Million Dollar Math Trivia Quiz

Answer: Goldbach's Conjecture

The conjecture was originally stated in a 1742 lecture from Goldbach to Euler. It has been verified for numbers up to 100 trillion, but that is not yet a proof. The Russian mathematician Vinogradov has come tantalizing close by proving every (large enough) odd number is the sum of THREE primes.

Unfortunately, you can no longer win a guaranteed million for a proof of this. The publisher of the book below put a time limit on the contest, and that limit expired in 2002.

Answer: Uncle Petros

The book, 'Uncle Petros and Goldbach's Conjecture' was written by Apostolos Doxiadis. The prize was set up as a promotional gimmick for the book (and actually would have cost the publishers much less than $1,000,000 even if the conjecture was solved...they insured the prize through Lloyd's of London).

Answer: P vs. NP

The problems in question are referred to as NP complete. Strangely enough, the question as to whether or not certain minesweeper configurations are possible fits in this category.

Answer: Hodge Conjecture

Even understanding what this problem said would be a pretty big accomplishment.

Answer: Poincaire conjecture

The geometric property in question is that the surface is "simply connected", meaning that any rubber band placed on the surface can be shrunk to a point while leaving the rubber band on the surface. To visualize this in 3 dimensions, imagine a rubber band placed on a doughnut. If you place it properly, you can move it around the doughnut but not take it off. (In essence, this is because the doughnut has a hole that say, an apple does not). Surprisingly, Perelman chose to reject the million dollars, stating that he felt his work was so closely tied with that of others who studied the problem that accepting the prize for himself would be unfair.

Answer: Riemann hypothesis

Riemann's function is f(s)= the sum from one to infinity of one over (n to the sth power), where the sum converges ... it is defined slightly differently elsewhere. The lines in question are the real numbers and the complex numbers with imaginary part 1 half, and the conjecture has been verified for the first 1.5 billion zeroes.

This is probably the most important unsolved problem in mathematics today. Interesting bit of trivia: The English Mathematician Hardy was an avowed Atheist. Nevertheless, once when there was a great storm, Hardy was forced to cross the sea and was scared for his life. To 'Solve' this problem, he sent a telegram ahead of him claiming 'I have solved the Riemann Hypothesis'. Upon arrival, he said that no, he hadn't actually solved it, but if there WAS a higher power, he was certain that power would not let him die with the false glory of having the world think he had solved the greatest problem in mathematics.

Answer: Yang Mills problem

The challenge is to unite the mathematical model with what is actually observed in the lab.

Answer: Navier-Stokes problem

The equations in questions are differential equations describing, for example, the ripples made by a boat in a lake and the air currents when a jet flies.

Answer: Birch and Swinnerton-Dyer conjecture

Specifically, the conjecture states that if the zeta function is 0, then the number of solutions is infinite. If the function is not zero, the number of solutions is finite.

Answer: Clay Mathematics Institute

More detailed descriptions of the last seven problems, along with conditions for the contest, can be found at www.claymath.org . I would be VERY surprised if any of the problems were solved in the next 10 years (I'm certainly not going to be able to handle any of them!)