Unsolved Problems

Unsolved Problems

Mathematics is full of unsolved problems.  In fact, it is what drives people to become mathematicians.  Some of these problems are famous, some are not.  Some of them are so famous that there are million dollar prizes attached to their solutions.  (Click here to see the problems and get the rules.)

Below are some of my personal favorites.  What I like about these problems is that they are so easy to understand.  And yet, they have withstood all attacks from the world’s greatest mathematicians … even the likes of Erdos, Euler and Gauss!

Enjoy and good luck.

 

Goldbach’s Conjecture:

Every even number greater than or equal to four can be written as the sum of two prime numbers.

Twin Prime Conjecture:

There are infinitely many twin primes. (Twin primes are pairs of primes whose difference is two.)

Odd Perfect Number:

Prove or disprove the existence of an odd perfect number.  (A perfect number is a number that is equal to the sum of its proper divisors.  For example, 28 = 1 + 2 + 4 + 7 + 14.)