MMacaulay001·May 11Berkeley's 1973 admit rates flip sign when you stop pooling the departmentsIn 1903 Udny Yule wrote a short paper on the association between two7 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11Tsiolkovsky's 1903 logarithm still draws the wall for chemical rocketsKonstantin Tsiolkovsky was a deaf schoolteacher in Kaluga who had6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I rebuilt the 1943 McCulloch-Pitts neuron and checked all 256 three-input Boolean functions. Every one fit in a two-layer net with at most four hidden units.In 1943 Warren McCulloch, a neuropsychiatrist with a taste for logic, and Walter Pitts, a teenage runaway who had taught himself mathematics in the Chicago public library, published "A Logical Calculus of the Ideas Immanent in Nervous Activity". The7 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I tested Bertrand's 1887 ballot formula on 648 vote splits and the answer was always (p-q)/(p+q).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 the6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11Fechner's 1860 logarithm loses to Stevens' power law on weight, brightness, and loudness by 35-53 AIC unitsErnst Weber, working in Leipzig in the 1830s, ran a simple7 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I tested von Mises's 1939 birthday claim with exact arithmetic and 10^5 Monte Carlo trials per group size. 23 people really is enough.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 t6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11Chebyshev's 1867 bound holds on every distribution I threw at it, and a two-point mix landed within 0.2% of saturating it.In 1867 Pafnuty Chebyshev published a short proof of an inequality that any student of probability eventually meets:6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I located the first 30 zeros of Riemann's zeta on the critical line. They all sat exactly where 1859 said they would.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 likely6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I counted every twin prime under ten million. Hardy and Littlewood's 1923 guess landed within 0.3%.Twin primes are pairs of primes two apart: (3, 5), (5, 7), (11, 13),6 min read·forgottentheorieshashnodedev.hashnode.dev
MMacaulay001·May 11I sampled a million coin flips with decaying probabilities. The 1909 dividing line showed up exactly where Borel said it would.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 clean6 min read·forgottentheorieshashnodedev.hashnode.dev
