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Maths in Action Lecture 2017

I was fortunate enough to attend a series of maths lectures on Thursday the 30th of November. It was held at the Emmanuel Centre, a church located near the Houses of Parliament. A total of 5 lectures were given over the course of 6 hours, by 6 different backgrounds, each an expert in their fields.

Fermat's Last Theorem | Source: LinkedIn

The first lecture was given by Simon Singh, an author and broadcaster. His chosen topic was Fermat’s Last Theorem, a theorem which Fermat claimed he could solve, although never wrote down the solution to, and a theorem that nobody ever managed to solve for 200 years after his death. Fermat’s last theorem states that for all values of n>2, and a, b and c ≠ 0 there are no integers which satisfy the equation a^n + b^n = c^n. I was disappointed that I wasn’t the one to find the proof for this theorem; however, this disappointment was lifted by how engaging the lecture was. Simon Singh has even written a book on Fermat’s last theorem, because, naturally, writing books is what an author does. To acquaint us with the seriousness of proofs, he started out with a problem and asked us to prove, that a chessboard could not be fully covered with dominos if two of its opposite corners had been taken out (assuming each half of every domino would cover a single square). This showed us how proofs must use mathematical reasoning, not speculation. He also introduced us to Euler’s conjecture, which used speculation to determine the fact that a specific rule would apply to all numbers up to and including infinity. This conjecture has now been disproved, and this showed us the importance of using mathematical proof. He talked to us about Andrew Wiles, who figured out the proof to Fermat’s theorem, and we were able to watch a small section of a documentary on this man, where it was made clear how important this discovery was to him. He had come across this problem as a teenager, and had, for the rest of his life, been thinking of ways to solve this problem. He finally solved it after graduating from his University and taking on a job as a lecturer. Unfortunately, we never got to meet this man in person.

The second lecture was my personal favourite and was given by Professor Kevin Buzzard of Imperial College. He graduated from the University of Cambridge as Senior Wrangler. This is considered to be the greatest achievement possible in the Western Hemisphere, and the toughest academic feat. His lecture was entitled ‘the Platonic Universe’, in which he, a mathematician, strayed outside of the realms of mathematics, and into the world of physics. He explored the limits of our universe and got us to think deeply about whether some numbers actually exist. For example, the number googol can be written on a piece of paper in words or as 10^100, but in actual fact, there are not enough particles, or even subatomic particles in the universe, that could be counted and added up, to give this number, he used this as an explanation for why computers work via proof, rather than counting every single number in a calculation. He also explored Planck’s, which is a period of time (10^-43 seconds) in which no changes in the universe can be seen whatsoever, which suggests that our universe is rather like a camera, with frames being taken an incomprehensible number of times per second.

An error log for all those errors?

The third speaker was the author and tutor Dr Colin Beverige. He, as a tutor, decided to give a presentation on revision techniques. His presentation was the most relevant and helpful for us. As students, especially of maths, we could directly relate to what he was talking about. He mentioned methods of revision such as colour coding, mnemonics and taking a good approach to answering questions. Of all the techniques he mentioned, perhaps the only one I disagreed with was the error log method. By this he meant that we should write down all the mistakes we made on a piece of paper, to ensure that we didn’t make them again. Surprisingly as a mathematician, he hadn’t considered the fact that there are some people out there who make too many mistakes, and may not have enough space to write them down [I have now started writing on my walls, floor and ceiling instead] (I will mention no names).

Iterated Prisoner's Dilemma | Source: By Jplotkin8, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=52585754 

Professor Karen Page of UCL gave the fourth lecture. She is another maths graduate, who once again looked outside her field of expertise for inspiration. This again paid off and resulted in her lecture being my second favourite out of the six. Her presentation was on game theory and therefore was based on economics. She talked about the prisoner’s dilemma, and how the best decision is always to cooperate, although irrational thinking can get in the way and lead to other outcomes. We even conducted an experiment (without knowing it was an experiment at the time) on ourselves. She proposed the idea that we were each given £100, and a person with which to share it. We could choose to share any amount of this money with someone else as we pleased. We were then put on the reciprocating end and asked how much money we would accept. The logical answer, as she [and I] pointed out, was to offer the lowest price possible, and accept whatever they wanted to give us, because who in their right mind would reject any amount of money if it is free. However, she then pointed out how it is wiser to be more irrational if this deal can be repeated multiple times because reputation can affect how generous a deal proposal will be. She then showed how all these techniques were applied to the BT auction deal.

The fifth speaker was Dr Lewney. His presentation was entitled ‘Are we Made of Maths?’ He asked questions such as ‘Did maths exist before humans did?’ I was disappointed to find out that many of these questions had no answers [it meant no gloating over my peers], however, the song at the end of his lecture once again lightened my mood. He, as a mathematician, naturally had created a song with lyrics about maths. He apparently had plagiarised and used a melody from a well-known song but I have no idea what that song was. Those who evidently did sang along to the lyrics displayed behind him. I can comfortably say that my singing skills are far superior to any I witnessed at the lecture.

The final lecture was given by Bobby Seagull, whose name is far more interesting than his lecture was (his name is genuinely very interesting). His lecture was on his four favourite mathematicians. These were Carl Gauss, Ada Lovelace, Blaise Pascal and Srinivasa Ramanujan. All of these mathematicians had made substantial contributions to mathematics. Carl Gauss’s outside-the-box thinking was discovered while he was still young. Ada Lovelace made substantial contributions to the development of computers, and some describe her as ahead of her time. Pascal is the most famous out all of these mathematicians, and through his work, he was not only able to influence the world of maths but that of physics as well. Finally, there was Srinivasa Ramanujan, the most notable of all, who, despite having no previous background in maths, went on to make substantial contributions to number theory, infinite theory and other fields of maths, went on to be elected the first Indian fellow of Trinity College Cambridge.

The host of these lectures was Ben Sparks, whom you may know from the YouTube channel, Numberphile. His lectures are free to attend (they’re literally everywhere on YouTube). [I can honestly say that the lectures were worth the harrowing trip on (under?) the London Underground.]