Short videos made with each of the four winners of Fields Medals (“the Nobel prize of maths”) have been released.

Click here to view them.

The video-makers have done a good job of making the videos accessible to non-specialists, yet without dumbing down.

I found the video with Caucher Birkar – an Iranian Kurd by origin, who came to Britain as a refugee, and is now a professor at Cambridge – particularly vivid. The name Birkar goes by is not his birth name, but one he chose when coming to Britain which means “migrant mathematician” in Kurdish. He expresses hope that his achievement may bring some pride and joy to the 40 million Kurdish people, still denied their right to self-determination in a state of their own.

The video with Peter Scholze is also excellent.

Most people with maths degrees – probably, I’d guess, most people with maths PhDs outside the particular areas of maths studied by the medallists – will not understand the technicalities of the medallists’ research. The videos are still worth watching.

Two of the medals this year have been awarded for work in algebraic geometry – roughly speaking, the study of the geometrical shape of the sets of solutions of algebraic equations. Students at Warwick and Cambridge universities, for example, can study algebraic geometry as a third-year option, but at many universities it is not even an option at undergraduate level. The field is quite old, but was revolutionised by new concepts in the 1950s and 60s (thanks mostly to French mathematicians), and has been very active ever since.

One medal has been awarded for work on partial differential equations – equations connecting rates of change of variables, rather than just the variables themselves, central to mathematical physics – and one for work on number theory (the theory of the counting numbers, 1, 2, 3… – again, a very old field, but one which has revitalised in recent decades).

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