 # These are seven-millennium math problems that are worth a million dollars each.

Doing math at school was probably one of your worst nightmares, but you need to crunch numbers if you really want to make it up to six figures. Speaking of math, there are math problems that are largely unsolved to this day. And to boast morale for solving them, there is a million dollar prize tag upon solving any one of them. Here are the seven millennium math problems — each worth a million dollars.

### #1. Poincaré Conjecture

Conjectured by French mathematician Henri Poincaré in 1904, it states that every simply connected closed three-manifold is homeomorphic to the three-sphere (topographically speaking) whereas a three-sphere is simply a generalization of the usual sphere to one dimension higher. Sounds weird? This was solved way back in 2002 by Russian mathematician Grigori Perelman, and the only one of the seven problems solved so far. Six million dollars more to go!

### #2. Birch And Swinnerton-Dyer Conjecture

Conjectured by British mathematicians Bryan Birch and Peter Swinnerton-Dyer in the early 1960s in England. It is also known as Birch-Swinnerton-Dyer Conjecture, it describes the set of rational solutions to equations defining an elliptic curve — a special kind of function that takes the form of something like y²=x³+ax+b. It is an open problem in the field of number theory and certainly worth a million bucks if you can have a go at it.

### #3. Hodge Conjecture

Conjectured by British mathematician Sir William Vallance Douglas Hodge in 1950, it is a major unsolved problem in algebraic geometry and complex geometry. The conjecture relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. If you’re familiar with this conjecture, prove it and win a million bucks overnight. Simple!

### #4. Naiver-Stokes Existence And Smoothness

Devised by Swiss legendary mathematician Leonhard Euler in the 18th century. The problem concerns the mathematical properties of solutions to the Navier-Stokes equations. This is a system of partial differential equations that describe the motion of a fluid in space. The solution to the Navier-Stokes equations is used in many practical applications. However, no one has been able to prove it yet. Grab a million dollars at the bank if you can.

### #5. P Versus NP

Actually known as polynomial (P) versus nondeterministic polynomial (NP) problem, it is a major unsolved problem in theoretical computer science and mathematics. This problem begs the question of whether all so-called NP problems are actually P problems. And, if the solution to the problem is easy to check for correctness, must the problem be easy to solve? We don’t know, but it’s worth a million bucks.

### #6. Riemann Hypothesis

Hypothesized by German mathematician Bernhard Riemann in 1859. Mathematically, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numberswith real part 12. Many mathematicians consider this to be the most important yet unsolved problem left in pure mathematics. As usual, it is worth a million bucks if solved.

### #7. Yang-Mills Existence And Mass Gap

Introduced in 1954 by Chinese-born American physicist Chen Ning Yang and American physicist Robert L. Mills. This is an unsolved problem in mathematical physics, where it describes the strong interactions of elementary particles that depend 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 (c). It is your last chance to win a million dollars.

Let us know if you can solve any of these problems.