Math and beauty

Are we blinded by mathematical elegance?

🏛 soc

I recently finished this nice book by Sabine Hossenfelder titled Lost in Math: How Beauty Leads Physics Astray. I first came to know about Hossenfelder through her blog post Do we need a Theory of Everything?, which was a commentary on the latest effort by Stephen Wolfram towards a theory of everything. Her thoughts resonated with me. She summarizes this pretty well in the concluding paragraph of the blog post,

… if you hear something about a newly proposed theory of everything, do not ask whether the math is right. Because many of the people who work on this are really smart and they know their math and it’s probably right. The question you, …, should ask is what reason do we have to think that this particular piece of math has anything to do with reality.

For a theoretical physicist whose career relies on inventing theories of reality, this was quite a pragmatic take. I was impressed. Her book, is then essentially about making this case in detail, through historical context and interviews with contemporaries. The writing is very honest off the bat, no pretense, making for an enjoyable read. The book elaborates on three key themes in theoretical physicals — simplicity, naturalness, and elegance.

On a funny note, Kepler first proposed that planets move around the sun in circles. He later admitted that the theory was wrong — planets do not move in circles, but in ellipses. This better theory was instead rejected because it did not meet the aesthetic standards of the time. Such was the obsession with beauty, he eventually became convinced that the planets play music along their paths, and concluded that “the Earth sings Mi-Fa-Mi”.

While the author acknowledges that it is increasingly challenging to produce groundbreaking work (a theme consistent among physisists over the past decade), corroborated through interviews with eminent physisists, there is a concerned commentary on modern scientific discourse.

In summary, we have more people, better connected than ever, who face increasing pressure to produce in specialized subfields with less financial security over shorter periods. This has made scientific communities an ideal breeeding ground for social phenomena.

For all the rant against the quest to find mathematical beauty in our world models, the authors remains hopeful that the next breakthrough in physics will happen in this century, and slips in a remark, “it will be beautiful”. Highly recommended read!

You can be wrong with math, but you can’t lie, … But it greatly aids obfuscation.

According to Leibniz,

the ugly is ugly because we don’t understand what beauty is.