I appreciate the point the article is trying to make, but I think this example is shoehorned in. You can misuse math without it being because you're "seduced by the beauty" of it.

I do agree with the author's example in physics. I have seen a lot of beautiful math in physics; look at lie algebras, monstrous moonshine and representation theory. Quite a bit of modern physics PhD dissertations are actually just math dissertations, and the same holds for a significant amount of new research in the field.

On the other hand I haven't seen that in finance. Highly exotic (read: "beautiful") mathematics is extremely rarely used in financial engineering. Pricing derivatives is decidedly mundane work compared to the brain-meltingly abstract mathematics deployed in high energy particle physics research. That's not to say it isn't difficult - it is difficult! But difficulty is better described by the word "complex" rather than "beautiful", and then of course financial engineering is complex. Then we should be talking about how getting mired in complexity can be bad for accountability and transparency.

This is a different thesis than the one presented by the author. Being led astray because you've built extremely brittle financial products using layers of complicated math is not the same as being more preoccupied with the elegance of a grand unifying theory than its agreement with reality.

But hey, maybe I'm just being pedantic. You can misuse mathematics in a lot of ways.

I've personally been getting a lot of satisfaction from learning Haskell and seeing how the functional programming community is taking ideas from abstract mathematics, like category theory, and is turning them into practical ways of thinking about programming.

I appreciate the effort to extend the story into CS, but I wonder if you have to be familiar with the particular work he's alluding to. The charge (as leveled against theoretical physics) is not that some people do pure mathematical work for the sake of beauty. The charge is that people who are supposed to be applying mathematics to reality are instead prioritizing mathematics and neglecting reality. To extend the analogy to CS, he must be talking about researchers supposedly trying to model real systems but instead just chasing beautiful math, but he isn't specific. Is it obvious to people in the know who or what he's talking about?

For practical programmers, I think the problem is the reverse of being "lost in math." Practical programmers use extremely general theoretical results because they don't want to do math, not because the math is more beautiful. If they applied the information they know about their particular problem, they could get more useful mathematical results, but since they want to stay as far away from (doing) theory as possible, they use whatever facts they remember from class, which are ironically the most purely theoretical ideas because those are the simplest and easiest to remember.

In the FP communities, I do sometimes see people overoptimize for TCO. Your datastructure is never going to be more than 10-100 deep. Don't worry about it. Just write the most legible recursive algorithm, not the most performant.

Her criticism has gotten more attention than justified by its merits. No one has argued that beauty holds precedent over truth

I feel the other way around: Applied mathematicians and physicists led the pure mathematicians astray. But I say this for a different reason. I feel that physics has become convoluted with a plethora of theories where this same beauty is interpreted wildly differently by different people. In other words, people all have different ways of thinking, different notions of beauty, and ultimately, this manifests into different (competing) notions in physics. These may even be equivalent notions and they may embody the desired perspective on beauty, but instead of consolidation there is extended differentiation.

My point is that physics has become ugly exactly because of physicists' ignorance towards mathematical elegance in favour of personal beauty. I don't think physics can become consolidated without exactly a stark appreciation for elegance.

IMO this is why category theory took so long to start appearing in physics: The physicists are caught up in their own idea of beauty rather than the mathematical tradition of finding the minimal sufficient proofs and theories (which I call elegance).

Regardless, you only can become lost in math if you have bad premises. Mathematics is a relative subject, abstracting the arbitrary of reality to axioms. And if the axioms do not hold, the theory is bunk. It will always be the case that more granularity is required in real-life situations. Mathematics is precise and sound; it's not gospel.

Ironic that intelligent mathematics types get caught up in what could be analogous to socially hurtful stereotypes.

I am going to follow the author.

Think of "problems" as abstract primitives: sorting, search, graph operations, optimization, etc. To give a concrete example, let's take a particular search problem: boolean satisfiability (SAT). The input is boolean formulas, and the output is "an assignment to the variables of this formula that make it TRUE."

Some problems are "NP-complete". The definition of NP isn't important for our discussion here. What is important is that NP-completeness or lack thereof is indeed a "beautiful" way to classify problems. Further, we expect NP-complete problems to be impossible to solve efficiently on every input. This is what the article means by "worst-case" or "overly pessimistic" theories.

SAT is NP-complete, so "classical complexity" would predict that SAT cannot be efficiently solved with computers. But often, SAT can be solved efficiently "in practice" using simple heuristics. So Moshe would say that classical complexity is simply wrong; it doesn't describe the "real-world" behavior of actually trying to solve SAT. While difficult-to-process formulas may exist, we "just happen" to only encounter easy-to-process formulas.

So, to summarize: the article criticizes researchers who focus only on worst-case complexity. While the theory is beautiful, we can point to many problems for which it does not accurately predict performance.

I think this criticism is a little strange, because most complexity theorists also work on "average-case" complexity; the study of when "typical" inputs are difficult vs easy to solve. This is mentioned at the very end of the article. Any working complexity theorist would immediately list these problems with worst-case complexity, and explain that it is an imperfect and primitive theory compared to how we would really want to understand when and how these problems are difficult. There is a great deal of work trying to understand what about each formula makes it difficult or easy to process, and why.

The issue is, we are nowhere near understanding even worst-case complexity. So theoretical research often toggles back and forth between the two settings, trying to make progress overall.

Computational complexity theory is a fundamental mathematical field that will only occasionally produce enough understanding to impact practice. For an example, see:

https://www.youtube.com/watch?v=FGtsqEwANWY&feature=youtu.be...

> In most cases, however, physicists are not aware they use arguments from beauty to begin with (hence the book’s title). I have such discussions on a daily basis.

> Physicists wrap appeals to beauty into statements like “this just can’t be the last word,” “intuition tells me,” or “this screams for an explanation”. They have forgotten that naturalness is an argument from beauty and can’t recall, or never looked at, the motivation for axions or gauge coupling unification. They will express their obsessions with numerical coincidences by saying “it’s curious” or “it is suggestive,” often followed by “Don’t you agree?”.

[…]

> What physicists are naive about is not appeals to beauty; what they are naive about is their own rationality. They cannot fathom the possibility that their scientific judgement is influenced by cognitive biases and social trends in scientific communities. They believe it does not matter for their interests how their research is presented in the media.

Have you read the book or any of her posts about the ideas in the book? There are in fact a lot of people who do claim that research programs and research dollars should be prioritized because of ideas like naturalness or beauty, even when decades of increasingly expensive and time-consuming work has led to no support for the natural or beautiful hypothesis.

[1] http://backreaction.blogspot.com/2019/02/a-philosopher-of-sc...

Here's Paul Dirac, writing in 1963:

"it is more important to have beauty in one’s equations than to have them fit experiment. [...] It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress."

Here's John Schwarz, one of the pioneers of string theory, explaining why he and a collaborator kept working on it in the early 1970s after quantum chromodynamics turned out to be a better way of dealing with the strong nuclear force and before it emerged as a promising approach to quantum gravity:

"We felt strongly that string theory was too beautiful a mathematical structure to be completely irrelevant to nature."

The idea that string theory is "so beautiful it must be right" is, I think, mostly a strawman -- you hear critics of string theory taking it down, rather than advocates of string theory talking it up -- but the idea that beauty is a reliable guide to truth in physics isn't so strawy.