> How much mathematics is needed anyway? In the day job, how many people have to use maths skills beyond arithmetic?
A lot. It's also pretty funny that your examples of useless math are 3 of the most concrete and directly applicable concepts in the entire set of human knowledge. Try, idk, ergodic Ramsey Theory next time.
> What about trigonometry?
Ever heard about FM radio? Or anything that takes a Fourier series? Anything using complex numbers? Game programming? Graphics? Positional encodings in large language models?
> Differential equations?
My brother in christ, literally Newton's second law.
> Integration and calculus?
Ever needed to numerically find the minimum of a function or solve an equation? Newton-Raphson? Literally all of machine learning?
The thing with math is that if you aren't familiar with the concepts then you don't know what you don't know.
I think you are just proving my point. As an example, FM radio. You and I know how that works, and, I reckon that just the two of us could build out our own station and hand-soldered receivers, even making it stereo. Personally though, I would hope that we would go straight to a DAB-style radio with a few data layers for weather, the schedule and whatnot.
However, from what I understand, the only people listening to FM radio are car-dependent commuters and people that have a trade, whether that be building, hospitality and so on. They all know how to find their favourite radio station and get the volume to a level that they can hear. What percentage of these people know how the radio works beyond that? Or are we talking rounding errors here?
As for LLM things, the hundreds of millions that have ChatGPT installed do not need to know any maths whatsoever. They just write prompts. There are some outliers, such as students trying to cheat on their science projects, maybe they should put down ChatGPT and pick up a textbook, but none of them need to know about 'positional encodings in large language models'. They just don't want any of that, the goal is not to do any 'system two' thinking.
This does not mean that a very small amount of programmers need to know such things, but the vast majority of people have better things to bother themselves with.
Game programming, it is the same again. Millions or even billions might spend their lives in front of consoles, but the people writing the games are relatively few in number, and when you take away the people making textures, running tests and whatnot, an even smaller number of people need to know the tricky maths.
I am not sure whether you were just trolling me or not. Where I live, most people have jobs where they definitely don't need to know anything more than basic arithmetic.
A lot. It's also pretty funny that your examples of useless math are 3 of the most concrete and directly applicable concepts in the entire set of human knowledge. Try, idk, ergodic Ramsey Theory next time.
> What about trigonometry?
Ever heard about FM radio? Or anything that takes a Fourier series? Anything using complex numbers? Game programming? Graphics? Positional encodings in large language models?
> Differential equations?
My brother in christ, literally Newton's second law.
> Integration and calculus?
Ever needed to numerically find the minimum of a function or solve an equation? Newton-Raphson? Literally all of machine learning?
The thing with math is that if you aren't familiar with the concepts then you don't know what you don't know.