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Spaces of high dimension play a central role in mathematics and its applications. We explore some aspects which completely contradict our intuition. We explore the structure of large convex sets, and we state a fundamental problem which remains a complete mystery.

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MT has made numerous contributions to probability theory and its applications, for which he received the Abel prize in 2024.

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The development of probability theory was originally motivated by problems that arose in the context of gambling or assessing risks. It has now become apparent that a thorough understanding of random phenomena is essential in today's world. For example, random algorithms underpin our weather forecast and large language models. In our quest for miniaturisation, we must consider effects like the random nature of impurities in crystals, thermal fluctuations in electric circuits, and decoherence of quantum computers. Talagrand has tackled many fundamental questions arising at the core of our mathematical description of such phenomena.

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