Comment by supertofu | Hacker News Reader

Comment by supertofu | Hacker News Reader

I was a late bloomer in almost every arena of my life. Developing social skills, having relationships, developing an identity independent of my family, etc. I'm also a late bloomer to mathematics.

I'm in my 30s and getting a bachelor's degree in Math now after a lifetime of math-phobia. Math was my worst subject because it never came easily or naturally to me, and so I assumed I must have been innately incapable of it. I didn't take a single math class during my first bachelor's degree.

I sure wish I could have learned math properly earlier in life, but my point with this comment is that it is never too late to learn math.

Learning mathematics "late" over the last couple of years has enriched my life in so many ways. Learning to write proofs has brought a sense of organization and calm to many other areas of my life. Complex problems and challenges in life feel so much more approachable, because I am much more skilled now in breaking down tasks to manageable components. I can see now how mathematics has influenced programming languages and computer science, and every time I can identify the mathematical underpinning of some program I use or write, I feel like I am peering into the heart of the universe.

Learning math early is a great hack, but so is learning math late :)

I am rooting for you! I just completed a Bachelor's of Mathematics in December before my 40th birthday this year. I am so glad to hear about the effects you're feeling as you learn. I too experienced a deep sense of calm and confidence as I learned to write proofs. Surprisingly, none of my younger classmates agreed! So I chalked it up to being older and more mature in general.

Now I feel vastly more mature than I did before I began my degree! I have that same belief and confidence that no problem I face is unsolvable. I've also discovered a much deeper love of learning itself, and a desire to continue studying long into the future, and that interest includes but is not limited to mathematics! I want to have many different hobbies and learn all about how the world works.

Math anxiety... it's a real thing. My wife has a brilliant level of intelligence but refused to approach the higher levels of math. Not out of lack of capability... just fear. She says things like "Math should have numbers in it, but no letters. I'm not about the kind of math with letters in it." And for example, she never completed her psych degree because a statistics course was required to complete it and she didn't want to take it.

It's like a fat person going to the gym for the first time. But once they start getting into the habit of working out and seeing the improvements, the anxiety goes away.

Anyway, congrats on overcoming your math anxiety.

How were you able to learn math later in life? I'm terrible at math and I know it causes my work to suffer.

I am planning to use Math Academy after my Master's degree. I did a beta and it was awesome, just wish I had taken more notes.

My two cents.

Math it's way easier than you think it is, it greatly depends on how you approach it. I really like the style of Robert Ghrist videos on YouTube.

A great tutor/video goes a long way. I wish I could share some resources but am a bit outdated on that.

The overall idea is that some people can explain math concepts in a very clear and straightforward way, while some others will write up a bunch of symbols and let you figure them out. Avoid the latter. As a note, those are usually the lowest performers in academia, lol.

You learn math best by doing math. Sure, good explanations help, but sometimes dry rigorous ones are preferable since it asks you to grapple with the subject.

>sometimes dry rigorous ones are preferable

My experience with the comments in this thread, the overwhelming majority of people I know IRL and the widespread sentiment that "Math is hard" does not seem to reflect that.

math is just formalizing ideas into symbols and creating rules to manipulate and understand the ideas further. It is really the "ideas" that are important but all school really teaches is the manipulation aspect of it which is a bit boring without understanding the ideas. Most of early mathematical education is of the form "assume we have so and so arcane formulation - here is what we can do with it by applying these rules whose truths you just have to memorize"

Similar to the OP, I had a lot of anxiety around math and academic performance. I dropped out of college at 18 and the highest math class I took was in high school (pre-calc), which I almost failed.

At age 33, I enrolled in community college and took Calc I-III, Linear Algebra, and Differential Equations. The community college hosts weekly "math jams" and offers free 1:1 tutoring.

I'm currently taking a Discrete Math and Probability class at UC Berkeley for fun this summer (CS70), which would have seemed absurd just a few years ago. The community college system in California is extraordinary; I'm glad I got to experience it first-hand.

