenerate triangles b0ee50d2be45
  185. How to break a math problem down from first principles 2e5921f6b340
  186. How to think like an algebraist 600243289312
  187. A lovely introduction to bayesian statistics 809ac7619152
  188. The three most common forms of mathematical proof 9d1363f3d9ee
  189. A much easier and shorter method is to note that the remainder is 1 for the first number and 3 for f98c7da65808
  190. A lovely little number theory result about the sum of cubes cc21ca089418
  191. The critical importance of planning your mathematical attack 28183488e93c
  192. The fairest dice in the house a0c69f046a81
  193. How abstract algebra can explain chemistry music and so much more 6f82dfaab1aa
  194. An introduction to probability generating functions 2d129428ecc2
  195. Sure in standard linear regression you are modeling a value that acts additively based on the c42ea1be494f
  196. Thanks so much will look into this 561cde431268
  197. Hi oliver 7ae0109dc6d4
  198. Thanks so much for this comment 1e2b28ec0cfe
  199. Can you pls expand a bit more mathematically on your point 22a895f8f210
  200. Hi tanya its a good question 631c63a75f16
  201. The question does not ask for us to suggest a a design of the lottery 728806c0febb
  202. Calculate the chances of keeping your job with this lottery problem 6ba1faea26b4
  203. Interesting 55755169b53d
  204. The king in the car park 5c4f02a5a6ef
  205. Hi danny i added a few more lines to make the algebraic manipulation more clear 50da6cc131ca
  206. These questions are neat and quick to solve but the challenge level does not come close to 7d9bf7a0662b
  207. Hi youssef there is an issue with this code the object chunks seems to come from nowhere and 2597739c6720
  208. I think symbols are used for abstraction which is one of the most powerful forms of human thought 73930f1be06f
  209. The era of the mathematician has arrived bc2d59b95245
  210. How to tell if you can be a great mathematician df5172610f5f
  211. Hi paul the seven rods have lengths of the integers 1 thru 7 81758cf0e349
  212. The remarkable relationship between the fibonacci numbers and the golden ratio 65c5be8091cf
  213. The different approaches come down to questions of philosophy rather than truth i think since both e56b8c3357ed
  214. I beg to disagree 84bc4ffb9bb3
  215. You can construct a regular 4294967295 gon with just a ruler and compass 3f0abcb3f612
  216. The greatest ever christmas song 8e7d1cb17ed4
  217. The two key trig identities worth memorizing 3df894d5f216
  218. Heres another unexpected appearance of e 7150cdbd0573
  219. How to generate fascinating sets of seemingly unlikely number equalities a42da31c1f10
  220. Logical thinking is the key to efficient problem solving d6a26d0be0b8
  221. This is not a factorization e1150c90f480
  222. As per my reply to your previous comment this is just a use of the inductive assumption not a 3c98efd86da1
  223. The fifteen rules that define the real numbers 7cadb7584e39
  224. Note that reflexiveness is the only requirement that does not have a condition if attached to dad307e54f48
  225. How to formally construct the real numbers from the rational numbers 771275c5cbb6
  226. Also i cant feed that back to the original examiners sadly e42abc8451cc
  227. What was it like to sit a math exam in the 19th century 5e273e1f77c5
  228. Six proofs of the infinitude of prime numbers 44b5ee10d791
  229. How do mathematicians comprehend infinity 0da6545fde75
  230. A fantastic introduction to projectile motion b54691e721c3
  231. A new proof of pythagoras theorem discovered by two teenagers 5160dcd0deb2
  232. Modeling the motion of projectiles 52bc30f84391
  233. I think there are two things to consider here 997224ea979e
  234. Why are odds a thing in regression fbe11bd2af0a
  235. Put your computer away and try some organized thinking instead 118457516924
  236. Im really surprised you did not reference the abel prize or the fields medal d76f98b0c4cd
  237. Facebook and twitter were born in 18th century europe e2a3c0f63358
  238. No need to apologise improved r code is always welcome if you have an alternative dd5ca8f1179f
  239. Five great programming and data science memes 823738cf8247
  240. Ok then if it helps readers wherever i use the term triangular triple they can precede that 690ba1c8a1ba
  241. Yes although it follows from the general laws of probability it is worth making this property 70f613890daf
  242. How to sum an infinite series e64e8a83394b
  243. How did londoners die in the 1600s a1486d05563e
  244. Also this article is a great read on how fundamental complex numbers are to recent scientific c9ad174b6a5f
  245. The beautiful and useful applications of logarithms 6ec352229d9b
  246. A mathematicians guide to using common sense bc17031ab2c4
  247. The three most common statistical tests you should deeply understand 174ef0221378
  248. Was this the most dangerous childrens toy ever c6f64835b097
  249. Fifteen questions to test your statistics knowledge 503453e1533a
  250. Yes its important foundational knowledge for galois theory 26d7bcb5ebb7
  251. A cute christmas calculus problem c6711944c7e6
  252. I think in this case a wormhole would open up and the universe would implode 1c46c3b482ba
  253. Modeling elastic and harmonic motion b4b12ad992d3
  254. Can a horse do math 2c93a34135b5
  255. My daily neuroplasticity workout 769f9e744263
  256. This feels like a semantic debate 4920ee305af8
  257. The ultimate heuristic the normal approximation a6c89984314f
  258. Five math discoveries that continue to surprise and delight 3ccc25a54e11
  259. The fascinating history of the infinite series aa983a0be581
  260. Estimating π using bayes theorem 127c9cea4345
  261. Modeling a ball bouncing down a staircase 278487b3691b
  262. Three things about regression that every data scientist should know 6e268945f8f2
  263. How well do you understand statistical distribution and expectation 5ac5a389ea96
  264. The amazing power of math in modeling movement 614cbcc4d899
  265. How many bodies are there in my refrigerator f3be7cedf394
  266. How to abstract your reasoning 19e21f108985
  267. Yes integration by parts only works when it is convenient 4c6533ee38c8
  268. A fascinating number theory problem with a surprising answer a5565bb8380b
  269. What did openai know and when did they stop knowing it 4dc56de4152d
  270. What was school math like in ancient egypt 9d5de1044437
  271. A gentle introduction to one of the toughest disciplines in math 4ca0e598e2d4
  272. The facinating and checkered history of the logistic function dee3c44f8e9d