Infinity Without End — From Zeno to Independent Worlds

Scene index

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1. 1450 BCE · Elea (Velia)To Arrive, First Travel Halfway — Zeno's Dichotomy
2. 2350 BCE · AthensA Process That Can Continue, Not a Completed Thing — Aristotle
3. 3250 BCE · SyracuseHolding Endless Pieces inside a Finite Proof — Archimedes
4. 41400 · SangamagramaCalculating Not Only a Series but What Remains — The Madhava Tradition
5. 51638 · LeidenThe Whole and a Proper Part Can Be Equally Numerous — Galileo's Paradox
6. 61666 · Woolsthorpe-by-ColsterworthCalculating Curves with Infinite Series — Newton's Plague-Retreat Manuscripts
7. 71735 · Saint PetersburgAn Endless Sum of Reciprocal Squares Meets the Circle — Euler's Basel Problem
8. 81821 · ParisAsking for Convergence Conditions instead of Trusting Infinitesimals — Cauchy
9. 91872 · BraunschweigBuilding Real Numbers from Gaps in the Rationals — Dedekind Cuts
10. 101874 · HalleThe Reals Cannot All Enter a Natural-Number List — Cantor
11. 111877 · HallePairing a Line Segment with the Points of a Square — 'I See It, but I Do Not Believe It'
12. 121888 · BraunschweigA Set That Pairs with a Proper Part of Itself — Dedekind's Infinite
13. 131891 · HalleA Number That Escapes Every Allegedly Complete List — The Diagonal Argument
14. 141900 · ParisIs There an Infinity between the Naturals and the Reals? — Hilbert's First Problem
15. 151902 · JenaGathering Every Set Produces a Contradiction — Russell's Letter
16. 161908 · GöttingenPreventing Sets from Being Formed at Will — Zermelo's Axioms
17. 171924 · GöttingenA Full Hotel That Can Still Admit a Guest — Hilbert's Metaphor
18. 181940 · PrincetonBuilding a Universe Where the Continuum Hypothesis Holds — Gödel
19. 191963 · StanfordBuilding a Universe Where the Continuum Hypothesis Fails — Cohen's Forcing