Alexander Masters

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, ‘explains the world’. Rich mathematics begins by spotting an oddity in the obvious.

There are lots of reasons why non-scientists should be forced to study mathematics, but it’s hard to see why mathematicians should bother with literature. Literature is part of the entertainment industry: emotional manipulation, crippled by cheap assertions and hollow arguments. Maths is intellectual. Maths has rigorous standards. Literature hides guff under its pretty phrases. Hart discusses the statistical challenges for the Oulipo group and their refusal to use the letter ‘e’ in thir clvr novls Sarah Hart, a professor of mathematics, wants us to see literature and mathematics as the ancients did – mutually supportive, central elements of a rounded education.  Once Upon a Prime is an eager, straight-forward book.

The deeper you get into physics, the simpler it becomes. The starting point of this wonderful book about Stephen Hawking’s ‘biggest legacy’ (which no one outside of physics has heard of) is the problem of our insignificance. Make a change in almost any of the slippery, basic physical properties of the universe and we’re toast – life would not be possible. If, for example, the universe had expanded even slightly more slowly than it did after the Big Bang it would have collapsed in on itself. Result? No us. A fraction faster and no galaxies would form, let alone habitable planets. In the incandescent beginning of the universe, each of these basic physical properties was as vacillating as a dream: they could have ended up being pretty much anything.

Helgoland is a craggy German island in the North Sea. Barely bigger than a few fields, it reaches high above the water on precipitous cliffs and is famous for its sweet air. It has a town and a harbour, and the 1,000-odd inhabitants speak a distinct dialect. In the summer of 1925, the 23-year-old physicist Werner Heisenberg went there to sort out his hay fever and solve the problem of reality. Helgoland is a slightly misleading title for Carlo Rovelli’s inspiring, chaotic, delightfully unsatisfactory book of popular quantum physics. It isn’t about Heisenberg’s months there or his mathematical insights; ‘Helgoland’ is Rovelli’s shorthand for Heisenberg’s pellucid state of mind.

The cosiest way to read The End of Everything, Katie Mack’s fast-paced book about universal death, is as a murder mystery. Everything in spacetime, including the reader’s understanding of much of the story, is in the shadows. Black holes, quarks and gluons, Cepheid variables, the Concordance Model? Mere words, strewn across the floor. Believability, restraint and common sense? Left at the door. In the middle of the carpet is our butchered universe. How did it die? Squashed (‘The Big Crunch’)? Boiled (‘Heat Death’)? Eviscerated (‘The Big Rip’)? Burst apart from every pore (‘Vacuum Decay’)? To one side, almost dancing with excitement, is Inspector Mack, a theoretical astro-physicist at Carolina State University.

The advantage of reviewing books by a friend is that you can invite him out for a walk across the South Downs and menace him with blunt questions. Books pages editors call this sort of thing ‘backscratching’ and ‘logrolling’, as if, instead of engaging in proper criticism, you and your mate had spent the time on a sauna holiday in Sweden. But cronyism lets you discover new things about writing, literature and yourself that are inaccessible to the ordinary critic. Cornelius Medvei, whose father lives in Sussex, a few fields away from me, has published three novels. They are fables that are witty, wry and thin (in terms of pages) and nobody except Susan Hill and I reads them.

Physicists have a nerve. I know one (I’ll call him Mark) who berates every religious person he meets, yet honestly thinks there exist parallel universes, exactly like our own, in which we all have two noses. He refuses to give any credit to Old Testament creation myths and of course sneers at the idea of transubstantiation. But, without any sense of shame, he insists in the same breath that humans are made from the fallout of exploded stars; that it is theoretically possible for a person to decompose on one side of a black hole and recompose on the other, and that there are diamonds in the sky the size of the moon.

I’ve got a mathematical problem. Birth of a Theorem is by one of the great geniuses of today, a cosmopolitan, liberal-minded man who helps his wife look after their children, likes big-hearted folk songs, welcomes diversity and wears the same jewellery as I do. But as a contribution to the genre of popular maths, the book stinks. To give the problem extra calculus, my favourite maths writer is a sour-faced white supremacist with a mouth the shape of staple, who thinks women in America should be deprived of the vote and apparently calls himself ‘Derb’.