Thread by @krzhang

Thread to explain why Conway gets no recognition.

Thesis: what is considered "important" in pure mathematics is purely a social construct. Corollary: why Conway doesn't get recognition from mathematicians.

Now that I have triggered some, I'll explain. 1/

https://twitter.com/grahamfarmelo/status/1252304939428216833

First, pure mathematicians are not (usually) conspiring to make pyramid schemes -- in fact, most of them are good-hearted people earnestly trying to ask themselves fundamental questions. However, this does not mean they're immune to groupthink and idea-incest. 2/

Second, pure math fundamentally lacks "skin in the game" in form of a relationship with the real world (and as we often see from physics or statistics, even those fields entangled with the real world can fail spectacularly when the incentive structures aren't well-designed). 3/

Third, pure math has a very high barrier to entry, and thus lacks critics who are knowledgeable enough to say something interesting. This means most criticism must come from its own practitioners, which creates incest.

Now, let's see what happens when we mix these three. 4/

First, a field gains initial success, solving 90% of the fundamental questions (that are often quite "easy" technically).

Then, they become pyramid schemes (often, but not always, with no sociopathic figurehead), this is self-justified since you need new Ph D. students. 5/

Finally, the language and *taste* calcifies. Now there's an idea of what math is "good" or "cool." These aren't testable or objective. They can't be. These are organic social constructs. 6/

In short, when wise people say "math is a social construct," they don't mean the *veracity* of math. They're talking about the *importance*.

Here is where Conway falters (for his colleagues) and delights (for everyone else):

Conway did any mathematics he thought interesting. 7/

By doing this, he is showing irreverance for the social norms other mathematicians have created as "important." As all of us know, when you act as if you don't care about what others seem "cool," you become "uncool." And that's exactly what happened with (some) mathematicians. 8/

They know he has technical chops and is an excellent problem solver *and* theory builder. But he's doing those things with games, pictures, weird number sequences. He's not doing those things with cohomology, sheaves, derived functors. 9/

They aren't necessarily even jealous; they're just confused. "Why isn't someone who is *able* to do these things doing them? Why is he wasting time?" 10/

Sometimes they will (again, with completely good intentions) tell Conway and/or people like him "you know, with your talents you can probably do some pretty important work." (I myself have gotten these comments, while doing "unimportant" work like consulting or blockchain) 11/

So when Conway does his (amazing) work, he's really doing it as a "people's mathematician." He's doing what *he* sees as fun and important, which makes it a more "vulgar" form of mathematics. For professional mathematicians trained on "classy" mathematics, their taste buds.. 12/

have also been trained (from their socially-constructed groups) to see "vulgar" math as less important, much in the way that a 90's classical TV critic may judge South Park or the Simpsons as "mainstream trash," or, as something deeply close to my heart, people saying that 13/

.. "videogames cannot be art." When they play videogames, their brain is *trained* to tell them that this is *supposed* to be bad, because "respectable" people are not playings games but are reading books, or so they think.

We mathematicians are no different.

RIP. 14/14

Addendum #1:

Nuance is hard. I mean "(elite) mathematicians don't recognize Conway's work as real." I don't mean that the mathematical community doesn't recognize him; he is obviously (to everyone, mathematicians or not) a genius and popular.

Addendum #2:

https://twitter.com/AlexKontorovich/status/1252600554376871938