World’s most charismatic mathematician: John Horton Conway


Here’s a good Guardian article about John Horton Conway – an unusual and remarkable mathematician.

From the article:

“John Horton Conway is a cross between Archimedes, Mick Jagger and Salvador Dalí. For many years, he worried that his obsession with playing silly games was ruining his career – until he realised that it could lead to extraordinary discoveries.

“On a late September day in 1956, John Horton Conway left home with a trunk on his back. He was a skinny 18-year-old, with long, unkempt hair – a sort of proto-hippie – and although he generally preferred to go barefoot, on this occasion he wore strappy Jesus sandals. He travelled by steam train from Liverpool to Cambridge, where he was to start life as an undergraduate. During the five-hour journey, via Crewe with a connection in Bletchley, something dawned on him: this was a chance to reinvent himself.”




An entertaining read, thanks!

In grad school I studied horned spheres in topology.

In my career I’ve often used Conway’s Game of Life as an illustration of arbitrarily high complexity arising from extremely simple sources. See Game-of-Life-JavaScript. And see the discussion at Wofram-Cellular-Automaton (Wolfram lives near us in MA) from which: “…there exist universal cellular automata that are capable of simulating the behavior of any other cellular automaton or Turing machine. It has even been proved by Gacs (2001) that there exist fault-tolerant universal cellular automata, whose ability to simulate other cellular automata is not hindered by random perturbations provided that such perturbations are sufficiently sparse.”



Physicists like these kinds of things: complexity arising out of simple properties and rules. Indeed, it is the goal of physics, and science generally, to reduce the apparently infinite complexity of the natural world to the working out of a few simple principles.

This is the goal of The Theory of Everything, which would be a theory that includes quantum mechanics and relativity, or put another way, the Standard Model and gravitation.

It is important to understand, however, that The Theory of Everything would not answer all questions. For one thing, the mathematical complexity would overwhelm us and our computers. For another thing, we explain things or understand things at one level of experience by reference to one or two levels deeper, not by taking things all the way to quarks, electrons, gluons, and photons. Thus we understand some aspects of biology as working out of principles of biochemistry, which itself arises from atomic and molecular physics and electric forces, which themselves are a part of quantum mechanics. But we would not expect that there will be a quantum theory of evolution, even though the rules of quantum mechanics apply to everything in the biological world.


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