Here's a question for all of you scientists and mathematicians out there. Given that there is

physical evidence that scientists and mathematicians derive aesthetic pleasure from some equations (Euler's identity e^

*i*π+1=0 often making the top of the list), is it possible that maths-heavy research is affected by a sense of aesthetics? In other words, might researchers be motivated to pursue a path they perceive as 'elegant' over a more messy option? And might this direct research away from potentially important, yet inelegant, findings?

To my mind, the first level of 'beauty' in physical theories is quite simple. The more of the physical world you can explain with fewer axioms, the more elegant the theory is. This view is, I believe, uncontroversial among scientists, but says little about the actual mathematics. I can explain the quite simple elements that make up the axioms of Relativity, but trying to explain to a lay person how the end product, a differential equation using tensors actually works in practice...

Of course a proper physicist is constrained by the evidence of experiments and observations. A theory may have one axiom and be exquisitely simple and elegant...yet explain bugger all.

As for 'messy equations'.... well, for example, we cannot solve exactly the dynamical equations (whether Newtonian, with General Relativity or QM) for systems with three or more bodies. Using our equations they extremely quickly become intractable and a mess when applied to the real world.

I suspect the gut instinct of most scientists and mathematicians would be, 'Don't be silly. We go where the evidence/maths takes us, elegant or otherwise.'

Mixing these two is a bit wrong in my book - physicists need proof of their theories through real world data through experiments, mathematicians are not constrained by this.

I suspect also that, much of the time, this is true. But do you think that a particularly alluring equation might lure you in, even for just a short time? That you might be tempted to turn first to the problem that looks pretty? That you might spend more time wooing it, hoping in vain to find the key to its chest of treasure, and only turn to its ugly stepsister/brother after all of your flirting and cajoling came to naught?

I don't see it this way. A physicist builds a theory (perhaps based on an observation), makes a prediction, finds or observes more data...and if it doesn't fit, then clearly something is wrong, in terms of their theory. A mathematican is looking to prove a theorem (usually) - and it either does or doesn't!

In other words, at the very least could the desire to find an 'elegant' solution delay scientific progress because, in the absence of other clear evidence, people make choices about research based on aesthetics?

I kinda reject the premise of what you've written here, namely the 'absense of other clear evidence'. In that case surely any theorising, no matter how elegant or how messy, gets you nowhere.

The problem is our ability to get the 'right' evidence. New evidence.

Currently General Relativity and Quantum mechanics both explain a great deal of our universe. But we know both are incomplete and both have holes. So we know that we should be trying to puzzle out some sort of Quantum Gravity theory that somehow encompasses both (at least that's our assumption). The issue and problem we have is that to build a theory like this we need to experiment with energies and masses that are way beyond our current means. In essence we really need to be experimenting next to

* real* black holes

. (Or coming up with very, very clever low-energy experiments or hopefully stumble across some observational anomaly that is big enough to show that the existing theories just can't 'cover' the anomaly!)

Unfortunately both established theories have been incredibly successful, it makes it much, much harder to find gaps and anomalies.

I could talk about some examples - String theory or Dark Matter/MOND and all the various issues they represent and have - but I'll leave it there for the moment!

Elegance in this context really applies to the process of solving a problem: clever, novel, efficient steps in reaching a robust conclusion in mathematics, or similar when proving a hypothesis through practical science.

No, this is a very narrow definition of elegance in mathematics or physics. A great many theorems or theories can have quite horrendous levels of calculation after starting with some simple axioms, but will end up with extremely elegant solutions.

the solution as in the example you give, can be beautiful, interesting, and pleasing, but I would argue that it is not in itself elegant.

Balderdash. It's not a solution, it's an Identity. And if you don't think the connection of five of mathematics most fundamental constants is not elegant, then you must live in another universe to me.

Not so much equations, but it really disturbs me how many current theories in science are based on statistics and models, both of which are subject to bias and IMO are little better than "we guessed stuff on a computer".

All theories in science are based on models. And many use statistics which are required to order the data and evidence to see if the model and it's assumptions are justified, surely??? Could you do it another way? We're also squirty, smelly humans - bias is something we are likely to have with us for ever