In the Dark

I did a lecture today about the Dirac Equation (which is almost 100 years old, having been first presented in 1928). You might think this is a difficult topic to lecture on, but it’s really a piece of cake:

This reminds me that a a while ago I posted about an interesting article on the BBC website that discussed the way mathematicians’ brains appear to perceive “beauty”. A (slightly) more technical version of the story can be found here. According to functional magnetic resonance imaging studies, it seems that beautiful equations excite the same sort of brain activity as beautiful music or art.

The question of why we think equations are beautiful is one that has come up a number of times on this blog. I suspect the answer is a slightly different one for theoretical physicists compared with pure mathematicians. Anyway, I thought it might be fun to invite people offer suggestions through the comments box as to the most beautiful equation along with a brief description of why.

I should set the ball rolling myself, and I will do so with the Dirac Equation:

This equation is certainly the most beautiful thing I’ve ever come across in theoretical physics, though I don’t find it easy to articulate precisely why. I think it’s partly because it is such a wonderfully compact fusion of two historic achievements in physics – special relativity and quantum mechanics – but also partly because of the great leaps of the imagination that were needed along the journey to derive it and my consequent admiration for the intellectual struggle involved. I feel it is therefore as much an emotional response to the achievement of another human being – such as one feels when hearing great music or looking at great art – as it is a rational response to the mathematical structure involved. But it’s not just that, of course. The Dirac Equation paved the way to many further developments in particle physics. It seems to encapsulate so much about the behaviour of elementary particles in so few symbols. Some of its beauty derives from its compactness- it uses up less chalk in a mathematical physics lecture.

Anyway, feel free to suggest formulae or equations, preferably with a brief explanation of why you think they’re so beautiful.

P.S. Paul Dirac was my (academic) great-grandfather.

This entry was posted on February 25, 2025 at 3:35 pm and is filed under Biographical, mathematics, The Universe and Stuff with tags Beauty, Dirac equation, mathematics, Particle Physics, Paul Dirac. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.