When Math is Worth a Million Dollars

Million-dollar prizes have been announced for solving some of the world’s most unsolved mathematical problems. Here is a brief look at these problems.

Source: www.discover.com/issues/dec-06/features/million-dollar-math-problems/

Math has left us with several dramatic and extraordinary problems as a true test of human knowledge and intelligence. For example, there is ‘Fermat’s Last Theorem’, which the mathematician Pierre de Fermat noted in the margin of his book over 350 years ago. Unfortunately, he did not leave behind a proof of the theorem. However, he wrote next to the theorem, “I have discovered a truly marvelous proof of this, but this margin is too narrow to contain it.” He died before this note was discovered. As a result, we never received his marvelous proof. But mathematicians did not give up. After seven years of relentless effort, Andrew Wiles published the proof of the theorem in 1994. But his proof involved the use of complex equations with ellipses. It is thought that Fermat did not use anything so complex in his own proof, since the time was quite ancient. So, what was his proof? Will this historic proof forever remain undiscovered?

In August 2006, Russian mathematician Grigori Perelman created a stir in the world of mathematics by solving the centuries-old ‘Poincaré Conjecture’. As his solution was proven correct, the problem will now be known as the ‘Poincaré Theorem’. For this achievement, Perelman was awarded the Fields Medal, which is considered as prestigious as the Nobel Prize. With this honor came an additional 1,500 Canadian dollars. However, Perelman declined to accept the medal and the prize money. He said that having his solution accepted was the greatest achievement for him.

So now the question is: are there any problems left for us? Fortunately or unfortunately, there are countless unresolved problems remaining in every part of the mathematical world. In 1900, German mathematician David Hilbert mentioned only 23 problems, predicting that mathematicians would spend the entire coming century working to solve them. And that’s what happened. Out of the 23, solutions have been found for 20, while 3 still remain unsolved.

In 2000, Cambridge’s ‘Clay Mathematics Institute’ identified 7 unsolved mathematical problems and announced a prize of 1 million US dollars for solving each problem. While Perelman has solved the Poincaré problem among these 7, the rest still remain unsolved.

(To be continued……)