There are numerous branches of mathematics, from arithmetic, geometry and algebra at an elementary level to more advanced fields like number theory, topology and complex analysis. Each branch has its own distinct set of axioms, or fundamental assumptions, from which theorems are derived by logical processes. While each branch has its own flavour, character and methods, there are also strong overlaps and interdependencies. Several attempts have been made to construct a grand unified theory that embraces the entire field of maths [TM220 or search for “thatsmaths” at irishtimes.com].

## Posts Tagged 'Group Theory'

### A Grand Unification of Mathematics

Published October 7, 2021 Irish Times Leave a CommentTags: Algebra, Analysis, Group Theory, Number Theory

### John Horton Conway: a Charismatic Genius

Published April 23, 2020 Occasional Leave a CommentTags: Games, Group Theory, Number Theory, Recreational Maths, Topology

John Horton Conway was a charismatic character, something of a performer, always entertaining his fellow-mathematicians with clever magic tricks, memory feats and brilliant mathematics. A Liverpudlian, interested from early childhood in mathematics, he studied at Gonville & Caius College in Cambridge, earning a BA in 1959. He obtained his PhD five years later, after which he was appointed Lecturer in Pure Mathematics.

In 1986, Conway moved to Princeton University, where he was Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics. He was awarded numerous honours during his career. Conway enjoyed emeritus status from 2013 until his death just two weeks ago on 11 April.

### The Brief and Tragic Life of Évariste Galois

Published August 15, 2019 Irish Times Leave a CommentTags: Algebra, Group Theory, History

On the morning of 30 May 1832 a young man stood twenty-five paces from his friend. Both men fired, but only one pistol was loaded. Évariste Galois, a twenty year old mathematical genius, fell to the ground. The cause of Galois’s death is veiled in mystery and speculation. Whether both men loved the same woman or had irreconcilable political differences is unclear. But Galois was abandoned, mortally wounded, on the duelling ground at Gentilly, just south of Paris. By noon the next day he was dead [TM169 or search for “Galois” at irishtimes.com].

Continue reading ‘The Brief and Tragic Life of Évariste Galois’

### Motifs: Molecules of Music

Published May 31, 2018 Occasional Leave a CommentTags: Group Theory, Music

*Motif*: A short musical unit, usually just few notes, used again and again.

A recurrent short phrase that is developed in the course of a composition.

A motif in music is a small group of notes encapsulating an idea or theme. It often contains the essence of the composition. For example, the opening four notes of Beethoven’s Fifth Symphony express a musical idea that is repeated throughout the symphony.

“It is difficult to imagine modern mathematics without the concept of a Lie group.” (Ioan James, 2002).

Sophus Lie grew up in the town of Moss, south of Oslo. He was a powerful man, tall and strong with a booming voice and imposing presence. He was an accomplished sportsman, most notably in gymnastics. It was no hardship for Lie to walk the 60 km from Oslo to Moss at the weekend to visit his parents. At school, Lie was a good all-rounder, though his mathematics teacher, Ludvig Sylow, a pioneer of group theory, did not suspect his great potential or anticipate his remarkable achievements in that field.

### The Klein 4-Group

Published February 12, 2015 Occasional Leave a CommentTags: Algebra, Group Theory

What is the common factor linking book-flips, solitaire, twelve-tone music and the solution of quartic equations? Answer: .

**Symmetries of a Book — or a Brick**

### The Langlands Program

Published March 13, 2014 Occasional Leave a CommentTags: Algebra, Analysis, Arithmetic, Group Theory, Number Theory

An ambitious programme to unify disparate areas of mathematics was set out some fifty years ago by Robert Langlands of the Institute for Advanced Study in Princeton. The “Langlands Program” (LP) is a set of deep conjectures that attempt to build bridges between certain algebraic and analytical objects.

### Speed Cubing & Group Theory

Published February 13, 2014 Irish Times Leave a CommentTags: Algebra, Algorithms, Group Theory, Puzzles

The article in this week’s *That’s Maths* column in the* Irish Times* ( TM038 ) is about Rubik’s Cube and the Group Theory that underlies its solution.

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