How to be successful as a research mathematician? Follow your gut

The most succinct or abstract is like a normal form, in that many different problems are reduced to one, combining the insights from those different problems, and combining all those researchers to create a larger community.

One effect is like how Latin used to be the language of professionals, so you'd better learn Latin if you want to access the knowledge base.

Watercooler guy has never heard of Mathematical Engineering or Edsger Dijkstra. If he had then he'd know that proof by construction is the method par excellence for showing an algorithm is correct.

The whole tirade on rigorous proofs and colonial mindset puzzles me.

From my understanding (I am European ...), rigorous proofs were increasingly seen as a need because as things like calculus progressed, any loose definition had a tendency to become a minefield. Think of the definition of derivatives, continuity. Also, at a time where things were getting mechanize because we could and it was a gain, it was natural to check if we could somehow mechanize math. After all, Pascal made a machine that could do sums, why not a machine for proofs ?

I don't think 'colonial' is the right word; I think it's more to do with theology and Europe's very twisted (and ongoing) history with it.

A very clear example is S Ramanujan's way of doing mathematics, where proofs were secondary to 'calculate, calculate, calculate, then hypothesize, then maybe prove' approach. This was not a one off thing, nor was his strange approach unique.

Indian traditional mathematics also follows SR's approach of compute & then generalize & then prove (which most working mathematicians actually follow to some degree anyway). India was ahead of much of the world in Math until the cusp of renaissance(finally culminating in the dev. of calculus a good hundred years before Newton, and possibly having traveled to and 'inspired' him with the Jesuit missions), and its outcome's are simply extraordinary.

Of course, the tradition was not given any credit whatsoever due to the prevalent racial-thinking in old-Europe; this now continues because Indologists continue to hold onto their inherited toxic racial thinking and prevent anyone else from touching this subject because 'Hindus are bad/dirty/nazis/ people' (you see this with Yoga, NSDR, Mindfullness,... to this day).

Regardless of all the 'credit allocation' business, and somewhat more importantly, it's actually really sad that this tradition is no longer alive, and is instead replaced with a cheap mimicry of Europe. C K Raju has written extensively on this.

It's also not like this way of doing math. is inherently worse. A lot of actual formal math, starting from the construction of real-numbers is actually very 'unreal' when you get down to it. The kinds of hiccups thrown up by real-numbers in the theory of computation needs to be seen to be believed. Chaitin even has a paper by the title 'How real are real numbers'... We actually get around many of these weird issues because the construction of formal mathematics is actually based on ensuring that discretization is stable (this doesn't work in TOC). Still one also can't deny the strides that modern mathematics has made, in large part built on formalization.

All said, to destroy any existing tradition (even Western) is extremely detestable. OTOH given that it is a jealous-monoculture (all of academia has become one big church-like monoculture at this point), the creation of a new tradition needs active support. I wish people would spend time on the latter instead of pointless race-wars (or DEI non-sense).

(edit: expand)

Well, it just means you're not a minority in the world of mathematics.