In 2000, the Clay Mathematics Institute of Cambridge, Mass., identified seven math problems it deemed the most "important classic questions that have resisted solution over the years." Several of them had in fact resisted solution for more than a century—the Rieman Hypothesis, for example, has confounded mathematicians since its formulation in 1859.To create a bit of frisson among the public for the so-called Millennium Prize Problems, the Clay Institute announced it would offer a one-million-dollar reward apiece for solutions to the problems.
Poincaré's Conjecture deals with the branch of math called topology, which is the study of shapes, spaces, and surfaces.
The Clay Institute offers this deceptively friendly-sounding doughnut-and-apple explication of the bedeviling problem: If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface.
Tao, who is usually quite cautious about announcing breakthroughs on major problems, mentions the possibility of adapting the paper you link to the actual Navier-Stokes equations. Tataru is actually working on the Clay problem, but given his expertise, the difficulty of the problem, and the relative lack of progress on any sort of constructive QFT in the past 20 years, it seems more likely that whoever told you this was referring to one of the many conjectures surrounding the classical Yang-Mills equations. Here's a good page that summarizes some attempts at a proof, along with some of the more serious work.
The fluids experts I have talked to seemed more sceptical, but then again when it comes to huge open problems, any opinion, including expert opinion, should be taken with a grain of salt. Four or so years ago or so a reasonably well respected person in the field called Deolalikar published what he claimed was a proof, Unfortunately despite a lot of interest at the time which suggested that, whilst it probably wasn't a complete proof, the ideas involved might well be interesting enough to lead to further progress, I haven't heard anything for a while.
Moreover, at least 20.6% of elliptic curves have rank 0, at least 83.75% have rank at most 1, and the average rank is at most 0.885.
Million Dollar Math Problem Solved
The most recent advancement I heard about was related to the Navier-Stokes equation. Also as a computer science major I both want to see it solved and at the same time I dread it.Terry Tao uploaded a paper to the ar Xiv on February 3rd of this year proposing a new approach to the problem. Edit : Thank you for the laugh to the reply below me and the knowledge to further down. NP is also HARD, i.e., people have had the most success in proving why current proof techniques will not work.His paper is here: a news article about his paper appeared here a couple weeks later: got excited in part because in the abstract and introduction, Prof. There's a lot of crackpot noise since it's such a well-known problem.The Riemann Hypothesis is one of seven Millennium problems named by the Clay Mathematics Institute (CMI).These are problems that have gone unsolved for decades or even centuries.Ever since French mathematician Henri Poincaré posed the conjecture in 1904, at least a half-dozen eminent mathematicians—and many lesser ones—have tried and failed to crack the problem.But a series of papers on the conjecture posted online in 20 by Russian Grigory Perelman have successfully withstood intense scrutiny by the mathematical community for the past four years—twice the number of years of public examination required by the Clay Institute.Students in school should not worry about their math curriculum getting changed once again as some of these millennium problems get solved.These problems have less of an effect on students and school than they do on more real world situations.Georg Friedrich Bernhard Riemann first came up with the Riemann Hypothesis 160 years ago.The reason people do not agree with Atiyah’s T(s) is because Atiyah says it has to have certain properties.