I didn’t find math particularly exciting when I was in high school. To be honest, I only studied it when I went to university because it initially seemed quite easy to me. But in my very first math lecture as an undergraduate, I realized that everything I thought I knew about math was wrong. It was anything but easy. Mathematics, I soon discovered, can be really exciting—especially if you go beyond the realm of pure arithmetic.
In physics, the truly surprising content—concepts that go against your intuition about the universe—emerges around high school, when students can glimpse the strange quantum world and encounter Einstein’s general and special theories of relativity. School mathematics cannot keep up with these wonders. You learn elementary arithmetic operations, integration and derivation, the basic handling of probabilities and vectors. If you’re lucky, ambitious teachers might show you a simple proof. And that’s it. So it’s no wonder that many pupils fail to develop a real passion for the subject.
Yet mathematics offers all sorts of surprises, such as the Banach-Tarski paradox, which states that you can double a sphere almost magically, or the fact that there are infinitely many different infinities. What really blew me away was discovering how deeply mathematics is interwoven with the strangest physical phenomena. It’s not necessarily quantum physics itself that gives rise to the incredible effects; no, the systems always follow the strict rules of mathematics. As chemist Peter Atkins put it in his 2003 book Galileo’s Finger, “Determining where mathematics ends and science begins is as difficult, and as pointless, as mapping the edge of a morning mist.”
Few examples illustrate the mixing of math and physics better than a discovery made by physicist Michael Berry. In 1984 Berry revealed a profound and largely unexpected geometric side to quantum mechanics. This geometry, Berry realized, gives quantum particles a kind of memory.
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