Jean Leray (1906-98): Master of applied mathematics

Article Abstract:

Jean Leray was born in 1906 and was educated at the Ecole Normale Superieure in Paris. Leray saw mathematics as a tool for modelling, and was inspired by problems im mechanics and physics. His studies of the Navier-Stokes equations were fundamental to fluid dynamics, and his 1934 paper on the Navier-Stokes equations was ahead of its time and remains unsurpassed. He was one of the main sources for the Bourbaki type of mathematics, and his energy estimates for partial differential equations were combined with ideas from algebraic topology.

Obituary, Mathematicians, Bourbaki group, Leray, Jean

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What you eat is how many you are

Article Abstract:

Decision-making can be cast into a mathematical model, and much has been built on the Homo oeconomicus. It is difficult to tell if an observed demand function is compatible with Homo oeconomicus, and solutions to the minimization problems must satisfy the Slutsky relations, a system of nonlinear partial differential equation. The Slutsky relations have been found to fail, but an experiment by M. Browning and P.A. Chiappori based on data from the Canadian Family Expenditure Survey, indicate that the Homo oeconomicus model is correct

Methods, Decision-making, Decision making, Usage, Mathematical models

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Agreeing on strategies

Article Abstract:

Philip J Reny's theorem introduces John F Nash's equilibria in situations where Nash's own result does not. Two examples are the game of timing (noisy duel), and an auction where bidders compete for a single indivisible prize. Nash equilibria are still achieved by brute calculation requiring that the agents have major computational power, or by trial and error, extending over generations. Reny's results significantly improve on Nash's work.

Research, Game theory

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