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by larryfreeman 1191 days ago
I keep hearing this about abstract mathematics "never" having an impact because it is too abstract and relates to pure mathematics. It's not true. Mathematics is a formal system that provides insights on surprising patterns. Surprising patterns can almost always be applied outside their intended area. And not surprisingly, non-Euclidean geometry and even the inability for mathematics to find certain proofs related to primes has resulted in breakthroughs in other areas. Surprising patterns take time to have effect mostly because they are not generally known until some genius is able to apply them outside their intended area.

I am 99.999% certain that you are wrong to say that "this kind of abstract mathematics will 'never' have any meaningful impact on day-to-day software engineering." I would be less certain if you replaced "never" with "will probably not have a significant impact in the short term".
2 comments
vecter 1190 days ago
I understand that there are sometimes deep connections between seemingly unrelated fields of mathematics. However, are there examples of applications of really pure abstract mathematics in the fields of say, symplectic geometry or differential topology (or any other very abstract fields), that have come to impact the lives of a significant number of software engineers?

Most programmers (myself included) spend their days using IDEs building a new API in a CRUD app or implementing a new UI widget in a mobile app. I may be unimaginative but I have a hard time seeing modular forms, fiber bundles, or exact sequences making a breakthrough in my life and impacting my programming.

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msm_ 1190 days ago
Agreed. That's like hearing about early group theory and disregarding it as abstract nonsense. Turns out it's pretty useful everywhere now, but at the beginning it was not so obvious.

I would also change the statement to "never have a direct impact on programming". Indirectly in 100 years this may lead us to a better understanding of physics (modular forms have some weird hypothetised connections to physics that I don't really understand), which may let us construct better computers, which will obviously have an impact on programming.

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