# 6 Amazing Mathematicians

By Hannah Bickerton Thursday, September 11, 2014

## 1) Paul Erdős ~ 1913-1996

*“If numbers aren’t beautiful, I don’t know what is”*

The son of two maths teachers, Hungarian mathematician Erdős lived and breathed maths. Erdős was fully committed to a life exploring the mathematical problems and was unperturbed by material concerns. Instead, he preferred to travel the globe; visiting universities and collaborating on projects with fellow mathematicians, usually staying a guest in their homes. (“Another roof another proof” was one of his favourite phrases). So prominent was he among other mathematicians, the Erdos number system was even developed to distinguish the level at which you were linked to him. An Erdős number 1 for example meant you had worked with him directly, Erdős number 2 means you had worked with one of his collaborators and so on.

Erdős’ main skill lay in solving problems for graph theory and number theory. He was praised for his ability for not only finding solutions to complex problems, but also the way he was able to structure them in a simple and eloquent way making them easy to interpret. His greatest known work was the prime number theorem, whereby you can find an approximate figure for the quantity of prime numbers equal to or less than any given number, something which later earned him the Cole Prize.

## 2) Thales ~ 624-546BC

*“A multitude of words is no proof of a prudent mind”*

Considered as one of the wisest of the ancient Greeks and one of the earliest documented mathematicians, Thales made huge advances in geometry. This may sound relatively unimpressive by today’s standards but back then people knew very little about the subject. In fact, the very definition of geometry in ancient Greek is “Earth measurement” the basis for which Thales made many of his mathematical findings, using only a rope and stake.

Thales was able to make calculations by exploring and questioning the world around him. Whilst studying the ancient Egyptian pyramids in Cairo, Thales managed to measure the height of each by using the sun. He determined that at the point his own shadow was exactly the same as his height, the shadow of the pyramid must also be identical to itself.

## 3) Alan Turing ~ 1912-1954

*“The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion.”*

A mathematician that truly influenced the modern world was Alan Turing, a Computer Scientist and master codebreaker. Playing a key role in artificial intelligence throughout the Second World War, as he was able to not only decipher cryptograms sent through from German Enigma Machines, but he also developed special codebreaking machines to do it for him. He is often recognised as having invented the first ever computer. To protect himself in the event of Nazi takeover, Turing converted a considerable amount of his fortune into silver bars which he buried it in various locations, with only a series of complex codes to reveal each site. Unfortunately he was never able to retrieve his fortune, because his codes were so complex that even he was unable to crack them. To this day they have never been found.

## 4) Grigori Perelman ~ 1966-Present

A 21st century Russian mathematician, Perelman is perhaps more prominent in his field for the refusal of a prestigious mathematic award than his actual contributions to the subject. However there is no doubt that he is one of the most brilliant mathematicians alive today. Remaining unsolved for over 100 years, the highly complex Poincaré Conjecture was finally solved by Perelman in one of the greatest mathematical breakthroughs of all time - the only one out of the seven Clay Millennium problems to be cracked. The Poincare Conjecture (simplified) states that there is no difference between a doughnut and a coffee mug, and each can be manipulated to take the form of the other without being broken. With his proof, Perelman was entitled to the $1 million prize money in acknowledgement of his achievement which he famously rejected. When asked the reason behind his controversial decision, Perelman replied, “I know how to control the Universe. Why would I run to get a million, tell me?”

## 5) Gerolamo Cardano ~ 1506-1576

*“Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.”*

Cardano was an eccentric, Italian mathematician who was far ahead of his time in the 16th century. Building on the work done by fellow mathematician Tartaglia on solving cubic equations, Cardano was the first person recorded to recognise negative numbers as possible roots. In his book, Ars Magna (1545), he published solutions for both quadratic and cubic equations, popular problems during the time that were yet to be solved.

However Cardano was perhaps more renowned for his contributions to probability theory, a topic he was able to advance through his extensive gambling habit which often left him penniless. His extensive study into the law of probability and ability to evaluate possible outcomes allowed him to position himself favourably when he played. Whilst this may not have not always led to a prosperous life for himself, Cardano’s methods of calculating risk certainly shaped the basis for the insurance industry significantly, which up until that point had not been performing well.

## 6) Sophie Germain ~ 1776-1831

*“Fearing the ridicule attached to a female scientist, I have previously taken the name of M. LeBlanc in communicating to you those notes that, no doubt, do not deserve the indulgence with which you have responded.”*

Born during the French revolution and thereby confined to her home, Germain started exploring mathematical studies, an unusual pursuit for a female during that time. As such, for most of her life, she faced a considerable amount of prejudice from family members and academic bodies, only able to progress under a fake name, M. LeBlanc, which allowed her to write and converse with prominent mathematicians and submit them her papers.

Due to their mutual interest in number theory, Germain was finally taken under the wing of mathematician, Carl Friedrich Gauss, who was impressed and accepting of the fact she was a woman. With Gauss as a mentor, she eventually made her most notable mathematical breakthrough, which states that one of x,y and z must be divisible by 5 for the equation x^5+y^5=z^5 , quite an achievement for someone who had never received a formal education. This was a huge advance in number theory, the workings of which helped in the eventual proof of Fermat’s last theorem by Andrew Wiles, (there is no solution for x^n+y^n=z^n where integers are greater than 2).