All of that predates this post; it's a mature field of math he's swiping at. He's a shitposter and this one isn't even informative.
He's got a few nuggets in there about finitism that are illuminatory. And on one hand, an engineer's, a programmer's, mindset doesn't need what can't be stored on a world-scale computer. But, such talk makes few friends in math.
I upvoted. I'm always interested in dispatches from mathematics, and you can learn a lot about both the practices and culture of a group by reading between the lines of their sarcasm.
> Myself, I don't know either languages [topology and physics]. Nevertheless, I am almost sure that...
So, he doesn't know topology and then proceeds to call topology (or some of it?) "soon to be trivialised".
> The king (abstract math) is dead. Long live the King (Concrete Mathematics).
The two complement each other. I don't think there ever has been a sensible fight other than the fight against ignorance and arrogance and the fight that is specific in it's subject matter. Category Theory and other abstract fields I would think get resistance at the time of introduction; concrete mathematics get resistance much after the fact for its specificity. In both cases one should be careful to either put on a pedestal or throw down the drain.
He's a combinatorist. He's trolling mathematicians who are specialized in more abstract fields who often hold views of contempt for computational, concrete fields like combinatorics. One of the main themes of modern mathematics is the use of algebraic, numerical, and combinatoric invariants to characterize abstract mathematical objects such as spaces. Doron is dishing out their own medicine in this post.
Whereas the are such contemptuous people it is just as bad to have the converse. In my experience the median number theorist is like today's physicists in that they are
resisting consolidation in favour of elaborateness.
Traditionally, category theory was treated with much disdain especially by concrete mathematicians. The fact that hipsters now think category theory is cooler than combinatorics doesn't in my opinion warrant swaying again the other way—any kind of evangelisation is inherently fraught with personal agendas.
It could be that the specific examples that he gave are really justified. But I don't really see the point of being a warrior for concrete mathematics or being a warrior for abstract mathematics. I don't even see the two as different fields rather different processes. And as I said earlier, I have found combinatorialists to be more contemptuous than category theorists, hipsters aside.