When we were in high school, math always felt like the least useful subject. For most of us, we thought we would never use math in real life or never gain anything money wise from it. However, for some of the geniuses out there, math can turn into more than just a career. If you solve one of these problems, you will not only be one of the most respected people on the earth, but you will also be a million dollars richer.

Obviously, I am not a math genius, so the explanations may not be thorough. If you would like to learn more about how these problems I will link the problem title with a detailed explanation from someone much smarter than I. Most of the problems are known as millennium problems, or generational problems that are searched for by millions.

## The Millennium Problems: The Hardest Math Problems Known To Man

Yang Mills and Mass Gap: Not that much is really known about this problem. Basically, we know that computer simulations suggest that an existence of a “mass gap” that exists in the solution of the quantum versions of the Yang Mills equation. To this day, no one has yet given proof for this equation.

Riemann Hypothesis: The Riemann Hypothesis is all about prime numbers. The hypothesis states that the Riemann Zeta function has zeroes only at the negative even integers and complex numbers with real part ½. Recently, famous mathematician Michael Atiyah brought forward a proof but it was proved insufficient. Out of all the million dollar math problems, Riemann’s hypothesis is probably the most famous.

P vs NP Problem: The P vs NP problem revolves around how math works. The problem essentially boils down to correlation in math. Is there a correlation between checking a solution and finding a solution? Although this problem seems particularly easy, it can be very complicated when you look more in depth.

Navier-Stokes Equation: The Navier-Stokes Equation is all about the movement of fluids and liquids. Even in a world where we revolve around liquids for survival, we still don’t much about how they move. If you can find a solution or a pattern in the movement, then you’ll be a million dollars richer.

Hodge Conjecture: The Hodge conjecture answer is “how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations” (claymath.org). However, exceptions are known when the solutions have less than four dimensions. So, the solution must be with the 4^{th} power and beyond.

Birch and Swinnerton-Dyer Conjecture-: Out of all the most complex problems of math, this one is probably the hardest to explain for the average person. Basically, the problem has to do elliptical curves and their relation to rational points. Honestly, this one’s a little hard to explain, so if you would like to learn more click the subtitle.

Beal’s Conjecture

Beal’s Conjecture: Beal’s Conjecture is another extremely complicated problem that seems so simple. The problem states that a^x + b^y = c^z when x, y, and z are three or greater and a, b, and c all have a common prime number. Despite the seemingly simplicity of the problem, no one can prove the rule or find an exception to the rule. :

## Honorable Mentions

From what I can tell, the Goldbach Conjecture no longer has an active prize. Back in 2000-2002, a million dollars was offered to anyone that could prove or disprove that every even number could be formed by adding two primes. To this day, no-one has yet solved this problem.

The Poincare Conjecture is the only millennium problem to ever be solved. The problem was solved by Russian mathematician Grigori Perelman. He chose to turn down the money and just left with his accomplishment.

Also, if you would like another math problem for you, here’s one. If you put five dollars into an investing account, and get five dollars back, how much did your money increase by? Now, what if this investing account went up by eight percent every year. How much would you make in ten years? You can learn that by signing up for the Acorns investing app here.

Sources:

Beal Prize. (n.d.). Retrieved January 02, 2021, from https://www.ams.org/prizes-awards/paview.cgi?parent_id=41

Gold for Goldbach. (2018, July 25). Retrieved January 02, 2021, from https://plus.maths.org/content/gold-goldbach

Millennium Problems. (n.d.). Retrieved January 02, 2021, from https://www.claymath.org/millennium-problems

Redirect Notice. (n.d.). Retrieved January 02, 2021, from https://www.google.com/url?sa=i