Departure question
Read the world behind shapePort 13 of 13Begin with lengths and angles, then move toward less visible properties of space: connection, holes, and dimension.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
Every planar map can be colored with only four colors so that adjacent regions differ. In 1976 Appel and Haken solved the 1852 problem by reducing the argument to finitely many cases and checking them by computer. It is widely described as the first major theorem proved with essential computer assistance, intensifying the question: "Is it a proof if no person can inspect every computation by hand?"
Year | People | Advance |
|---|---|---|
1852 | Francis Guthrie | A question from his brother: noticed while coloring a map of Britain |
1879 | Kempe | Published a false proof that stood for 11 years |
1890 | Heawood | Found the flaw in Kempe’s proof and proved the Five Color Theorem |
1976 | Appel + Haken | Checked 1,936 cases by computer using 1,200 CPU hours |
1996 | Robertson et al. | Simplified the proof to 633 cases |
2005 | Gonthier | Formalized the proof in Coq for complete machine verification |
A landmark of computer-assisted proof — the first major theorem whose full computation was impractical to retrace by hand. Simpler proofs and formal verification followed.
Any map can be colored with 4 colors — first major theorem proved by computer.
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
London student Francis Guthrie was coloring a map of the counties of England when he conjectured that four colors would always suffice.
The recorded place matches a canonical map anchor
Continue this scene on the mapArthur Kempe published a proof that was accepted for eleven years before a flaw was found in 1890.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearA computer checked 1,936 configurations, producing the first celebrated computer-assisted proof. Some mathematicians objected that a proof no person could inspect end to end was not really a proof.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearFrequency assignment, timetable scheduling, compiler register allocation, GIS map coloring, and conflict avoidance.
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.
Begin with lengths and angles, then move toward less visible properties of space: connection, holes, and dimension.
Open the number voyage
Begin with lengths and angles, then move toward less visible properties of space: connection, holes, and dimension.
Open the number voyage
Begin with lengths and angles, then move toward less visible properties of space: connection, holes, and dimension.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Four Color Theorem
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.
