Millennium Prize Problems
Of the seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved:
- P versus NP
- Hodge conjecture
- Riemann hypothesis
- Yang–Mills existence and mass gap
- Navier–Stokes existence and smoothness
- Birch and Swinnerton-Dyer conjecture.
The seventh problem, the Poincaré conjecture, has been solved. The smooth four-dimensional Poincaré conjecture is still unsolved. That is, can a four-dimensional topological sphere have two or more inequivalent smooth structures?
Read more about this topic: List Of Unsolved Problems In Mathematics
Famous quotes containing the words millennium, prize and/or problems:
“At the end of one millennium and nine centuries of Christianity, it remains an unshakable assumption of the law in all Christian countries and of the moral judgment of Christians everywhere that if a man and a woman, entering a room together, close the door behind them, the man will come out sadder and the woman wiser.”
—H.L. (Henry Lewis)
“He saw, he wish’d, and to the prize aspir’d.
Resolv’d to win, he meditates the way,
By force to ravish, or by fraud betray;
For when success a lover’s toil attends,
Few ask, if fraud or force attain’d his ends.”
—Alexander Pope (1688–1744)
“I have a horror of people who speak about the beautiful. What is the beautiful? One must speak of problems in painting!”
—Pablo Picasso (1881–1973)