Writer: Dan Jacobson
Editor: Karolay Lorenty
To many, the idea of “recreational mathematics” may seem like an oxymoron. After a mathematical education progressing from mind-numbing recitation of twelve-times-tables in primary school, to the tedium of circle theorems in high school, it would make sense that the last thing you would want to do is more maths. However, the value of recreational mathematics lies in the ability of mathematics to, first, make you smile and, second, make you understand the world in a new way.
John Horton Conway, the English mathematician who died at the age of 82 on 11th April 2020 following complications from COVID-19, was probably the most eminent name in recreational mathematics. In addition to the significant contributions he made to the field of pure mathematics, most famously group theory (not sure if this is capitalised?) and Conway notation, he maintained a passion and obsession with mathematical games and puzzles, including sprouts and philosopher’s football.
His playfulness and curiosity established him as one of the most eccentric, inspirational, and recognisable faces in the field of mathematics. Professor Simon Kochen, his close friend and Princeton collaborator, described him as a “magical genius”. His lectures, which he delivered whilst a professor at Cambridge and Princeton, were often vastly oversubscribed, and characterised by enthusiastically delivered stories and even rolling on the floor laughing during his 1994 talk at the International Congress of Mathematicians. He was also known for his incredible generosity in sharing his time. According to stand-up mathematician Matt Parker speaking on the More or Less podcast, Conway had a “seemingly infinite amount of patience” at conferences where he was often considered a “maths deity”. However, his lasting legacy, to his subsequent chagrin, came in what is now known as “Conway’s Game of Life”.
Otherwise known as ‘Life’, this game is designed to simulate a population of cells which interact with each other in a 2D “world” following a set of specified rules governing how their interactions affect their status. The rules that Conway selected for Life were designed specifically to ensure a number of properties, including unpredictable dynamics and evolving patterns. Indeed, it is truly incredible to watch Life at work: clumps of cells compressing and expanding, before morphing into one another and breaking apart. This is shown in this simulation with ‘KINESIS’ acting as the initial configuration of the world.
I do not think it is surprising that Conway’s legacy is intertwined with Life, whether he wanted this or not. Whilst he has softened on the issue, he initially stated that he “hated” Life, as it overshadowed far more, in his opinion, interesting work which he had conducted. However, in the initial article about Life, published by Martin Gardner in Scientific American’s ‘Mathematical Games’ column, Conway concluded by remarking that it is “marvellous to sit watching on the computer screen”. And I don’t think he was surprised that, 50 years on, the imagination driven by these simulations has not waned.
However, I believe that his most significant contribution was his outlook on what it should mean to be a scientist. In an interview for the mathematics YouTube channel Numberphile, Conway said, following his major mathematical breakthrough in his late 20s concerning monster group theory, “it was so nice not worrying anymore, that I thought ‘I’m not going to worry anymore. Ever again.’”
In recent times, this attitude of ‘not worrying’ led to the ‘Free Will Theorem’, which he formulated with Professor Kochen. The theorem states that if we have free will, meaning that our choices are not entirely determined by past events, then basic subatomic particles should also have free will. This work, a bold amalgamation of quantum physics, geometry, and philosophy, is a prime example of the breath-taking creativity that scientists may display if given the opportunity simply to ‘not worry’.
Although Conway may have been the best evidence for the outdated mythology of the scientific ‘lone genius’, his approach was decidedly collaborative, interdisciplinary, and driven primarily by curiosity and passion. I believe that his attitude embodied the spirit with which we conduct good science, and also create good scientists. Conway left a lot more, not just for mathematicians but scientists in general, to think about. This is the time to do so.