Dr. Cary Oberije, a postdoctoral researcher in The Netherlands, has found that mathematical models can be used to accurately predict patients' responses to treatment. Prediction models were used to analyze lung cancer patients' likelihood of survival and...

# When Will I Use Math?

## WeUseMath.org

# Millennium Prize Problems

As new discoveries are constantly being made in the field of mathematics, there are still a number of unsolved problems. Many of these problems, once solved, will help to improve the quality of our daily lives.

In 2000, the Clay Mathematics Institute selected 7 different unsolved problems and offered a prize of $1 million per problem for those who find a solution. They chose to call these problems the “millennium problems”. (http://www.claymath.org/millennium/)

These problems include:

**Birch and Swinnerton-Dyer Conjecture**

Ever tried to solve a quadratic equation? You just used the quadratic formula right? How about an equation of the form:y

^{2}= x^{3}- xThe graph of this equation is called an elliptic curve. It turns out you can describe these curves using algebraic terms and geometric terms. The Birch Swinnerton-Dyer Conjecture says there is a connection between these two descriptions.

http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/

**Hodge Conjecture**

http://www.claymath.org/millennium/Hodge_Conjecture/

**Navier-Stokes Equations**

http://www.claymath.org/millennium/Navier-Stokes_Equations/

**P vs NP**

Ever played minesweeper? Ever wondered how fast a computer could beat the game? So do computer scientists! There are very many problems for which it is not known how fast they can be solved. The P vs NP problem seeks to show that these problems can be solved in polynomial time.

http://www.claymath.org/millennium/P_vs_NP/

**Poincaré Conjecture**

Solved by Grigori Perelman in the early 21st century.

If something looks like a sphere, smells like a sphere, and tastes like a sphere, is it a sphere? In dimension two, the answer is easy. In dimensions four and greater, the answer is still yes. For a long time, the answer for dimension three was unknown until Perelman solved the problem in the early 2000’s.

http://www.claymath.org/millennium/Poincare_Conjecture/

**Riemann Hypothesis**

In calculus you learn that the series

converges when p > 1. People have asked what happens when we treat p as a variable in the complex plane? It turns out this new function is related to prime numbers. The function has zeros at the negative even integers and in a small strip. Reimann’s Hypothesis is that all these extra zeros have real part equal to ½. If this is true, it implies that the primes are well spaced.

http://www.claymath.org/millennium/Riemann_Hypothesis/

**Yang-Mills Theory**

http://www.claymath.org/millennium/Yang-Mills_Theory/

Know how math applies to real life, a new discovery in math, a math tidbit or an unsolved math problem? Submit a "Did You Know?" entry to the site!

The most common question students ask math teachers at every level is “When will I use math?” WeUseMath.org is a non-profit website that helps to answer this question. This website describes the importance of mathematics and many rewarding career opportunities available to students who study mathematics.

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