[throwawaymath]

> About 10 years ago, in the wake of the 2008 financial crisis, the Nobel Laureate economist Paul Krugman made the same point with respect to economics and mathematics in an influential article titled "How Did Economists Get It So Wrong?" His main answer was: mistaking mathematical beauty for truth. "As I see it," wrote Krugman, "the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth."

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.

[roenxi]

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.

[mikorym]

Exactly. Mathematics is the study of which statements follow from which assumptions.

I have difficulty what the term "economics" means, but usually my best intuition is to regard it as modelling of economic phenomena rather than engineering economy from theory.

[neokantian]

> Most of the evidence points to the economists abusing assumptions, which is hardly a mathematics problem.

Agreed. Economics is about the real world. Therefore, it has to be empirical. That means that axiomatically deriving conclusions from assumptions is not legitimate in economics. Still, in the context of empirical knowledge, we have only two usable methods: the scientific or the historical one. Economics cannot be validated by testing experimentally. Hence, economics cannot possibly rest on a sound method. Therefore, economics is fundamentally not a legitimate academic discipline.

[Nasrudith]

There is a difference between non-repeatable in same state and non-scientific. Applying absolute standards of rigor is ironically also unscientific.

We know that hyperinflation is a way to screw over an economy utterly. It can and will fail and in the best case be the equivalent of dissolving the currency and going bankrupt.

The most benign form of it that may not techically count would involve massive growth as well and the devaluation wouldn't be a pathology but a reflection that yes, a well honed spear, flint knives, a badket, and a few carved bone pieces of jewelry may have been respectable wealth for nomadic hunter-gathers but aren't really worth anything compared to even the contents of a jalopy in the great depression.

Just a steel knife or pot would be grand artifacts because they are better in performance than anything else they could find.

That their old currency isn't worth anything is reflective of the fact that past production has been rendered obsolete and the old goods are worth little.

[neokantian]

> There is a difference between non-repeatable in same state and non-scientific.

No, there isn't.

> Applying absolute standards of rigor is ironically also unscientific.

The rules governing science are not determined by science itself. Science experimentally tests propositions about facts. Rules about science are propositions about other propositions. Hence, science has absolutely nothing to say about its own rules. Therefore, propositions about the scientific method are necessarily unscientific.

[jgamman]

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).

[Symmetry]

I think Kurgman was talking about the economics profession rather than the finance profession when he said that. My understanding is that the DSGE models many economics grad students use do have some sophisticated math involved.

[sideshowb]

Maths doesn't have to be complex to be beautiful.

I haven't read the Krugman article cited but the context makes me think of all the stuff around perfect competition and efficient markets, which is beautiful imo. Unfortunately it doesn't describe reality very well.

[vladislav]

Agreed. There's a huge difference between mathematical beauty in theoretical physics and in economics, the latter not really being on the radar in modern math. The author is conflating mathematical beauty with the "fancy math" effect of being able to easily publish papers in fields that aren't very mathematical just by having equations as part of the analysis. It's not like economists have found some amazingly beautiful theory (by modern math standards), they just use math to promote/legitimize their work.

[mikorym]

I agree totally. A lot of people tried to bury the 2008/2009 crisis in philosophy, whereas there is a simple "model" to described what happened: bad debt.

[cma]

> 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.

Not sure if they stick to mundane math, but Renaissance Technologies did pretty well hiring mathematicians and theoretical physicists.