Archive for June, 2015

Increasingly Abstract Algebra

In the seventeenth century, the algebraic approach to geometry proved to be enormously fruitful. When René Descartes (1596-1650) developed coordinate geometry, the study of equations (algebra) and shapes (geometry) became inextricably interlinked. The move towards greater abstraction can make mathematics appear more abstruse and impenetrable, but it brings greater clarity and power, and can lead to surprising unifications.

Evariste Galois, Sophus Lie and Emmy Noether.

Evariste Galois, Sophus Lie and Emmy Noether.

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Emmy Noether’s beautiful theorem

The number of women who have excelled in mathematics is lamentably small. Many reasons may be given, foremost being that the rules of society well into the twentieth century debarred women from any leading role in mathematics and indeed in science. But a handful of women broke through the gender barrier and made major contributions. [TM070: search for “thatsmaths” at irishtimes.com ]

Death of the philosopher Hypatia, by Louis Figuier [Wikimedia Commons].

Death of the philosopher Hypatia, by Louis Figuier
[Wikimedia Commons].

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Game Theory & Nash Equilibrium

Game theory deals with mathematical models of situations involving conflict, cooperation and competition. Such situations are central in the social and behavioural sciences. Game Theory is a framework for making rational decisions in many fields: economics, political science, psychology, computer science and biology. It is also used in industry, for decisions on manufacturing, distribution, consumption, pricing, salaries, etc.

Theory of games and economic behavior. Centre: John von Neumann. Right: Oskar Morgenstern.

Theory of Games and Economic Behavior.
Centre: John von Neumann. Right: Oskar Morgenstern.

During the Cold War, Game Theory was the basis for many decisions concerning nuclear strategy that affected the well-being of the entire human race.

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The Tragic Demise of a Beautiful Mind

John Nash, who was the subject of the book and film A Beautiful Mind, won the Abel Prize recently. But his journey home from the award ceremony in Norway ended in tragedy [see this week’s That’s Maths column (TM069): search for “thatsmaths” at irishtimes.com].

Russell Crowe as John Nash in the movie A Beautiful Mind.

Russell Crowe as John Nash in the movie A Beautiful Mind.

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