Normen is a Master's student in Applied Mathematics. He wrote the story below back when he was still a bachelor's student.
My favourite mathematics subject
In the Bachelor phase of Applied Mathematics, you get to work with the mathematics of real numbers, among other things: this is the set that contains all integers greater than zero. I am fascinated by puzzles and challenges that require the answer to be a round number. The problem can seem so simple, yet the answer can be so hard to find! In the first year you become familiar with prime numbers, groups and bodies in the Discrete Mathematics I and II classes. Mathematicians define groups and bodies to minimise clutter. On top of that, you can assemble them in such a way that they have a direct application for society. In our Algebra and Security class, taught in quartile 3 of the second year, this application becomes evident when you look at the different coding methods that are used all around the world. For example, when you do Internet banking, there is always a green lock to the left of the URL bar. If you click on it, depending on the Internet connection, you can see how the bank in question makes sure your bank details are safe.
All the terms you see in the image above are now familiar to me, and I also know now that these security measures are backed by a great deal of mathematics. The method I like the best is RSA, in which you make use of the fact that given a large integer n (think more than 80 figures), it is impossible for today’s computers to find prime numbers p and q, so that n = pq. Basically, this means that your PIN code is protected by an n integer, and that an outsider can only get hold of it if he knows how to find the p and the q. The three men who thought up this method in 1976 are now rolling in money.
The most famous theorem in mathematics
A topic I focused on in the first quartile of my second year is Fermat's Last Theorem. Everyone knows that how to find natural numbers a, b and c so that a2 + b2 = c2 (for example, a=3, b=4, c=5). It has even been proven that there is an infinite number of positive integer solutions for a, b and c. But in the 17th century, Pierre de Fermat thought: If I change the squares in this equation into cubes (a3 + b3 = c3), will it still be possible to find a, b and c? After many tries, he began to believe more and more firmly that such an a, b, c triplet could not exist. This also seemed to be true for the fourth power and higher, and so Fermat formulated the following conjecture: No positive integers a, b, c, n can be found for which
an + bn = cn , n ≥3 is true.
Except for the trivial solution a = b = c = 1. In 1631, Fermat claimed to have found a relatively short and simple way of proving his conjecture. However, he said the margin of the book he wrote this problem in was too small for the explanation, therefore he did not share it. What is amazing about his conjecture is that when you look at it, it seems so simple, yet for more than 350 years, the greatest mathematicians have tried in vain to prove Fermat’s Last Theorem. Some were even driven to despair trying. In 1993, Andrew Wiles was able to put an end to this centuries-long search in over a 100 pages worth of proof.
Normen is at the moment a MSc student in the programme Applied Mathematics. Read more about his experciences as a MSc student.