Departure question
Find the edge of solvabilityPort 2 of 5Cross mechanical procedures, proof, quantum computation, learning, and strategy to explore the limits of calculation and choice.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
"Reduce a theorem exhaustively to finitely many cases, then use a computer to verify every case." This differs from checking many examples. The 1976 Four Color Theorem, the 2014 Flyspeck formal verification of the Kepler conjecture, and the 2016 Boolean Pythagorean Triples result are prominent examples. Trust depends on the completeness of the reduction and on independently checking the program or proof certificate.
Year | Theorem | Role of the computer | Scale |
|---|---|---|---|
1976 | Four Color Theorem | Checked a finite unavoidable set of configurations by program | Large-scale computation for its time |
1996 | Robbins conjecture (Boolean algebra) | EQP automated prover (McCune) | 8 days of automated search |
1998 | Kepler conjecture (sphere packing) | 5,000 inequalities + LP | Hales 1998 → Flyspeck 2014 |
2014 | Flyspeck (Hales verification) | Fully formal verification in Coq + HOL Light | Years of collaboration |
2016 | Boolean Pythagorean triples | SAT solver | About 200 terabytes of data generated during the computation |
2021+ | Lean and the Mathlib ecosystem | Collaborative formalization of theorems and libraries | Many collaborations, including formalization of the PFR theorem |
Trust in a computer-assisted proof depends less on a computer/no-computer divide than on complete reduction, inspectable code or certificates, independent rechecking, and a clearly identified small trusted base.
When the proof is too long for humans — the new mathematical methodology.
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Appel and Haken combined a finite reduction with extensive computer checking. The result made the inspectability of computer-dependent proofs a central question.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearThomas Hales proved that no arrangement of equal spheres is denser than the familiar close-packed arrangements. Checking the proof required years of computer work.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearMarijn Heule, Oliver Kullmann, and Victor Marek produced an enormous computer-assisted proof with a 200-terabyte certificate — far beyond what a human could read line by line.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearProof assistants such as Lean, Coq, and Isabelle let computers check formal proofs down to their logical foundations, and their combination with AI is opening a new era.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearThe Four Color Theorem, the Kepler conjecture, Boolean Pythagorean triples, large-scale checks of Riemann zeros, and formal verification of critical systems.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Cross mechanical procedures, proof, quantum computation, learning, and strategy to explore the limits of calculation and choice.
Open the number voyage
Cross mechanical procedures, proof, quantum computation, learning, and strategy to explore the limits of calculation and choice.
Open the number voyage
Cross mechanical procedures, proof, quantum computation, learning, and strategy to explore the limits of calculation and choice.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Computer-Assisted Proofs
Concepts opened from here
No direct successor port is curated yet.
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
