For 150 years the city of Lvov was part of the Austro-Hungarian Empire. After Polish independence following World War I, research blossomed and between 1920 and 1940 a sparkling constellation of mathematicians flourished in Lvov [see this week’s *That’s Maths* column in *The Irish Times* (TM063, or search for “thatsmaths” at irishtimes.com).

### Café Mathematics in Lvov

Published March 5, 2015 Irish Times Leave a CommentTags: Analysis, History

### The Birth of Functional Analysis

Published February 26, 2015 Occasional Leave a CommentTags: Analysis, History, Set Theory

Stefan Banach (1892–1945) was amongst the most influential mathematicians of the twentieth century and the greatest that Poland has produced. Born in Krakow, he studied in Lvov, graduating in 1914 just before the outbreak of World War I. He returned to Krakow where, by chance, he met another mathematician, Hugo Steinhaus who was already well-known. Together they founded what would, in 1920, become the Polish Mathematical Society.

### MGP: Tracing our Mathematical Ancestry

Published February 19, 2015 Irish Times Leave a CommentTags: History

There is great public interest in genealogy. Many of us live in hope of identifying some illustrious forebear, or enjoy the frisson of having a notorious murderer somewhere in our family tree. Academic genealogies can also be traced: see this week’s *That’s Maths* column in *The Irish Times* (TM062, or search for “thatsmaths” at irishtimes.com).

### 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**

### Perelman’s Theorem: Who Wants to be a Millionaire?

Published February 5, 2015 Irish Times Leave a CommentTags: Topology

This week’s *That’s Maths* column in *The Irish Times* (TM061, or search for “thatsmaths” at irishtimes.com) is about the remarkable mathematician Grisha Perelman and his proof of a one-hundred year old conjecture.

Continue reading ‘Perelman’s Theorem: Who Wants to be a Millionaire?’

### The Steiner Minimal Tree

Published January 29, 2015 Occasional Leave a CommentTags: Algebra, Algorithms, Gauss, Maps, Topology

Steiner’s minimal tree problem is this: **Find the shortest possible network interconnecting a set of points in the Euclidean plane.** If the points are linked directly to each other by straight line segments, we obtain the *minimal spanning tree*. But Steiner’s problem allows for additional points – now called Steiner points – to be added to the network, yielding *Steiner’s minimal tree*. This generally results in a reduction of the overall length of the network.

### Plateau’s Problem and Double Bubbles

Published January 22, 2015 Occasional Leave a CommentTags: Algorithms, Fluid Dynamics, Physics, Topology

Bubbles floating in the air strive to achieve a spherical form. Large bubbles may oscillate widely about this ideal whereas small bubbles quickly achieve their equilibrium shape. The sphere is optimal: it encloses maximum volume for any surface of a given area. This was stated by Archimedes, but he did not have the mathematical techniques required to prove it. It was only in the late 1800s that a formal proof of optimality was completed by Hermann Schwarz [Schwarz, 1884].