Here are talks I have given, or am giving, at various venues: schools, universities, societies …

### The Invention of Numbers and Zero

This goes from the very early use of counting to the marvellous ‘place-value’ system in use today. This system is sometimes credited to the Arabic world over a thousand years ago, sometimes to India and China some two thousand years ago, but was invented by the Sumerians more than four thousand years ago. Only in the 20th century was this fully understood, and the concise nature of their floating-point, base-60 system made it a wonderful vehicle for calculations.

View complete article### Les belles aux bois dormant

This talk, at a History of Mathematics conference on the topic of Symmetry, described the discovery of the ‘sporadic groups’ — exceptional building blocks in the mathematics of symmetry — during the 1960s and 70s

View complete article### The Eurozone Crisis and Wagner’s Ring

This was the topic of a TEDx at UCL. The talk paralleled an article I wrote for *History Today*, July 2012, p.5

### Symmetry and the Monster

This describes the mathematical quest for all the basic building blocks for symmetry, and the people who made it all possible. Starting with the ancient Greeks we move to a young man in early nineteenth century France who used a mathematical interpretation of symmetry to solve a great mathematical problem. From there we move rapidly to the second half of the twentieth century when mathematicians compiled a full list of the basic building blocks for symmetry, including a mysterious new one dubbed The Monster. I have given this talk in many countries on three different continents — here is a sample.

View complete article### The Quest to go beyond Euclid

This describes the history of geometry from Euclid in about 300 BC to Europe in the eighteenth century. Euclid laid down five axioms, and geometers writing in Arabic, and later in Latin, made repeated attempts to show that the axiom on parallel lines was a consequence of the other four. I give a convincing but false proof of this. At the end we see why it is wrong, and how in the eighteenth century three mathematicians independently created a plane geometry where the parallel postulate fails. Here is a sample.

View complete article### The Mayan Calendar

In December 2012 a great cycle in the Mayan calendar came to an end … and nothing happened. Why was the Mayan calendar such a big deal? Why do some people claim it was an extremely ‘accurate’ calendar? And where does its big connection with the number 13 come from?

View complete article### The Modern Calendar

This describes how the modern calendar developed from the old Roman Republican calendar via Julius Caesar’s reforms and later those of Pope Gregory XIII. In the process we find out about the Ancient Egyptian calendar, why Julius Caesar and Pope Gregory made their reforms, how Christians calculated the date of Easter, and why the Eastern Orthodox Church now has different dates of Easter and Christmas.

View complete article### Gilgamesh

The Epic of Gilgamesh the world’s oldest epic. In this talk I outline the story, and draw comparisons with the Biblical narrative in Genesis, and Homer’s Odyssey. I also explain who Gilgamesh was and how the epic developed.

View complete article### The Cuneiform Writing System

Cuneiform developed in Mesopotamia and was used for languages from Babylonian and Sumerian in Mesopotamia to Elamite in Iran and Hittite in Turkey. It is the world’s earliest writing system and this talk explains how it worked, what it developed from, and how it was eventually replaced by the alphabet.

View complete article### Languages of the World

This starts with a quick run through the languages of Europe and the Near East, finding how English fits into a larger scheme that includes ancient languages such as Latin, Greek and Sanskrit. Those languages stem from a common source called Indo-European, and after describing other sources, I illustrate how they disperse by using an intriguing example from the Far East.

View complete article