# Mathematics

### Those magnificent men and their stargazing machines

Where is science bred? Is it where the physical circumstances are right – clear skies for astronomy, for example? Where raw materials are abundant – coal for organic chemistry? Where minds freely meet? Where the enlightened patron rules? Violet Moller’s first book, The Map of Knowledge, examined the spread through the centuries of the ideas of Galen, Euclid and Ptolemy by focusing on seven, mainly Mediterranean cities, from Alexandria to Venice, where scientific knowledge was gathered, augmented and promulgated anew, ensuring the survival of classical learning into the modern period. But why these men and these cities? Are people or places the drivers? Is geography a reliable guide, a storytelling

### Bayes’s Theorem: the mathematical formula that ‘explains the world’

Here’s a profound question about beards: is the number of acrobats with beards the same as the number of bearded people who are acrobats? Go with your gut instinct. It’s not a trick question. If you answer ‘yes’, then you’ve understood the central idea behind Bayes’s theorem. If you’re one of those people who likes to titter about how bad you are at mathematics, stop it. Retake your GCSE, learn how to pin this obviousness down in symbols, and you can produce artificial intelligence, forecast stock market collapses and understand this: P(A|B) = (P(B|A)∙P(A))/(P(B)) This is Bayes’s equation, the formula which, as Tom Chivers insists in this remarkable, bold book,

### We should all embrace the power of games

If both players in a game of draughts stick to their optimal moves, the game will always end in a draw. You or I might have guessed that anecdotally. But being a mathematician, Marcus du Sautoy knows it for sure. The calculations that proved it took 200 desktop computers 18 years to perform. The Prussian High Command used a game called Kriegsspiel to test the abilities of aspiring officers When such a simple game produces such numerical complexity, imagine the fun a mathematician can have with something like Go, the Chinese institution whose number of possible games contains an estimated 300 digits. (The number of atoms in the observable universe

### The improbable genius of John Venn

There aren’t many mathematicians who can claim to have bowled out Australia’s number one batsman. But then John Venn, who died 100 years ago today, was no ordinary scholar. Born in Hull and brought up in Highgate, he was also an Anglican priest – the ninth consecutive one in his family – with a magnificent Victorian beard. He won gardening prizes for his roses and white carrots. He was a keen advocate of women’s rights. And as the founding father of Venn diagrams, still the world’s most beloved tool for representing set-relationships, he can probably boast greater name-recognition than any other modern mathematician.  Next time you’re in Cambridge, pop into Gonville and Caius

### Why is Durham trying to ‘decolonise’ maths?

Is maths racist? That’s the question apparently troubling the department of mathematical sciences at Durham University at the moment. As the Telegraph reports, the department has put out a new guide on ‘decolonisation’, urging maths academics to ensure their teaching is ‘more inclusive’ and not dominated by a Eurocentric view on the world. Of course, exploring the overlooked contribution of non-western thinkers to mathematics would be no bad thing. But this guide goes a fair bit further down the ‘decolonisation’ rabbit hole. It urges academics to introduce more non-white thinkers into their classes, thus presenting their race as more important than their merit or impact. And it urges academics to

### Waiting for Gödel is over: the reclusive genius emerges from the shadows

The 20th-century Austrian mathematician Kurt Gödel did his level best to live in the world as his philosophical hero Gottfried Wilhelm Leibniz imagined it: a place of pre-established harmony, whose patterns are accessible to reason. It’s an optimistic world, and a theological one: a universe presided over by a God who does not play dice. It’s most decidedly not a 20th-century world, but ‘in any case’, as Gödel himself once commented, ‘there is no reason to trust blindly in the spirit of the time’. His fellow mathematician Paul Erdös was appalled: ‘You became a mathematician so that people should study you,’ he complained, ‘not that you should study Leibnitz.’ But

### The insidious attacks on scientific truth

What is truth? You can speak of moral truths and aesthetic truths but I’m not concerned with those here, important as they may be. By truth I shall mean the kind of truth that a commission of inquiry or a jury trial is designed to establish. I hold the view that scientific truth is of this commonsense kind, although the methods of science may depart from common sense and its truths may even offend it. Commissions of inquiry may fail, but we assume a truth lurking there even if we don’t have enough evidence. Juries sometimes get it wrong and falsehoods are often sincerely believed. Scientists too can make mistakes

### How time vanishes: the more we study it, the more protean it seems

Some books elucidate their subject, mapping and sharpening its boundaries. The Clock Mirage, by the mathematician Joseph Mazur, is not one of them. Mazur is out to muddy time’s waters, dismantling the easy opposition between clock time and mental time, between physics and philosophy, between science and feeling. That split made little sense even in 1922, when the philosopher Henri Bergson and the young physicist Albert Einstein (much against his better judgment) went head-to-head at the Société française de philosophie in Paris to discuss the meaning of relativity. (Or that was the idea. Actually they talked at complete cross-purposes.) Einstein won. At the time, there was more novel insight to

### Sadness and scandal: Hinton, by Mark Blacklock, reviewed

In 1886 the British mathematician and schoolmaster Charles Howard Hinton presented himself to the police at Bow Street, London to confess to bigamy. A theorist of the fourth dimension, he had looked destined to forge a career that would align him with the most renowned academic figures of the age. Now, with a conviction, a brief imprisonment, and ‘illegitimate’ twin sons attached to his name, his reputation was ruined. Unable to find employment, he fled with his first family to Japan. Mark Blacklock’s novel tells us what happened next. We initially encounter Hinton at Yokohama harbour where, with his four sons and his first wife, Mary, he is about to

### Coronavirus has made amateur mathematicians of us all

‘What is the point of learning maths? When do you ever actually need it? How does it ever affect your life?’ That’s the frequent complaint of my school-age children, labouring over their times tables and number bonds. It was my complaint as I struggled to tell median from mean, or sine from cosine. Well. Now we have a nation and a world bewitched and terrified in equal measure by a ground-level demonstration of what an exponential function does. Our entire society is being shaped for a generation by that elegant, predictable, horrifyingly steepening curve. One shred of comfort in this catastrophe is the thought that no journalist will ever again