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orangesHere are some unsolved mathematical problems:

  • Goldbach’s conjecture: Can every even integer greater than 2 be written as a sum of two primes?
  • Twin Prime Conjecture: A twin prime is a pair of primes with difference 2, such as 11 and 13. Are there infinitely many twin primes?
  • Does the Fibonacci sequence contain an infinite number of primes?
  • Are there infinitely many perfect numbers?
  • Are there any odd perfect numbers?

The Clay Mathematics Institute posted seven unresolved problems in 2000; they also offer a prize of $1.000.000 for each solution. One of the problems has been solved (Poincaré Conjecture – solved by Grigoriy Perelman, 2002-3); the six remaining problems are described in simple terms in sub-pages here.