Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme

Switch Atlas

Source

Clay Mathematics Institute

Research Foundation

A private, nonprofit foundation established in 1998 by Landon T. Clay, dedicated to increasing and disseminating mathematical knowledge. In 2000 it named the seven Millennium Prize Problems, each carrying a one million dollar award for a correct solution; the Poincare conjecture (solved by Grigori Perelman, who declined the prize) remains the only one resolved as of this writing.

Facts
Citation
Publisher
Clay Mathematics Institute
URL
https://www.claymath.org/millennium-problems/
Source Type
Institutional Page
Assessment
Reliability Tier
1
Sources
Clay Mathematics Institute
Clay Mathematics InstituteView the Source
Claims Backed By This Source (143 claims)

This source backs 143 claims across the atlas. As facts: 100 well-attested. As cited relationships: 11 holds, 9 connected. Plus 23 entities citing it as a general reference with no single fact or relationship attached.

Disposition By Topic

  • Conjectures, 62 claims: 41 well-attested, 8 holds, 2 connected, 11 general references.
  • Open Questions, 42 claims: 30 well-attested, 6 connected, 6 general references.
  • Mathematicians, 18 claims: 13 well-attested, 5 general references.
  • Articles, 8 claims: 8 well-attested.
  • Theorems, 7 claims: 3 well-attested, 3 holds, 1 general references.
  • Sources, 5 claims: 5 well-attested.
  • Branches of Mathematics, 1 claims: 1 connected.

Well-attested

100

Articles

Discovered Twice, on Opposite Sides of a WallMathematics' Most Wanted

Conjectures

ABC ConjectureBirch and Swinnerton-Dyer ConjectureHodge ConjectureNavier-Stokes Existence and SmoothnessP versus NPRiemann HypothesisYang-Mills Existence and Mass Gap

Mathematicians

Chen-Ning YangGrigori PerelmanHenri PoincaréLeonid LevinRobert MillsStephen CookWilliam Vallance Douglas Hodge

Open Questions

Do all nontrivial zeros of the Riemann zeta function really lie on the critical line?Do smooth, globally defined solutions to the three dimensional Navier-Stokes equations always exist, or can a solution break down in finite time?Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Does the rank of an elliptic curve's group of rational points really equal the order of vanishing of its L-function at s equals one, for every elliptic curve?Is every efficiently checkable problem also efficiently solvable, or is checking genuinely easier than solving?Is every Hodge class on a smooth complex projective algebraic variety really a rational combination of the cohomology classes of actual algebraic subvarieties?

Sources

Clay Mathematics Institute

Theorems

Poincare Conjecture

Holds

11

Conjectures

P versus NPRiemann HypothesisYang-Mills Existence and Mass Gap

Theorems

Poincare Conjecture

Connected

9

Branches of Mathematics

Differential Equations

Conjectures

Hodge Conjecture

Open Questions

Do all nontrivial zeros of the Riemann zeta function really lie on the critical line?Do smooth, globally defined solutions to the three dimensional Navier-Stokes equations always exist, or can a solution break down in finite time?Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Does the rank of an elliptic curve's group of rational points really equal the order of vanishing of its L-function at s equals one, for every elliptic curve?Is every efficiently checkable problem also efficiently solvable, or is checking genuinely easier than solving?Is every Hodge class on a smooth complex projective algebraic variety really a rational combination of the cohomology classes of actual algebraic subvarieties?

General References

23

Conjectures

ABC ConjectureBirch and Swinnerton-Dyer ConjectureHodge ConjectureNavier-Stokes Existence and SmoothnessP versus NPRiemann HypothesisYang-Mills Existence and Mass Gap

Mathematicians

Chen-Ning YangGrigori PerelmanHenri PoincaréRobert MillsWilliam Vallance Douglas Hodge

Open Questions

Do all nontrivial zeros of the Riemann zeta function really lie on the critical line?Do smooth, globally defined solutions to the three dimensional Navier-Stokes equations always exist, or can a solution break down in finite time?Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Does the rank of an elliptic curve's group of rational points really equal the order of vanishing of its L-function at s equals one, for every elliptic curve?Is every efficiently checkable problem also efficiently solvable, or is checking genuinely easier than solving?Is every Hodge class on a smooth complex projective algebraic variety really a rational combination of the cohomology classes of actual algebraic subvarieties?

Theorems

Poincare Conjecture

Take a Related Quiz

Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.