Fractals, such as this stack of spheres created using 3-D modeling software, are one of the mathematical structures that were invented for abstract reasons yet manage to capture reality. Image: Illustration by Tom Beddard
- The deepest mysteries are often the things we take for granted. Most people never think twice about the fact that scientists use mathematics to describe and explain the world. But why should that be the case?
- Math concepts developed for purely abstract reasons turn out to explain real phenomena. Their utility, as physicist Eugene Wigner once wrote, “is a wonderful gift which we neither understand nor deserve.”
- Part of the puzzle is the question of whether mathematics is an invention (a creation of the human mind) or a discovery (something that exists independently of us). The author suggests it is both.
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Most of us take it for granted that math works—that scientists can devise formulas to describe subatomic events or that engineers can calculate paths for spacecraft. We accept the view, initially espoused by Galileo, that mathematics is the language of science and expect that its grammar explains experimental results and even predicts novel phenomena. The power of mathematics, though, is nothing short of astonishing. Consider, for example, Scottish physicist James Clerk Maxwell’s famed equations: not only do these four expressions summarize all that was known of electromagnetism in the 1860s, they also anticipated the existence of radio waves two decades before German physicist Heinrich Hertz detected them. Very few languages are as effective, able to articulate volumes’ worth of material so succinctly and with such precision. Albert Einstein pondered, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?”
As a working theoretical astrophysicist, I encounter the seemingly “unreasonable effectiveness of mathematics,” as Nobel laureate physicist Eugene Wigner called it in 1960, in every step of my job. Whether I am struggling to understand which progenitor systems produce the stellar explosions known as type Ia supernovae or calculating the fate of Earth when our sun ultimately becomes a red giant, the tools I use and the models I develop are mathematical. The uncanny way that math captures the natural world has fascinated me throughout my career, and about 10 years ago I resolved to look into the issue more deeply.
This article was originally published with the title Why Math Works.