Explaining the unreasonable effectiveness of the natural sciences in mathematicsby Marcus Chown / September 1, 2019 / Leave a comment
Galileo was one of the first to realise a profound truth about the Universe: mathematics expresses perfectly the behaviour of the physical world. “Philosophy is written in the grand book (I mean the Universe) which stands continually open to our gaze,” he wrote. “But it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. This book is written in the language of mathematics, and its characters are triangles, circles and other geometrical figures, without which it is humanly impossible to understand a single word of it.”
Since the 17th century, mathematics has time and time again demonstrated that Galileo was right—it is indeed the unique language of the Universe. Among its spectacular successes have been the predictions of the existence of radio waves, black holes, antimatter, the Higgs boson and gravitational waves. In 1960, the Austrian physicist Eugene Wigner articulated what many had been thinking since the time of Galileo when he remarked on “the unreasonable effectiveness of mathematics in the natural sciences.”
So why is mathematics so effective in distilling the essence of the world? How is it possible that someone sitting at a desk can write down an arcane mathematical formula that predicts the existence of something previously unsuspected—something that people later discover actually exists in the real world? To put it more bluntly: why does the Universe have a mathematical twin that appears to mimic it in every way? “The astonishing effectiveness of mathematics in physics has enthralled me since I was a schoolboy,” says the former scientist and science writer Graham Farmelo. And now it has prompted him to explore the connection in his book The Universe Speaks in Numbers.
Perhaps the most striking example of mathematics predicting things in the real world was provided by the British physicist Paul Dirac, the subject of Farmelo’s bestselling biography The Strangest Man (2009). The thought processes of most great physicists are essentially like those of normal people (though souped-up). They seek everyday mechanical analogues of the Universe, which they can then describe mathematically.
Famously, this was the method of James Clerk Maxwell, a Scot who in the 1860s created a model of…