Lost in Math?

"the particular work" he is referencing is computational complexity theory; a long-running attempt to mathematically characterize which problems can be efficiently solved with computers and which cannot. I work in complexity theory, and this does make the objects of his criticism obvious to me. I'll try to explain below.

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...

It is possible to be too critical about a magazine article, but it can't be stated enough that the evidence that economists are abusing maths is weak.

Most of the evidence points to the economists abusing assumptions, which is hardly a mathematics problem. Most assumptions can lead to elegant math. The biggest problem in modern economics as practiced is the tacit assumption that because practically all people would like to be able to consume more the system should favour consumers over savers. Which is a logical non-sequitur, so that can't be pinned on mathematics.

They may as well call the modern approach to interest rates the "Global War on Savers". Anyone attempting to save without moving into stocks & other assets will be wiped out long term.

The risk from using maths is irrelevant compared to the damage done by assuming a bad value structure - and there are so many forces influencing the value structure (particularly political ones) that I don't see how mathematical beauty could be a problem for economics as a discipline.

I don't know - pricing options using Black-Scholes uses assumptions (i think normal bell curves) that aren't exactly true and LTCM for instance went under showing that. i think the big difference between economics and physics is that maths is used in finance as 'credibility' and the mortals just assume it's correct because the wizards say it is and crank the dial up to 11 (sub-prime affected a lot of normal people). In physics, the wizards are just talking to other wizards and the mortals don't even enter the discussion (honestly, LHC is cool and all but other than a couple thousand physicists, no-one would notice if it stopped working).

Not recently.

Dirac did believe his equation had to be right as it was so elegant, however it turns out we now interpret it differently now

Although I admittedly only do mathematics through physics, I can't really think of any. If it's oversimplified, it's wrong and therefore not beautiful. Beauty is often given after discovery rather than on the way