Galois was ahead of his time. In his teens, he was able to determine necessary and sufficient conditions for algebraic solutions of polynomials to exist. He barely attended college, but most of his contemporaries could not understand his work. He submitted research papers that were either lost or “incomprehensible.” It was only 14 years after his death that the mathematics community was able to recognize the value of his work.
The Nobel Prize are prestigious awards given each year to individuals (as well as organizations) who have contributed significantly in cultural and scientific advances.
Alfred B. Nobel, the inventor of dynamite, bequeathed 31 million Swedish kronor in 1895 (about 250 million dollars in 2008) to fund the awards for achievements in Chemistry, Physics, Physiology and Medicine, Literature, and Peace. In 1901, the first set of awards were given, and in 1969, the Nobel Foundation established the Nobel Prize for Economics.
But did you ever wonder why there was no Nobel Prize of Mathematics? » Read more
The Fermat’s Last Theorem is one of the hardest problems in the history of mathematics. The problem was written by Pierre de Fermat in 1637, and it was only solved more than 300 years later — in 1995 by Professor Andrew Wiles.
But what is exactly the Fermat’s Last Theorem?
The Fermat’s Last Theorem is an extension of the Pythagorean Theorem. Recall that the Pythagorean Theorem states that given a right triangle whose side lengths are and hypotenuse , is satisfied. For example, a right triangle with side lengths , and has hypotenuse .
There are some interesting things that we can see if we examine the side lengths of right triangles. For instance, if we let the triples be the side lengths of a right triangle, where is the hypotenuse, we can find triples such that all lengths are integers. The triples , , are integer triples, and they satisfy the Pythagorean Theorem. These triples are called Pythagorean Triples. It is not also difficult to see that there are infinitely many Pythagorean Triples (Can you see why?). » Read more