How the belief in beauty has triggered a crisis in physics
Having studied both pure physics and pure mathematics, my impression is that physicists don&#x27;t really do mathematics, they use a pidgin form of symbolic expression related to mathematics with the specific goal of studying natural systems. And this is a pretty subtle point to explain to anyone who has not experienced both cultures significantly. But the MO of studying systems that can be measured in physical reality, is a constraining principle. Mathematics is not constrained to so-called reality and as a result can fly higher and see farther; it has a better imagination, if you will.<p>Burden me not with any reminders about reality, people needing to get up to make the donuts or whatever. I know all that. I&#x27;m not knocking reality, reality&#x27;s great. Nor do I need reminding how beautiful and strange and wild and cool some of the math in physics really can be. Utterly, utterly rad, without a doubt. But working with such high-dimensional spaces, such high-rank&#x2F;high-variable transformations, and such high-density symbolic representations, as physics seeks to do, requires a much freer and more &quot;artistic&quot; approach than some kind of mental slavery to what can be seen. (By which I mean, what can be measured.) Physicists need more pure math, and when I say pure, I actually prefer the term theoretical math. Because physicists need to design their own math, and that is in one sense what theoretical mathematics means.<p>Physicists are better at what laypeople think of as mathematics--huge whiteboards, filled with esoteric symbols, furrowed brows and chalk-stained hands jittering through the air in some magnificent, halting dance of frustration &amp; eureka. That&#x27;s what people think of when they think of &quot;doing mathematics&quot;. But physicists don&#x27;t really do what mathematicians do, not really, not completely. And all those purely esoteric maths that no one except pure mathematicians ever get to see, say, topology, homology, algebraic geometry, abstract algebra, etc, are hiding some real gems of thought.<p>I&#x27;d like to see Physics, finding itself at a halt, go and start to study all the Mathematics it&#x27;s been putting off.