[plurinshael]

Having studied both pure physics and pure mathematics, my impression is that physicists don'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.

Burden me not with any reminders about reality, people needing to get up to make the donuts or whatever. I know all that. I'm not knocking reality, reality'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/high-variable transformations, and such high-density symbolic representations, as physics seeks to do, requires a much freer and more "artistic" 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.

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 & eureka. That's what people think of when they think of "doing mathematics". But physicists don'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.

I'd like to see Physics, finding itself at a halt, go and start to study all the Mathematics it's been putting off.

[vladTheInhaler]

I'm pretty sure guys like Ed Witten are doing real math. Or at least he fooled the mathematicians thoroughly enough that they gave him a fields medal. I'm neither a physicist nor a mathematician, but your characterization seems a bit unfair.

[acqq]

> I'd like to see Physics, finding itself at a halt, go and start to study all the Mathematics it's been putting off.

And that kind of approach is exactly what Sabine Hossenfelder in the article criticizes, I my opinion significantly unfairly. The critics (she is surely not the only one) exactly complain that, for example, the "string theory" is more math than physics because it can't be "immediately verified" or they complain that the most of the experiments are "not confirming" the most obvious variants of the expected results of the new theory candidates. But the science shouldn't be reduced to the short-term goals and only to the processes which are "guaranteed to work." That's exactly when we won't see further from our noses.

And if the critics say that the "alternative theories" don't get enough funding, I posit that the average "alternative theories" are typically even more conservative than what is widely accepted physics (by the virtue of the accepted physics being already "unintuitive" enough and having the steeper learning curve than practically all "alternatives" are ready to accept).

We should all appreciate that one the most impressive achievements of the 20th century physics, the General Theory of Relativity has its fundamental support in the famous Michelson-Morley experiments which also didn't confirm the expectations of the 19th century physicists.

So we have to achieve enough experimental results against some approaches, and more than that, with enough precision, to even have the chance of finding out the new rules, if the new rules in the form that we're used to find them even could be found. We must be open to the experiments, and be happy even when the "most hoped" results don't happen.

On another side, when Sabine Hossenfelder is more precise and when she addresses some specific aspects, I can surely agree with some of her statements, for example:

"The criticism of heliocentrism based on the argument that the absence of observable parallax implied the stars had to be “unnaturally” far away was wrong for exactly this reason: They had no probability distribution but erroneously postulated one by assuming that the stars should be likely to have similar distances to the planets as the planets have among each other. We now understand the distribution of stars and their typical distances comes about dynamically during structure formation and that there is nothing “unnatural” about the distance of our Sun to the other suns."

Her criticism, however, is that currently physicists are "looking for the lost keys under the street lamp" because "in the dark they can't see them." But even if it sounds funny or misguided, it is true that in the dark not much could be seen, and before we actually check the already properly lit areas we can't expect more from looking into the dark where we really see too little. Investing in the flashlights can be reasonable, but also only once the lit areas are actually checked.

And we should also not forget that the current physics already enlightened immense parts of the universe. The "dark areas" were never so amazingly small as they are now.