We need to pivot math towards intuition and accessibility.
Math has built a gated, inaccessible institution which - by design or not - served as a moat.
I believe math has little to do with mathematical notation - intuition is much more important. One can have intuition but not be able to “read math” - much as many musicians don’t “read music”.
Reading math however does not guarantee ideas or intuition. And those are what math needs.
> Math has built a gated, inaccessible institution which - by design or not - served as a moat.
This has always been my problem with math going all the way back to college. It was obvious to me that the concepts were far less hard than the combination of notation and esoteric jargon with liberal use of symbols and weird letters made them seem. Math felt (and still does feel) "encrypted."
The impression math gave off is of an arcane discipline that uses its arcane-ness as a gatekeeping tactic, intentionally or not, and makes itself intentionally hard for newcomers to learn without being hand-held by members of the guild.
Of course I can say the same about a lot of computing, and I'm old enough to remember efforts to make computing more approachable like easier to learn languages and GUIs being mocked and scoffed at by "real programmers."
I think this is a pretty typical human group behavior.
I think this underlies a lot of AI hate from these communities today. AI makes it easy for outsiders to bash their way into the field with the help of an LLM. Yes, this often results in low-effort "slop," but if used correctly it can also help people climb the learning curve really fast. I've had great luck having an LLM make me some passable "slop" and then explain it and go around with me as we fix and refine it, explaining each step, and as it does so it feels like we are learning together. It's very powerful and I, as the student, can control exactly how the teacher presents the material.
I was able to do this to finally start grasping the math behind LLMs themselves: attention layers, tensors, etc.
A lot of people have a powerful visceral probably instinctive reaction to large numbers of migrants entering their area. "Build the wall!" I suspect this is brain stem stuff going back to evolving under conditions of scarcity where migrants meant less food.
> the concepts were far less hard than the combination of notation and esoteric jargon with liberal use of symbols and weird letters made them seem
I really don't get the hate for mathematical notation here, do you have specific examples? Notation is a necessary tool to express complex ideas compactly so that others can understand them. It allows you to carry out technical proofs that confirm things that are "obvious". Then it uses previously introduced concepts to build new concepts on top of them. This keeps mathematics interconnected, there's value in explaining a concept in terms of already known things rather than just vibing it.
> makes itself intentionally hard
It doesn't make itself intentionally hard, it is just hard. You can simplify some expositions and make concepts easier to understand intuitively but it won't necessarily give you the skills to actually work with them in mathematical practice (which is the point of mathematics as a discipline).
My theory is that people run into the inevitable difficulty of math and rather than look inwards and come to the conclusion they aren't as smart, or special as they once thought, they blame "the system". It can't be that they haven't tried hard enough or aren't smart enough, it's the gated community who hides behind esoteric jargon that stops them from being successful in their mathematical studies.
They believe this despite the fact that there are a million different textbooks, all explaining the same concepts in different ways, or different branches that specify the same structures with unique methods. It's really strange when I read threads like this. I'm not the greatest at math either, but that's because it's a hard thing to be good at.
To learn math is an exercise in humility. You must struggle hard, do hundreds of problems, spend years refining your understanding, redoing proofs, finding counter examples, just to be at a good undergraduate level. Much harder than pretty much all CS classes, except maybe Theory of Computation, which is pretty much math.
Yes, that could be the case. I'm not a mathematician but I gave my fair share of struggle towards trying to understand the mathematics behind physics that I was studying. You don't need to know what a smooth manifold is to solve problems in classical mechanics, just as you don't need to know what a tensor product of vector spaces is to learn what tensors are in the context of neural networks. The former is always harder because the standard of rigor is higher, and that's because of different goals. So it could be that a person tries to look up what a tensor is, finds the mathematician's definition first, thinks "what the hell is this", then finds a simpler explanation in applied contexts and goes away with the idea that mathematicians unnecessarily complicate things, because the reason why the mathematical definition has to be so complicated escapes them.
strideashort · · focus · HN ↗
Math has built a gated, inaccessible institution which - by design or not - served as a moat.
I believe math has little to do with mathematical notation - intuition is much more important. One can have intuition but not be able to “read math” - much as many musicians don’t “read music”.
Reading math however does not guarantee ideas or intuition. And those are what math needs.
api · · focus · HN ↗
This has always been my problem with math going all the way back to college. It was obvious to me that the concepts were far less hard than the combination of notation and esoteric jargon with liberal use of symbols and weird letters made them seem. Math felt (and still does feel) "encrypted."
The impression math gave off is of an arcane discipline that uses its arcane-ness as a gatekeeping tactic, intentionally or not, and makes itself intentionally hard for newcomers to learn without being hand-held by members of the guild.
Of course I can say the same about a lot of computing, and I'm old enough to remember efforts to make computing more approachable like easier to learn languages and GUIs being mocked and scoffed at by "real programmers."
I think this is a pretty typical human group behavior.
I think this underlies a lot of AI hate from these communities today. AI makes it easy for outsiders to bash their way into the field with the help of an LLM. Yes, this often results in low-effort "slop," but if used correctly it can also help people climb the learning curve really fast. I've had great luck having an LLM make me some passable "slop" and then explain it and go around with me as we fix and refine it, explaining each step, and as it does so it feels like we are learning together. It's very powerful and I, as the student, can control exactly how the teacher presents the material.
I was able to do this to finally start grasping the math behind LLMs themselves: attention layers, tensors, etc.
A lot of people have a powerful visceral probably instinctive reaction to large numbers of migrants entering their area. "Build the wall!" I suspect this is brain stem stuff going back to evolving under conditions of scarcity where migrants meant less food.
renyicircle · · focus · HN ↗
I really don't get the hate for mathematical notation here, do you have specific examples? Notation is a necessary tool to express complex ideas compactly so that others can understand them. It allows you to carry out technical proofs that confirm things that are "obvious". Then it uses previously introduced concepts to build new concepts on top of them. This keeps mathematics interconnected, there's value in explaining a concept in terms of already known things rather than just vibing it.
> makes itself intentionally hard
It doesn't make itself intentionally hard, it is just hard. You can simplify some expositions and make concepts easier to understand intuitively but it won't necessarily give you the skills to actually work with them in mathematical practice (which is the point of mathematics as a discipline).
jackling · · focus · HN ↗
They believe this despite the fact that there are a million different textbooks, all explaining the same concepts in different ways, or different branches that specify the same structures with unique methods. It's really strange when I read threads like this. I'm not the greatest at math either, but that's because it's a hard thing to be good at.
To learn math is an exercise in humility. You must struggle hard, do hundreds of problems, spend years refining your understanding, redoing proofs, finding counter examples, just to be at a good undergraduate level. Much harder than pretty much all CS classes, except maybe Theory of Computation, which is pretty much math.
renyicircle · · focus · HN ↗