It is often assumed by members of the public that in order to be good at mathematics, one needs to be quick, and the faster one can solve a problem the better one is in the subject. This idea may have been disseminated by the fact that in examinations students are expected to solve a number of problems in a specified time interval. Perhaps also prevalent in people’s minds is the perception that most mathematical problems can be solved in a relatively short time by smart mathematicians that are able to carry out quick thought processes.

However, the history of mathematics is riddled with instances of problems that took a long time to solve or that are still open after several decades or centuries. For example, it took mathematicians 357 years to confirm ‘Fermat’s Last Theorem’, and the proof contains over 100 pages of deep mathematics developed over several centuries. Mathematics is endowed with conjectures that have so far remained unsolved and that influence its development.

One of these is Goldbach’s Conjecture, which simply states that every even whole number greater than 2 can be written as the sum of two primes. The conjecture was first proposed by the German mathematician Christian Goldbach in a letter he sent to Leonhard Euler on  June 7, 1742.

In the year 2000, the Clay Mathematics Institute established seven problems referred to as the ‘Millenium Prize problems’, which “were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium”. Anyone who solves any of these problems is awarded one million US dollars. So far, only the Poincaré Conjecture has been solved. The solution was provided by the Russian mathematician Grigori Perelman, who, perhaps surprisingly, turned down the prize that accompanied the solution.