Discovering the Impossible — When Failure Became a Theorem

Scene index

See the whole route before choosing

1. 1300 BCE · AlexandriaWhat Can Lines and Circles Build? — The Elements' Tool Grammar
2. 2250 BCE · SyracuseChange the Tool and the Angle Splits into Three — Archimedes' Neusis
3. 31637 · LeidenTranslating Geometric Problems into Degrees of Equations — Descartes
4. 41799 · ModenaSeeking a Proof That the Formula Does Not Exist — Ruffini
5. 51824 · OsloProving There Is No Radical Formula for the General Quintic — Abel
6. 61830 · ParisWhy Are Some Equations Solvable and Others Not? — The Galois Criterion
7. 71837 · ParisTurning Two Millennia of Failed Constructions into a Theorem — Wantzel
8. 81882 · FreiburgThe Transcendence of Pi Makes Squaring the Circle Impossible — Lindemann
9. 91900 · ParisA Request for a Method Receives a Negative Answer — Hilbert's Tenth Problem
10. 101928 · GöttingenAsking for a Procedure That Decides Every Logical Sentence — The Decision Problem
11. 111930 · KönigsbergIncompleteness Is Announced at a Meeting Expecting Completeness — Gödel
12. 121931 · ViennaA System Reads Its Own Sentences and Finds the Boundary of Proof — Incompleteness
13. 131936 · PrincetonRefuting a Universal Decision Procedure with Lambda Calculus — Church
14. 141936 · CambridgeTurning the Human Calculator into a Machine and Proving Some Runs Cannot Be Decided — Turing
15. 151970 · Saint PetersburgThere Is No Universal Decider for Integer Equations — The DPRM Theorem