Weird Maths by David Darling

Author:David Darling
Language: eng
Format: epub
Tags: Maths;Mathematical;Science;Puzzles;Problems;Facts;Prodigy;Infinity;Discovery;Solutions;Mensa;IQ;Fun;Weird;Wonderful;Paradox
Publisher: Oneworld Publications
Published: 2017-12-12T14:05:40+00:00

Countless mathematicians have commented on the enigmatic nature of prime numbers. They’re the simplest of things to describe – so simple that children in elementary school are taught what they are and are often asked to name the first few of them or say whether a number is prime or not. Agnijo himself became fascinated with primes at a very early age and with some of the unsolved problems that surround them. In time, this led to his fascination with other great mysteries of number theory.

Primes are also much like the atoms of the numerical universe, from which all other natural numbers are built. You’d think there’d be every reason to hope and suppose that they obeyed strict laws and that it should be easy to predict where the next one occurred along the number line. Yet, these most elemental of mathematical building blocks are shockingly unruly and capricious in their behaviour. It’s this tension between expectation and reality, and the strong suspicion that some organising principles of great importance lie just beyond our grasp, which has fascinated mathematicians since antiquity.

Looked at individually, or in small groups, the primes do indeed appear lawless. But viewed en masse, like shoals of fish or murmurations of starlings, a previously hidden level of organisation emerges. One of the most curious discoveries about them happened by accident. While sitting listening to a dull lecture in 1963, the Polish mathematician Stanislaw Ulam started doodling on a sheet of paper. He wrote down a square spiral of numbers, starting with 1 in the centre, and gradually working his way outward along a rectangular grid. He then circled all the primes and noticed something surprising. Along certain diagonals of the spiral, as well as some horizontal and vertical alignments, prime numbers were unusually dense. Larger Ulam spirals, produced using computers and containing tens of thousands of numbers, continue to show these patterns. In fact, it seems that they stretch out as far as we care to calculate.

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