A French stamp honouring Évariste Galois.

On the morning of May 30th, 1832, a young man stood 25 paces from his friend. Both men fired, but only one pistol was loaded. Évariste Galois, a 20-ye(...)

A spiral has appeared over the past decade or so on the beach between Booterstown station and the Merrion Gates, southeast of Dublin. A sandbank (pictured) has gradually built up, driven by the action of the sea waves, and has assumed a form close to a logarithmic spiral.

We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a spiral staircase. But (...)

Flight plan: the geodesic arcs – one northerly, one southerly – show the shortest routes between Singapore and Quito. They are shorter than the line of the equator between the two points as Earth is not a perfect sphere

Geodesy is the study of Earth’s shape and size, and of variations in its gravitational field. Earth was originally believed to be flat, but many clues(...)

I sometimes tease a certain teenager of my acquaintance when, for example, she looks gloomily into our fridge and asks: “Do we have any, like, food?” 

The inability of most teenagers to complete a sentence without interjecting the work “like” at least once is usually considered a bad habit.  And(...)

Danielle Dutton: Her second novel is a “vibrant rendition of a unique historical figure”. Photograph: Sarah Shatz

With a fondness for fame that would outshine any of today’s X Factor hopefuls, Margaret Lucas Cavendish, duchess of Newcastle-upon-Tyne, took pleasure(...)

Astrology: a tool for interpreting the world? Illustration: Thinkstock

A time traveller from Jesus’s day would be shocked at what has happened to the discipline of astrology. Once ranked as a serious science, it is now a(...)

‘Descartes’ Meditations, Bro’: ‘Sometimes I really do dream crazy s*** like my face is not a face, it is instead a paper cup filled with Jell-O and booze.’

Could I convince you to read Meditations on First Philosophy, a work by René Descartes considered to be the founding text of modern philosophy? What i(...)

The principle of freedom of conscience is as important as majority decision-making. Photograph: Getty Images

The relationship of church and state in education is under renewed scrutiny. Plans to create more diversity in patronage have fallen flat, and prom(...)

if we think of the mind not as an object but as a process, or an emergent state of the brain – in the way that life is an emergent property of a cell or a living organism – then you have much less of a problem in thinking how the mind, or mental states, emerge from brain states.

The nature of the mind has vexed philosophers and scientists for centuries. Though seemingly of esoteric interest, the issue has profound implications(...)