4.1. Millennium Prize Problems or how to get a million dollars


The Millennium Prize Problems are seven problems in the field of Mathematics stated in 2000. These are old problems. Nowadays, six of the seven problems remain unsolved. A correct solution to any of them would result in a million dollar prize. $1,000,000 is about 900,000 euros.

The only solved problem is the so-called Poincaré conjecture (now called Poincaré theorem as it has already been proven). It was originally posed in 1904 by the French mathematician Henri Poincaré, and was only solved a century later by the Russian mathematician Grigori Perelman. He was awarded the $1,000,000 prize in 2010... but he declined the award! (wow!)

Perelman also declined the Fields Medal, which is one of the most relevant prizes in Mathematics (there is no Nobel Prize in Mathematics). He said:

Everybody understood that if the proof is correct, then no other recognition is needed. I'm not interested in money or fame.

The Fields Medal is granted every four years on the occasion of the International Congress of Mathematics to recognize outstanding mathematical achievement. The medal is made of gold and shows the face of the brilliant Archimedes (§34). Contrary to other prizes that are usually awarded to senior scientists, the Fields Medal can only be won by mathematicians under the age of 40. This may sound strange, but remember that most important discoveries are made by young men and women with a great scientific creativity (which tends to decrease with age).

Another hard-to-solve problem was Fermat's Last Theorem, which was indeed a conjecture for almost 400 years until the British mathematician Andrew Wiles solved it. He first attempted to give a valid proof in 1993, when he was 40, but there was a little mistake that he could not correct until 1995. By then he was 42, past the limiting age to receive the Fields Medal! Nevertheless, the International Mathematical Union gave him a silver plaque in recognition for his proof.

To conclude, here you have the list of the 6 millennium problems that remain unsolved… just in case you want to try to win a million dollars (and surely a Fields Medal).

• The Riemann hypothesis (§8)

• Yang-Mills Theory and the Mass Gap Hypothesis

• The P vs. NP problem (§17)

• The Navier-Stokes Equations

• The Birch and Swinnerton-Dyer Conjecture

• The Hodge Conjecture