--- title: "Macaulay001 (@oladimeji2025) | Hashnode" description: "Macaulay001 (@oladimeji2025) writes on Hashnode. Read their latest articles and follow their work." url: "https://hashnode.com/@oladimeji2025" --- @oladimeji2025 # Macaulay001 @oladimeji2025 · Joined May 2026 ### [I tested Bertrand's 1887 ballot formula on 648 vote splits and the answer was always (p-q)/(p+q).](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq?utm_source=hashnode&utm_medium=feed) In 1887 Joseph Bertrand sent a four-page note to the \*Comptes Rendus\* of the French Academy. The question he asked is one you can pose to a child. Two candidates run for office. A wins with p votes, B loses with q < p. The ballots are pulled from the 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq?utm_source=hashnode&utm_medium=feed) [May 11](https://hashnode.com/posts/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq/6a025d702d1b69abf22b821f) ### [I tested von Mises's 1939 birthday claim with exact arithmetic and 10^5 Monte Carlo trials per group size. 23 people really is enough.](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough?utm_source=hashnode&utm_medium=feed) In 1939 Richard von Mises published a short paper with the unwieldy title \*Über Aufteilungs- und Besetzungswahrscheinlichkeiten\*. Inside is the calculation that everyone now calls the birthday paradox. Pick 23 people at random. The probability that t 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough?utm_source=hashnode&utm_medium=feed) [May 11](https://hashnode.com/posts/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough/6a025d6e859efcceac079c31) ### [Chebyshev's 1867 bound holds on every distribution I threw at it, and a two-point mix landed within 0.2% of saturating it.](https://forgottentheorieshashnodedev.hashnode.dev/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it?utm_source=hashnode&utm_medium=feed) In 1867 Pafnuty Chebyshev published a short proof of an inequality that any student of probability eventually meets: 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it?utm_source=hashnode&utm_medium=feed) [May 11](https://hashnode.com/posts/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it/6a025d6b2d1b69abf22b821d) ### [I sampled a million coin flips with decaying probabilities. The 1909 dividing line showed up exactly where Borel said it would.](https://forgottentheorieshashnodedev.hashnode.dev/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would?utm_source=hashnode&utm_medium=feed) In 1909 Émile Borel was working through a problem about decimal expansions of real numbers, and he proved a small lemma to dispatch a side case. Eight years later, Francesco Paolo Cantelli sharpened it. Together the two halves became one of the clean 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would?utm_source=hashnode&utm_medium=feed) [May 11](https://hashnode.com/posts/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would/6a025d662d1b69abf22b8219) ### [I located the first 30 zeros of Riemann's zeta on the critical line. They all sat exactly where 1859 said they would.](https://forgottentheorieshashnodedev.hashnode.dev/i-located-the-first-30-zeros-of-riemanns-zeta-on-the-critical-line-they-all-sat-exactly-where-1859-said-they-would?utm_source=hashnode&utm_medium=feed) In November 1859, Bernhard Riemann submitted an eight-page memoir to the Berlin Academy. The paper was about prime numbers. Buried in the middle, almost as an aside, was a sentence that has shaped analytic number theory ever since: it is very likely 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-located-the-first-30-zeros-of-riemanns-zeta-on-the-critical-line-they-all-sat-exactly-where-1859-said-they-would?utm_source=hashnode&utm_medium=feed) [May 11](https://hashnode.com/posts/i-located-the-first-30-zeros-of-riemanns-zeta-on-the-critical-line-they-all-sat-exactly-where-1859-said-they-would/6a025d642828387794138fa1)