There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. The Riemann hypothesis. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. such that , where is the totient function. 14. 15. 16. The Clay Mathematics Institute ( of Cambridge, Massachusetts (CMI) has named seven "Millennium Prize Problems," selected by focusing on important classic questions in mathematics that have resisted solution over the years. In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert's problems), a number of which have now been solved, but some of which remain open. K.