Wednesday 4 December 17:30 - 18:30

Lecture theatre 200
City and Guilds Building
Imperial College London, South Kensington Campus

Tickets Unavailable
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Why computers can't replace mathematicians (yet)

Science & Technology

The lecture is free to attend and open to all, but registration is required in advance.

A drinks reception will follow the lecture at 18.30 in City and Guilds building concourse.


In 1900, David Hilbert presented his list of 23 mathematical challenges for the 20th century. Hilbert’s 10th problem asked for what we would now call a computer algorithm to decide whether a given Diophantine equation has integer solutions. Diophantine equations are among the oldest problems in mathematics. In spite of their innocent appearance, and substantial effort over the centuries, these equations remain quite thorny.

Surprisingly, Yuri Matiyasevich proved in 1970 that the algorithm that Hilbert was asking for does not exist. This is a manifestation of the fundamental limits of formal mathematical systems that were discovered by Kurt Gödel in 1931 and further developed by the mathematician and computer pioneer Alan Turing.

Nevertheless, enormous progress had been made in our understanding of Diophantine equations over the last decades. One of the most profound insights of 20th century mathematics are the intimate connections between number theory and geometry: geometric properties of Diophantine equations (the “shapes” defined by these equations) determine their arithmetic properties.

Johannes Nicaise is a Professor of Mathematics at Imperial College London. In his inaugural lecture he will illustrate these connections between number theory and geometry, present the results by Gödel, Turing and Matiyasevich, and outline some important open problems to demonstrate that different branches of mathematics are often intertwined in fascinating ways.


Johannes Nicaise (o1981) is Professor of Mathematics at Imperial College and the University of Leuven (Belgium). His field of research is algebraic geometry, which connects algebra, geometry and number theory and has important interactions with other fields, including theoretical physics. Johannes obtained his Master’s Degree at the University of Leuven in 2001 and his PhD at the University of Leuven and the École Normale Supérieure de Paris in 2004. He has held positions at the Centre National de Recherche Scientifique (CNRS) in France and at the University of Leuven before joining Imperial College in 2015. He was awarded with a Starting Grant of the European Research Council, the 2017 Ferran Sunyer i Balaguer Prize, and visiting Professorships at the Universities of Freiburg and Munich.

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