An astrodynamical miracle is happening in the sky above. Our ability to launch a space-probe from the revolving Earth to reach a moving target billions of kilometres away almost ten years later with pinpoint accuracy is truly astounding. “New Horizons” promises to enhance our knowledge of the solar system and it may help us to understand our own planet too.

[See this week’s That’s Maths column (TM071): search for “thatsmaths” at irishtimes.com].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.

### Emmy Noether’s beautiful theorem

Published June 18, 2015 Irish Times Leave a CommentTags: Algebra, Mechanics

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 ]

Continue reading ‘Emmy Noether’s beautiful theorem’### Game Theory & Nash Equilibrium

Published June 11, 2015 Occasional Leave a CommentTags: Algorithms, Applied Maths, Computer Science, Games

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.

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.

### The Tragic Demise of a Beautiful Mind

Published June 4, 2015 Irish Times Leave a CommentTags: Algorithms, Games, Number Theory

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].

**In a nutshell: ** In web maps, geographical coordinates are projected as if the Earth were a perfect sphere. The results are great for general use but not for high-precision applications. Continue reading ‘Maps on the Web’

### Mercator’s Marvellous Map

Published May 21, 2015 Irish Times Leave a CommentTags: Geometry, Geophysics, Spherical Trigonometry

Try to wrap a football in aluminium foil and you will discover that you have to crumple up the foil to make it fit snugly to the ball. In the same way, it is impossible to represent the curved surface of the Earth on a flat plane without some distortion.** ** [See this week’s *That’s Maths* column (TM068): search for “thatsmaths” at irishtimes.com].