[maweki]

There's a line between the discovered stuff and the invented stuff. I always love to see it spelled out in different ways.

I tell my students that you can understand And rediscover the science part by understanding basic principles, by applying mathematical logic.

While the engineering part you need to learn, as the engineering decisions are full of conventions and constraints of the time of invention and the people inventing.

But understanding the science and knowing roughly the constraints gets you very far. There are usually only a few superficialities left, like concrete syntax, that are basically impossible to "understand" and need to be "learned".

[bjornsing]

Is there? When it comes to math and abstract concepts such as these I can see no such line. To me it seems e.g. the real numbers were invented about as much as they were discovered. Same goes for the semaphore.

(Of course the exact syntax and semantics of let’s say semaphores in POSIX belong to a different category. But I’m not sure I’d want to call it an “invention”.)

[vanderZwan]

Well, the examples so do fall more under the abstractly provable side of things when it comes to their behavior.

But take the Sieve algorithm that was posted yesterday[0], or Powersort[1] (Timsort with its bugs fixed). To some degree those are more engineering discoveries about which algorithm behaves best with real-world data. Although Powersort actually involves a lot of formal maths to prove it does not have degenerate edge-cases, so maybe I should have stuck with Timsort.

[0] https://news.ycombinator.com/item?id=38850202

[1] https://www.wild-inter.net/publications/munro-wild-2018

[twoodfin]

This is a much-debated question in the philosophy of mathematics.

One of the stronger arguments that the real numbers were discovered, rather than invented, is their “unreasonable effectiveness” in aiding our exploration and understanding of the physical world.

The same can’t be said for equally abstract but clearly invented concepts such as the rules of chess.

[vlovich123]

I think it’s a mixture of both, but using its ability to explore the physical world as the benchmark seems myopic because math can be used to describe universes other than our own. Our universe just happens to be the one we focus on because that part of mathematics is particularly interesting, but if anything it means the structures we put in place to manage that aspect are invented not discovered.