Fermat’s Last Theorem

By Author: Isabella Evans
Total Articles: 11
Comment this article

We constantly hear of an innumerable amount of theorems in Math and in many other subjects. Different people from different countries during various time periods in history have produced some marvelous theorems that have helped mathematicians and scientists to bring forth new technologies and applications.

Some theorems begin as conjectures, which are simply opinions or statements that have not been proved formally. One particular conjecture that baffled mathematicians for over 350 years is what is called “Fermat’s Last Theorem”. This conjecture was introduced by an amateur French mathematician, Pierre de Fermat. His conjecture states that:

There are no three positive integers (a, b & c) which can satisfy the equation an +bn = cn for any integer n more than 2.

This conjecture was written on the margin of one of the books he wrote, and interestingly, he has mentioned that “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain”.

Most of us know and would remember the Pythagoras theorem, which says that a2 +b2 = c2 if a, b and c are the lengths ...
... of the sides of a right angled triangle and c is the hypotenuse. Therefore, we know that there are combinations of 3 positive integers a, b and c which satisfy the equation when n=2. It is also easy to see that the equation holds if n=1, but according to Fermat, this equation does not hold for any integer n>2. Therefore no matter how much we try, we will not be able to find three positive integers a, b and c when n=3, n=4 etc.

Unfortunately, Fermat died before he could explain what his marvelous demonstration was; and mathematicians of all ages and capabilities tried for over 350 years to prove this conjecture, intrigued by the fact that it is so simple to understand, yet so seemingly impossible to prove.

Finally, in 1995 British mathematician Andrew Wiles produced a proof, which is very long (over 100 pages!) and involves very complex mathematics. Hence it is now accepted as a theorem. Wiles was 10 years old when he first heard of this problem, and as an adult, dedicated 7 long years simply trying to find this proof.

To this day no one knows (and possibly never will), if Fermat actually did have a proof for his conjecture, as he said in his margin; and if he did, then what it was. It could not have been the same as Wiles’ proof since this involved much more modern math than what was known in Fermat’s time. Can you think of a different and simpler way to prove this theorem? If you could, then maybe that’s what Fermat was thinking too, and you could become the next famous mathematician of all time!

There are many interesting mathematical theorems and stories, as well as about mathematicians who dedicated their lives to the subject. Teaching in Australia should focus on this kind of interesting areas of subjects, apart from the subject content. It would make students realize that they also can contribute to the growth of that subject, if they have the interest.

Visit iExel for more information on teaching in Australia or tutors in Melbourne.