Hacker News Reader

Comment by revskill | Hacker News Reader

My wish is for math to remove all the gatekeeping layers and one day, everyone can do maths, just like with programming.

View on HN

Everyone can do maths. All you need is pencil and paper. Or download Lean, if that's your preference.

Of course it's possible that instead of "no gatekeeping" what you mean is "free tutoring".

I'm curious, what do you see as "gatekeeping layers" in math? Books? Material? Pedagogy? Nomenclature? Something else?

Not OP, but I'd like to add the term “learning complexity reduction” which relates closely to “pedagogy”.

Reflecting on my experience as a CS graduate with a strong interest in math (though not very advanced knowledge), I realize I would have benefited from a more intuitive, black-box approach when first engaging with complex topics, rather than diving straight into their intricacies.

I think this is kinda like the C++ vs Python as your first language question. C++ is better if you want to really learn programming but it’s harder to get to the magic of your first real program. Python gets people making programs sooner but it’s harder to build good habits and get that deep understanding. It depends what your goals are. There’s stuff like this for math but it’s kinda like trying to learn math from 3Blue1Brown videos. They sure help, but you eventually need the rigor

I'm not suggesting that you can fully learn math in this way. My point is that the approach you take can boost your confidence and motivate you to progress further. Of course, some people don’t need that kind of push or entry point.

I've seen other great examples of this from good professors. For instance, in probability and statistics courses, we would validate our results by combining theoretical concepts with simple Monte Carlo simulations to ensure they matched.

Sure, I don't disagree. But there's a lot of trash and not a lot of gold. It is hard to find the gold and to make the problem even worse, what's gold is trash to others. Worse than that, what may be trash to you at one point in time may be gold at another, and vise versa. It's unfortunate, but I think this is true in any learning process. There's lots of great programming articles on Medium, but you're more likely to learn garbage, and even more likely to not know you are.

Not really gatekeeping, but as someone who likes to self-study, not having solutions is very annoying.

I totally get that. I was fortunate to get properly educated up through essentially the level of an undergraduate math degree (minus maybe typology), but then continued learning a lot on my own. It’s common to hear that the struggle is part of the learning process. The more I’ve advanced the more I find this to be true. It’s that struggle that makes you pay attention to the small details that are so critical. I was also fortunate to have a professor who would pester me and he later told me he wanted me to be confident in my results, because eventually I would have no one to double check (and he was right). The struggle really helps with this.

I think the main difference between learning provisioning and math is a compiler. To learn either you can only learn by doing. Reading and lectures aren’t enough. What is hard to learn in math is to be the compiler yourself. To be able to verify “programs” (do I even need quotes here?). This is a very powerful tool to add to your tool belt and one I think even helps in programming.

I hope others can add advice here and words of encouragement. The struggle is real, but it is part of the process, for better or for worse.

I work as a private tutor for proof-based math, and I have a lot of students who've spent some time self-studying before coming to me. The comment by godelski matches my experience: the biggest obstacle seems to be the fact that it's hard to learn how to check your own proofs if no one has ever taught you how. I see a lot of variation in how well people have managed to develop that skill on their own.

Having more textbooks with solutions to the exercises would probably help a lot with this, especially if you used the solutions judiciously. I think the fact that this isn't more common sadly has a lot to do with their role in undergraduate teaching: every exercise that has a solution in the back of the book is one that college students can very easily cheat on. I definitely agree that it's frustrating that the product has to be made worse for everyone else just because some people would misuse the better version. Far from the only such case in the world!

Yeah it’s a catch-22. I’m in grad school and occasionally I get to be instructor. When I am I focus far less on tests and more on homeworks and projects (I do ML so it’s well suited for that style). The homeworks are made to be “play around” and the project is to be very self driven (with plenty of help, but they are juniors or seniors so they be fairly self reliant) and to find passion.

The reason I do this is because grades matter so much to students that even if they care to learn material they are incentivized to cheat (and subsequently cheat themselves). I think a lot of academics still don’t get this and are resistant to change (it is a lot of work to create a class but not to much once you worked everything out).

I think this confidence thing is also something that needs to be learned in every subject. Even in CS the compiler, type checking, and even unit tests aren’t enough (though they are extremely useful).

I should also say, one unfortunate thing I find in academic teaching of coding is we often don’t look at code. There’s not enough time. But to me this feels like trying to grade a math proof by looking only at the first and last lines. I think this builds lots of bad habits and over confidence

Do you have any favourite books? like maybe 2 or 3 that you'd grab in the event of ww3 or a zombie apocalypse? I'm always on the look out for good self-learning maths books.

These books are what i would consider the best books for self-study. (I have gone through many textbooks after i went back to school to study statistics.)

• Real Analysis: A Long-Form Mathematics Textbook

• Proofs: A Long-Form Mathematics Textbook

• Mathematical Logic Through Python

• A Course in Calculus and Real Analysis

• A Course in Multivariable Calculus and Analysis

• Differential Equations With Applications and Historical Notes

• Probability and Random Processes (Grimmet)

• Probability Through Problems

• Fifty Challenging Problems in Probability with Solutions

• The Simple and Infinite Joy of Mathematical Statistics

• An Introduction to Error Analysis

Thank you for those, the Logic through Python one looks interesting at first glance. I've discovered a peculiarity about my own learning style with maths. If I can implement a concept in code, I can remember and understand it better!

the only potential gatekeeping ive noticed in mathematics is (some) teachers that arent really teaching but more just showing off what they know. its a waste of everyone's time. i say potential because im sure its not always the teachers' fault, its likely just me being dumb.

There are definitely some people that either don't understand that their explanations are completely confusing to beginners or that don't even care. Sadly, teaching isn't always valued in academia.

Unfortunately lots of things are obvious or easy after you’ve learned them but seemingly impenetrable before then. Think about calculus. I failed my first time but now it’s easy. Though I think this makes me a better teacher because it’s harder to forget that it was hard at one point.

What gatekeeping? Anyone is free to do math to the extent of their abilities. Math is known for accepting contributions from other fields. You don't need special credentials in math to publish a book or paper about math. It helps but it is not essential. Some academic positions are very difficult to get without a proper degree in the subject but that applies to every field, and for good reason.

Not OP, but I read it like they meant gatekeeping == lack of skill, because OP seems to think that everybody knows programming now thanks to AI.

I hope I am misreading this.

> one day, everyone can do maths, just like with programming.

Everyone can absolutely not do programming with an AI.

What is true tho is that everyone who cannot write program code, also cannot evaluate if the code the AI produces is correct.

And we who do write alot of code are not all that impressed.

Programming should remove all gatekeeping one day so everyone can do programming

And gatekeeping, so many of us want to gatekeep but there too, other gatekeepers stand in our way

Just build a gate around their gate.

Yes, like the Fields Medal. Everyone should get a Fields Medal, that way we're all winners.

Or the Riemann Hypothesis! Why not call it the American Hypothesis? That way everyone could think it.

Reply on news.ycombinator.com