It has come to my attention that there is a maths camp taking place at Balliol College, Oxford, with the intention of subjecting young aspiring mathematicians to new ideas. Since one of the volunteers at the camp is advertising cp4space there, we decided that it would be a good idea to inspire the trainees with randomly selected examples of influential mathematicians:
I’ve decided to adopt a vaguely chronological approach, so we shall begin in Alexandria, a city in Egypt built by the eponymous Alexander the Great. It was the centre of education in the ancient world, and thus could be regarded as a 2000-year-old counterpart of Cambridge. Nevertheless, its library was far more aesthetically pleasing than our UL, and it is absolutely tragic that it no longer exists.
Hypatia was born in the fourth century AD, and eventually became head of the Platonist school of philosophy. She shifted the focus from empirical observation to more rigorous mathematical proof, thus helping to incorporate mathematics into physics. Indeed, one of her many accomplishments was determining the motion of celestial bodies, not unlike how Gauss predicted the trajectory of Ceres in his youth.
Hypatia also developed ideas from Diophantus’ Arithmetica, Euclid’s Elements and Apollonius’ Conics (three very influential mathematical texts from Ancient Greece), amongst others.
You’ve probably heard of the famous poet Lord Byron, who had a number of interesting eccentricities including keeping a pet bear in the hallowed halls of Trinity College, Cambridge, where it would roam the vast, impressive courtyards and cause something of a stir amongst fellow Trinitarians.
His daughter, Ada Byron, went into a very different discipline, becoming the first computer programmer. She developed an algorithm for computing Bernoulli numbers on the Analytical Engine, the first programmable mechanical computer, which was designed by the Lucasian Professor of Mathematics, Charles Babbage (who also went to Trinity).
Most impressively, however, she realised that the Analytical Engine had a theoretical superiority over Babbage’s earlier Difference Engines and the calculating machines of Pascal and Leibniz, in that it could be programmed to perform functions of arbitrary complexity instead of mere routine calculations. Indeed, this insight could have resulted in Turing-complete computers being built long before Alan Turing.
Unfortunately, since it was mechanical and vastly complicated, the Analytical Engine was not built within Babbage’s lifetime. Indeed, only part of it has been reconstructed, and there is currently an effort to realise it in its entirety.
Ada Byron was also somewhat promiscuous — another attribute with which I can empathise. Indeed, together with my scandalous and outlandish (albeit successful!) expenses claims from the UKMT, some people have suggested respacing my name to form ‘Ada M.P. Goucher’…
A contemporary of Gauss and Legendre, Sophie Germain originally concealed her identity and used the pseudonym M. LeBlanc. Gauss acknowledged her genius in correspondence with Olbers; hence, she was certainly a mathematician of the highest calibre. Her work on Fermat’s Last Theorem was the first non-trivial progress since Fermat and Euler, and resulted in primes of the form (p − 1)/2 being called Sophie Germain primes.
(For some reason, the factorisation of is named after her, despite being completely trivial.)
In our universe, there are many symmetries. For instance, the laws of physics are invariant under translation (homogeneity), rotation (isotropy) and Lorentz transformations (Lorentz invariance). Using the Hamiltonian formulation of mechanics, Emmy Noether was able to show that each of these symmetries gives rise to a conservation law (e.g. conservation of linear momentum, angular momentum and energy).
She also contributed to pure mathematics; a Noetherian ring is one where all ideals are finitely generated. There is an Emmy Noether Society at Cambridge named in her honour, which have hosted talks by mathematicians such as Ruth Gregory. They also gave out free cake in the CMS, which was definitely worth attending.
One of the most prolific mathematicians of the 20th century was Paul Erdős. His collaborators and doctoral advisees include many famous mathematicians; for instance, he was the advisor of Professor Béla Bollobás FRS, who was in turn the advisor of Professors Imre Leader and Timothy Gowers, the latter of which advised Professor Ben Green. (They all went to Trinity as well — not that I’m advertising this amazing college, which is far better than Balliol.)
Tragically, Ben Green is no longer with us, but will always be remembered and his legacy shall live on in his students, including Professor Vicky Neale. Vicky Neale, Vesna Kadelberg, the absolutely brilliant IMO team leader James Cranch and I have been heavily involved in the organisation of a competition called the MOG, which some of you will be sitting in September. Good luck, and I hope this cp4space post has inspired you…