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Maybe. As a parallel, I know C# and F#. They are programming languages. They are built on top of Microsoft products like the JIT and more basically Assembly lan

Maybe. As a parallel, I know C# and F#. They are programming languages. They are built on top of Microsoft products like the JIT and more basically Assembly language. I have no idea how assembly works - in my years of experience I’ve never had an issue that required I dig that deep into it. Does that mean I can’t be effective with higher-level tooling because I do not know the absolute basics?

munificent 11d ago
The entire point of a programming language design is to give you an abstracted environment with a complete coherent semantics so that you don't need to understand what's going on under the hood. You can be effective at using C# and F# to solve other problems specifically because they are very well designed at the goal of abstracting over the lower level hardware. But if your goal is to build an intuition of how programming languages themselves are implemented and how computer hardware works, then, using those languages will be counter productive. If you're trying to use math to solve arithmetical problems, then by all means using AI to help. But if you're trying to advance the math field itself, then actually knowing how math works is probably essential. Put in more concrete terms: if someone wants to be a working mathematician without learning the fundamentals of math, then how do they even know what prompts to the AI are worth writing? In what way are they adding any value to the process at all?
- qubex 11d ago
  I never said one should not know the fundamentals of mathematics, I was trying to express it’s a damned lot easier when once understood you can delegate the lesser aspects to machinery. Abacus, calculator, computer, CAS, now AI: the mathematician’s understanding and intuition are still fundamental, but the instruments they can rely upon are levelling the playing field (and indeed, it is a great field in which to play).

munificent 11d ago

The entire point of a programming language design is to give you an abstracted environment with a complete coherent semantics so that you don't need to understand what's going on under the hood. You can be effective at using C# and F# to solve other problems specifically because they are very well designed at the goal of abstracting over the lower level hardware. But if your goal is to build an intuition of how programming languages themselves are implemented and how computer hardware works, then, using those languages will be counter productive. If you're trying to use math to solve arithmetical problems, then by all means using AI to help. But if you're trying to advance the math field itself, then actually knowing how math works is probably essential. Put in more concrete terms: if someone wants to be a working mathematician without learning the fundamentals of math, then how do they even know what prompts to the AI are worth writing? In what way are they adding any value to the process at all?

qubex 11d ago
I never said one should not know the fundamentals of mathematics, I was trying to express it’s a damned lot easier when once understood you can delegate the lesser aspects to machinery. Abacus, calculator, computer, CAS, now AI: the mathematician’s understanding and intuition are still fundamental, but the instruments they can rely upon are levelling the playing field (and indeed, it is a great field in which to play).