$Social media can be a snarky place, with people locked in an endless game of one-upmanship. I am sad to say this behavior can also be seen among scien$

Is mathematics the empress of science? A physicist weighs in.

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2025-01-17 13:30:03

Social media can be a snarky place, with people locked in an endless game of one-upmanship. I am sad to say this behavior can also be seen among science enthusiasts when debating over which discipline is more fundamental. People often take a reductionist view in these arguments, claiming that sociology is merely applied psychology, psychology derives from biology, biology arises from chemistry, and, of course, chemistry is applied physics. As a physicist, I can get behind this way of thinking. To my mind, physics is the queen of sciences.

However, one school of thought goes a step further to dismiss all of science as simply a recursive application of applied mathematics. If physics is the queen of science, then mathematics is the empress. There’s an xkcd comic that humorously illustrates the debate, and some noteworthy physicists have made similar claims.

For example, in 1960 the physicist Eugene Wigner published a paper called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” While his position is often overstated among online combatants, he comments on the uncanny parallels between mathematics and physics, marveling at how well mathematics works. The physicist Max Tegmark has postulated that reality doesn’t just parallel mathematics; rather, reality is mathematics, and all mathematical structures are representations of a variety of realities. In his proposal, the different mathematics describes real universes embedded in a larger multiverse. This proposal is controversial — there is a reason that some in the theoretical community refer to Tegmark as “Mad Max” — but there are certainly some who would argue for the primacy of mathematics over physics.