### Get 5,000 inkles to start making predictions and become legendary.

## Rationales

### "http://math.stackexchange.com/questions/634890/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stokes-equatio/649373#649373"

##### GradualStudent sold The Navier-Stokes Equation at 28.51%

##### March 28, 2014 @ 07:00am PDT

### "Turbulent flow is cool, that's gotta be interesting to solve"

##### GradualStudent bought The Navier-Stokes Equation at 12.61%

##### October 10, 2013 @ 07:19pm PDT

### "Seems the most tractable."

##### GradualStudent bought Hodge Conjecture at 10.73%

##### October 22, 2011 @ 07:34pm PDT

### "this would solve the rest of them."

##### GradualStudent sold P vs NP Problem at 13.15%

##### September 19, 2011 @ 08:50pm PDT

Show more## historical trend

## Background information

In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven Prize Problems. The first person to solve each problem will be awarded $1,000,000 by the CMI. Which will be solved first? This market will based the winner on the date that the Clay Institute names the winner of one of the prizes. Note: The Poincaré Conjecture is not included as it was solved before this market started, although Perelman has not accepted the prize money.## More information about the possible answers

## Birch and Swinnerton-Dyer Conjecture

Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like

x2 + y2 = z2Euclid gave the complete solution for that equation, but for more complicated equations this becomes extremely difficult. Indeed, in 1970 Yu. V. Matiyasevich showed that Hilbert’s tenth problem is unsolvable, i.e., there is no general method for determining when such equations have a solution in whole numbers. But in special cases one can hope to say something. When the solutions are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behavior of an associated zeta function ζ(s) near the point s=1. In particular this amazing conjecture asserts that if ζ(1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1) is not equal to 0, then there is only a finite number of such points.

## Hodge Conjecture

In the twentieth century mathematicians discovered powerful ways to investigate the shapes of complicated objects. The basic idea is to ask to what extent we can approximate the shape of a given object by gluing together simple geometric building blocks of increasing dimension. This technique turned out to be so useful that it got generalized in many different ways, eventually leading to powerful tools that enabled mathematicians to make great progress in cataloging the variety of objects they encountered in their investigations. Unfortunately, the geometric origins of the procedure became obscured in this generalization. In some sense it was necessary to add pieces that did not have any geometric interpretation. The Hodge conjecture asserts that for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually (rational linear) combinations of geometric pieces called algebraic cycles.

## None

All problems will resist a solution indefinitely.

## P vs NP Problem

Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students, and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP-problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair taken from your coworker’s list also appears on the list from the Dean’s office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known universe! Thus no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.

## Riemann Hypothesis

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function

ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation

ζ(s) = 0lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

## The Navier-Stokes Equation

This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.

## Yang-Mills and Mass Gap

The laws of quantum physics stand to the world of elementary particles in the way that Newton’s laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the “mass gap:” the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics.

## Discussion

Sort by:Date## benthinkin (ADMIN) • Mon Oct 26 2015 at 09:14am PDT

This question has been refunded due to its long timeframe.

## Polyergic • Mon Oct 26 2015 at 12:27pm PDT

Why is a long lifetime a reason to refund? Your system allowed a much longer lifetime when this was created, why the sudden unannounced and retroactive policy change?

## benthinkin (ADMIN) • Mon Oct 26 2015 at 12:51pm PDT

Hi Polyergic, we’re winding down this site, and will suspend all forecasting in December. You can sign up for our new sports site at sportscast.cultivateforecasts.com and we’ll be launching a site focused on finance, economics, and politics shortly.

## GradualStudent • Fri Mar 28 2014 at 07:05am PDT

Apparently solution to Navier Stokes was a corollary to a larger more abstract theorem. The paper comes down to particular Theorem 6.1 for which a counterexample has been found, and that error was acknowledged by the author. This may still be the first Millennial Problem to be solved, but seemingly hasn’t been solved yet.

http://math.stackexchange.com/questions/634890/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stokes-equatio/649373#649373

## ecotax • Sun Jan 12 2014 at 03:31am PST

Neither my Russion nor my math skills are good enough to check this claim:

http://bnews.kz/en/news/post/180213/

http://m.slashdot.org/story/196717

But it looks like this question may soon be answered with Navier-Stokes.

## ecotax • Wed Jan 22 2014 at 01:58pm PST

I’m not the only one having trouble reading this, apparently:

http://www.newscientist.com/article/dn24915-kazak-mathematician-may-have-solved-1-million-puzzle.html

## GradualStudent • Fri Mar 28 2014 at 06:56am PDT

I’m surprised there could be a shortage of Russian-speaking mathematicians (“However, the combination of the Russian text and the specialist knowledge needed to understand the Navier-Stokes equations means the international mathematical community, which usually communicates in English, is having difficulty evaluating it.” )

## santok • Mon Nov 28 2011 at 09:55am PST

I DONT KNOW WHAT ANY OF THIS MEANS :)

## GradualStudent • Mon Sep 19 2011 at 08:49pm PDT

Overlap with another market? http://home.inklingmarkets.com/markets/27125

## Polyergic • Thu Dec 04 2008 at 02:49pm PST

Well, there is the end date of 09/04/20; I suppose “None” should pay if no prizes are awarded by then.

## simon_ • Tue Sep 04 2007 at 02:38pm PDT

how could anyone buy “none”? it can literally never get paid… stupid.

## futurebird • Mon Sep 03 2007 at 04:56pm PDT

I spoke too soon… someone has bought it.

## santok • Mon Nov 28 2011 at 09:56am PST

I LOVE UR AVATAR

## futurebird • Mon Sep 03 2007 at 04:55pm PDT

No deadline, but if any problem is answered the none option should go to zero… People want to make money by playing this option in the mean time. But I guess I could try to remove it and just let people who want to do that short every stock.

## Polyergic • Mon Sep 03 2007 at 03:57pm PDT

Without a deadline the “none” option can’t win – it can only continue to not lose.

Is there a deadline?