Workshop season · 30 days
20th-Century Crisis & the Birth of the Computer — 1900 to 1963
At the 1900 Paris ICM Hilbert discussed ten problems; the published paper contained the full list of twenty-three. In the early 1920s he proposed a program to formalize classical mathematics and justify its consistency by finitary methods. Over 30 days we follow how Russell's paradox (1901–1902), Gödel's incompleteness results (1930–1931), and Cohen's independence proof (1963) redrew the scope of those aims, while work on computability grew into computer science.
Start anywhere. Every reading remains available after the season ends.
- Day 1
David Hilbert
Explore this question →Season opens — 1900 Paris ICM, ten problems discussed and all twenty-three published
- Day 2
Georg Cantor
Explore this question →1874 hierarchy of infinity — the crisis seed grew from uncountable infinity
- Day 3
Infinity
Explore this question →Infinity — philosophy before Cantor, foundation of mathematics after
- Day 4
Cantor's Infinity — What He Saw But Did Not Believe
Explore this question →Infinity even its discoverer doubted — 50-second cinematic, the inner landscape of the crisis
- Day 5
Gottlob Frege
Explore this question →Begriffsschrift 1879 — published by Louis Nebert in Halle while Frege taught at Jena, laying foundations for modern predicate logic
- Day 6
Bertrand Russell
Explore this question →16 June 1902 — 30-year-old Russell wrote to Frege about the briefly stated paradox he had discovered in 1901
- Day 7
Continuum Hypothesis — Proven Independent of ZFC
Explore this question →Cantor's lifelong question — is there an infinity between ℵ₀ and ℵ₁? (resolved on Day 28)
- Day 8
David Hilbert
Explore this question →Hilbert's early-1920s program — formalize classical mathematics and justify its consistency by finitary methods
- Day 9
Infinite Series
Explore this question →Infinite series — soil of Hilbert's 6th problem (axiomatising physics), the bridge to quantum mechanics
- Day 10
Emmy Noether
Explore this question →1915-1933 Göttingen — symmetry, conservation, and structural abstract algebra
- Day 11
Alfred Tarski
Explore this question →1933 Warsaw — recursive truth definitions for specified formal languages and the adequacy requirement of Convention T
- Day 12
Andrey Kolmogorov
Explore this question →1933 Moscow — axiomatising probability, proving axiomatisation still works in the crisis era
- Day 13
Probability
Explore this question →Probability — after Kolmogorov's axioms, even uncertainty becomes mathematics. The next day asks what Gödel's theorems imply about the scope of axiomatisation
- Day 14
Kurt Gödel
Explore this question →1930 Königsberg announcement → 1931 paper — two theorems exposing limits to the aims of Hilbert's program
- Day 15
Incompleteness Theorems
Explore this question →Incompleteness — the 38 pages of Über formal unentscheidbare Sätze I (Monatshefte 38) changed mathematics' self-understanding of 2,000 years
- Day 16
von Neumann's Life — One Man, Five Fields
Explore this question →A translator across fields — quantum mechanics, game theory, wartime research, EDVAC, cellular automata, and collaborators
- Day 17
John von Neumann
Explore this question →1932 quantum mechanics + 1944 game theory + 1945 EDVAC: linking axioms, strategies, and programs without erasing collaborators
- Day 18
Measure and Lebesgue Integration
Explore this question →Foundation of Hilbert space — the measure theory von Neumann's 1932 quantum mechanics rested on
- Day 19
Alan Turing
Explore this question →Cambridge 1936, age 24 — using an idealized machine to define both the power and limits of algorithms
- Day 20
Alonzo Church
Explore this question →1936 Princeton — lambda calculus gave a negative answer to Hilbert's decision problem 5 months before Turing, and Church supervised Turing's PhD
- Day 21
Turing's Life — Journey to the Apple
Explore this question →1912-1954 — computation, codes, machine intelligence, morphogenesis, and the harm caused by state prosecution
- Day 22
Claude Shannon
Explore this question →1948 Bell Labs — the crisis ended in bits: information became a measurable quantity
- Day 23
Information Entropy
Explore this question →Information entropy — Shannon entropy = the unit of uncertainty, the crisis era's last great axiomatisation
- Day 24
Paul Erdős
Explore this question →1913 Budapest — pure number theory exploded even during the crisis, the start of the wandering genius
- Day 25
Prime Number Theorem
Explore this question →Prime Number Theorem — 1896 Hadamard & de la Vallée Poussin: the great number-theory theorem just before the crisis, flowing into the Erdős generation
- Day 26
L. E. J. Brouwer
Explore this question →1907 Amsterdam — foundations of intuitionism plus the 1911 fixed-point theorem from his early classical topology. The 1928–29 Mathematische Annalen editorial conflict marked the climax of the Grundlagenstreit
- Day 27
Paul Cohen
Explore this question →Spring 1963, Stanford — invented forcing to establish the ¬CH relative-consistency direction, complementing Gödel's 1940 result for CH
- Day 28
Continuum Hypothesis — Proven Independent of ZFC
Explore this question →Gödel 1940 + Cohen 1963 — resolving Day 7: ZFC decides neither CH nor ¬CH
- Day 29
Transfinite Numbers
Explore this question →Transfinite ℵ — a 90-year mirror from Cantor 1874 to Cohen 1963: the crisis became new mathematics
- Day 30
Alan Turing
Explore this question →From limits to a new field — the Day 19 model meets contemporary and later engineering on the way to computer science