Birth Of A Theorem

Cedric Villani’s book “Birth of a Theorem” has recently been released and received positive revies, such as this one by Hannah Fry. I had been dubious about buying this book due to the apparent high level mathematical content of parts of it, but about 3 weeks ago BBC Radio 4 featured it as their book of the week – after hearing the extracts I have ordered the book. 

Julien Rhind-Tutt’s reading of extracts from Villani’s book is very engaging – though I think it has perhaps lost something by not being read by Villani. The episodes are available for another week or so here –  I’d encourage you to listen if you can.

Cedric Villani is a Fields Medal winning (in 2010) French mathmeatician, who works primarily on mathematical physics. The Fields Medal is highly prestigious as it is only awarded every 4 years and only to mathematicians under 40. He won the Fields medal for his work on non-linear Landau Damping and the Boltzmann Transport equation, in 2012 he wrote a book, “Théorème Vivante”,in French, describing the road to the proof of his theorem and it is this which has been translated into English and published as “Birth of a Theorem” in 2015.

Villani gives a really nice insight into the world of a mathematician, and I could definitely recognise the panic he felt when there was no tea available – “Panic! Without the stimulating leaves of camelia sinesis I couldn’t possibly face the hours of calculation which lay in store”, he then goes on to describe breaking into Princeton to procure some tea. In the first episode he paints a nice picture of how consuming mathematics can be – “While the children excitedly open their Christmas presents, I’m hanging exponents on functions like balls on a tree and lining up factorials like upside down candles”. He also describes his wife being being taken aback seeing his “face contorted by ticks and twitches” as he thought about the problem he was working on over dinner. My wife says that in the final year of my PhD she would often have to say things to me more than three times because I would just zone out into a world of my research – I think it can be very hard being with a mathematician at times! It is certainly easy to feel for him when he describes receiving the rejection email from Acta Numerica – if you have spent countless hours on a problem, to have the paper rejected is crushing.

On his website there is an introduction to Boltzmann like transport equations in his survey paper “A Review of Mathematical Topics in Collisional Kinetic Theory” despite being an introduction it is still incredibly dense. I’ve studied a particular version of the Boltzmann equation – The Neutron Transport Equation – and a few pages in I am struggling to follow this easily. I think I would have to expend an awful lot of time in order to be able to understand the mathematical parts of his book. Indeed, if I ever could, it is likely that only a few hundred mathematicians in the world understand his and Clément Mouhot’s proof!

Cedric Villani also appered on Start The Week on 9th March 2015, a podcast of which is available here which is also worth spending the time to sit down and listen to properly.

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