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Caucher Birkar

Fields Medal


A Kurdish refugee, now Cambridge University maths professor, Caucher Birkar was awarded the Fields Medal in 2018, the highest honour in mathematics, for his contributions to algebraic geometry. The Fields Medal, often called the Nobel Prize of Mathematics, is awarded every four years to mathematicians below 40 years old. 

Prof Birkar’s research has focused on classifying geometrical shapes and describing their building blocks. He says he loves mathematics because it provides a precise way of thinking of a concept, and that there is inner beauty in mathematical structures. As an analogy, he compared it to a flower. Everyone can appreciate a beautiful flower, but scientists will examine the colours of a flower, how it interacts with insects, and how it lives. “The beauty is not visual but abstract.”

Of algebraic geometry, he recognised a link between algebra and geometry. Algebra is the study of equations, while geometry is the study of shapes. The two offer different ways of looking at the same problems. 

Algebraic geometry can be applied in many areas including economics, robotics, and science. One significant application is in computer communications. Elliptic-curve cryptography based on algebraic structure of elliptic curves is used to secure the transmission of messages between computers.  

Prof Birkar was born in the Kurdish region in pre-revolution Iran, one of six children. His parents stressed the importance of education, sending the children to the village school. It was Prof Birkar’s oldest brother Haidar, who introduced him to calculus. Thereafter, he devoured books on mathematics which he borrowed from the local library. 

He was accepted into the University of Tehran to study mathematics. In his final year he travelled to England where he sought and was granted asylum. He joined the University of Nottingham to finish his studies. However, there was no one in that university who specialised in algebraic geometry, the field he hoped to enter. 

In 2002 at a conference in Cambridge, he met Vyacheslav Shokurov, a mathematician at Johns Hopkins University who specialised in birational geometry, a subfield of algebraic geometry. Shokurov advised Prof Birkar to complete his PhD degree and the rest is history.

Prof Birkar is the Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics at Cambridge University.