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From the technology that fuels cell phones to understanding the mechanics behind the flight of a bat, mathematics is deeply embedded in our world, but we often fail to see it. Mathematician Cédric Villani, director of Institut Henri Poincaré, Paris, and 2010 Field's medallist, spoke during the mathematics session at ICTP's 50th Anniversary and put the spotlight on mathematics and the fascinating ways in which it forms the basis of scientific and logical methods.
There is much to learn even from the triangle, one of the basic shapes in geometry, he pointed out. "The study of triangles teaches you to think and organise and make proofs," said Villani. "Sometimes in geometry of triangles you have miracles like four points on a single line, or three lines that come together, and you say, 'Wow! That's amazing!’ but then you learn you can explain these, and that's the whole approach of science, you see things which are like miracles, and then you learn that there is something behind the scene, and the explanation is never less beautiful than the miracle itself," he said.
To underline why knowledge of mathematics is an extremely powerful tool, Villani cited the example of a competition organised by CERN. The Higgs Boson Machine Learning Challenge required participants to find a mathematical method and objectively analyse signals to recognise the signature of the Higgs Boson. Knowledge of mathematics, said Villani, allowed a team of computer science specialists who knew nothing about theoretical physics to attack the problem and perform better than any other team.
"In a way, mathematics can be considered the most personal of all sciences," said Villani, "it teaches you how to find the solution yourself, not just blindly follow your teacher. “At the same time, Villani pointed out that it is also a very social activity. "You have to talk and discuss and be immersed in the environment. You have to go and meet people. It's a human thing, getting into science."
Villani's complete talk is available on the ICTP YouTube Channel.
The video of his interview that followed the talk will be available soon.
