Departure question
Test the floor beneath mathematicsPort 7 of 8Meet paradox, incompleteness, and independence in attempts to build a foundation for mathematics from sets.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
Seven problems selected by the Clay Mathematics Institute in 2000, with a million-dollar prize for each. Perelman's 2002-2003 preprints resolved the Poincaré conjecture; he later declined both the Fields Medal and Clay prize. The other six remain open.
Problem | Field | Status | What it asks |
|---|---|---|---|
Poincaré Conjecture | Topology | Solved (Perelman, 2003) | Topological characterization of the 3-sphere |
P vs NP | Complexity theory | Unsolved | Polynomial-time verification = polynomial-time solution? |
Riemann Hypothesis | Number theory and complex analysis | Unsolved | Do all nontrivial zeros of ζ(s) have Re=1/2? |
Yang–Mills | Mathematical physics | Unsolved | The mass gap in quantum field theory |
Hodge Conjecture | Algebraic geometry | Unsolved | Algebraic cycles ↔ Hodge classes |
BSD Conjecture | Number theory | Unsolved | Elliptic-curve rank ↔ L-function |
Navier–Stokes | Fluid dynamics | Unsolved | Do smooth solutions exist for 3D fluids? |
Seven of the deepest questions in mathematics. After more than two decades, only one has been solved — and its solver declined the prize.
Seven problems with $1M each — only Poincaré conjecture solved (and prize refused).
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
The Clay Mathematics Institute announced seven great problems for the 21st century in Paris, with a $1 million prize for each, inspired by Hilbert’s 1900 list.
The recorded place matches a canonical map anchor
Continue this scene on the mapGrigori Perelman used Ricci flow to prove the Poincaré conjecture, the only one of the seven yet solved. He declined both the Fields Medal and the $1 million prize.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearP versus NP, the Hodge conjecture, the Riemann hypothesis, Yang–Mills existence and mass gap, Navier–Stokes existence and smoothness, and the Birch and Swinnerton-Dyer conjecture remain among mathematics’ deepest mysteries.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearThe limits of efficient computation, the future of internet security, mathematical foundations of quantum field theory, and central questions in number theory.
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.
Meet paradox, incompleteness, and independence in attempts to build a foundation for mathematics from sets.
Open the number voyage
Meet paradox, incompleteness, and independence in attempts to build a foundation for mathematics from sets.
Open the number voyage
Meet paradox, incompleteness, and independence in attempts to build a foundation for mathematics from sets.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
Millennium Prize Problems
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.
