Originally broadcast on BBC Radio 3 in 2011

These four essays under the title ‘Symmetry and the Monster’ open up the world of mathematics, and describe one of the journeys which have preoccupied some of the greatest mathematical brains from the early 19th century to now. It’s a chronological journey, presented by Mark Ronan, Professor of Mathematics at the University of Illinois in Chicago, and Hon. Professor of Mathematics at University College London.

He begins the journey even further back than the 19th century, in the time of the Babylonians, who tussled with the increasing complexity of equations. But the start of a new mathematical era was pioneered by a precocious young French revolutionary Evariste Galois, who was tragically killed in a duel at point-blank range at the age of 20 in 1832. He left a legacy in the form of a letter which described his discovery of ‘group theory’ and that became the building block for future generations.

From France the story moves to Norway in the early 20th century when Sophus Lie became fascinated by Galois’ work, and then on to Germany, to the University of Gottingen. But when the Nazis came to power, the Jewish diaspora of the 30’s stripped Germany of its academic stars, and one of its leading mathematicians Richard Brauer set off for North America and settled in Toronto.

The quest started by Galois became ever more complex, as mathematicians followed a multi-dimensional route into what Mark Ronan describes as ‘atoms of symmetry’. And the fourth and final programme shows how the size and range of the discovery emerged into the appearance of the Monster – which needs 196,883 dimensions to live in. And it is the Monster that seems to connect to other branches of mathematics and physics. As one mathematician has said, “I have a hope that sometime in the 21st century physicists will stumble upon the Monster group, built in some unsuspected way into the structure of the universe.”




One of the great mathematical journeys of discovery is traced by Professor Mark Ronan in a new series of The Essay on BBC R3 called ‘Symmetry and the Monster’. In the first programme he describes the short life of French mathematician Evariste Galois, who was killed in a duel in 1832, shot at point blank range, when he was just 20. On the eve of his death Galois wrote a letter which became his mathematical legacy, taking mathematics on to a new level with the creation of what was to be called ‘group theory’. This was to lead in the following century to the discovery of a mathematical phenomenon which was named the Monster.


The tortuous way mathematical discoveries are handed down through the generations is continued in the second of Professor Mark Ronan’s series of Essays, on Tuesday April 29, under the title ‘Symmetry and the Monster’. The scene moves from Paris in the 1830’s to Norway, France and Germany half a century later, where a mathematician named Sophus Lie (pron – Lee) managed to escape wars and imprisonment, and came up with new mathematical formulas which inspired future mathematicians and physicists, and paved the way for the revelation of the Monster.


The Nazis obliterated many of their country’s finest talents when they forced Jewish academics to flee the country or face murderous consequences. One group of academics who joined the diaspora were mathematicians and in the third of this week’s ‘Essays’ under the title ‘Symmetry and the Monster’, on Wednesday April 30, Professor Mark Ronan shows how the German mathematician Richard Brauer (pron: Brower, as in ‘tower’) continued his mathematical journey in America, a journey which resulted in one of the great mathematical discoveries of our time – the Monster.


Professor Mark Ronan concludes his series of four Essays when he arrives at a phenomenon which has 196,883 dimensions. A mathematical journey which began in Paris in the 1830’s has led a sequence of mathematicians to build on each others’ theorems and discoveries until in the late 20th century a particular phenomenon was identified and named the Monster. As Mark Ronan says, ‘196,883 dimensions is quite a lot of dimensions even for a mathematician’. But the story doesn’t end there, since that mathematical quest has now been linked to string theory and potentially to the understanding of the universe in which we exist.


N.B. Some music & extracts have been edited from the original broadcast version due to copyright restrictions


Prof Mark Ronan


Richard Bannerman/Neil Gardner


Richard Bannerman




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