Seconding Cal JC hype. I sandwiched a JC in between two stints at traditional 4-year schools. All of the instructors at the JC seemed miles more interested in teaching than their university counterparts. They were almost universally more approachable and invested in your education.

Describe the math jams, if you would please. Is this just open tutoring labs for all areas of math? Or is it something different?

You can start simple. Read Basic Mathematics by Serge Lang and do all exercises. Solutions are included. That book basically covers all mathematics up to junior high in a rigorous but approachable fashion. Serge Lang was a great mathematician. Then you move to logic, calculus, linear algebra and probability. Afterwards, focus on more specific areas that interest you.

Springer Undergraduate Texts in Mathematics and Dover have lots of elegant and concise textbooks that can help you. At the beginning, the key is to move slowly and build some solid foundations.

I'll quote my other comment:

If you want to learn math, a good place to start would be AoPS curriculum https://artofproblemsolving.com/store/recommendations

Continue with Susan Rigetti's curriculum https://www.susanrigetti.com/math

You can get answers to your questions here https://www.reddit.com/r/learnmath/ and here https://math.stackexchange.com/

The core of math, as GP mentioned, is learning proofs.

I would go as far as to say that most high school “math” and “math” taught in many college courses is borderline irrelevant.

It’s like learning how to paint by memorizing names of colors. Learning to fix a car by reading parts list.

Painters can tell you about colors and mechanics parts but you don’t become like them by making those things your goal.

The only way to learn math is to learn proofs rigorously.

Calculus isn’t math, it’s just calculus. Algebra, linear algebra, they’re not math. Any “math” without rigorous definitions and theorems with proofs for each one isn’t math. (memorizing names of colors isn’t being a painter)

This book seems a good start. This is not advanced math. It’s an introduction to math- if you don’t know this you don’t know math. https://richardhammack.github.io/BookOfProof/Main.pdf#page=8

Stuff like what’s in this book is taught starting in week 1 for Waterloo computer science degree.

It’s life changing knowledge because you can use math to understand almost anything.

> The core of math, as GP mentioned, is learning proofs.

That is the midpoint, the core goal of math is getting enough intuition that facts are obvious, the proofs are just a guide to get you there.

This means you shouldn't study proofs, you should study facts, the proofs are just an example of how to support that fact, you can prove things in many different ways and also many things can be constructed in many different ways and still have the same properties. All of that is much easier when you think in terms of facts instead of proofs.

If you struggle with proving something then you don't understand it. If you memorize a proof for it, then you still don't understand it. The right path to take is to build understanding and then the proofs comes on their on.

It’s a cliche mathematician debate. I don’t disagree. In any case, if you aren’t able to do proofs, you don’t do math.

> The core of math, as GP mentioned, is learning proofs.

Well it may be the core but it's not the purpose. As an engineer and later quant I actually use math for practical purposes in everyday life. It wasn't like this in the beginning, I remember primary school was a torment of being fed math olympiad-style problems and hating it. Then somewhere in gymnasium I discovered electronics and everything changed. Math became not just useful but inevitable and from then on learning of math for my own purposes went hand in hand with practical applications in electronics, from simple equations to matrices to differential equations, numeric calculus etc.

Of course there's also always the "standard math" (for passing the SAT/baccalauréat) and entering the good schools, that's inevitable. One can say that "Learning Math Ahead of (the vast majority of) Others" is the way to get ahead :)

I think there's a problem in American english in particular. We call the subject 'math', but I think the british 'maths' is more appropriate. There's multiple different kinds of mathematics. Not just one. The American misnomer makes a lot of people falsely believe that grade-school/high-school math is the 'path' into higher math. It's not.

That's not to dismiss the importance of arithmetic (and this is what I believe we should call grade school math operations): everyone should know how to add, subtract, multiply, divide, etc. But the core of mathematics is logical thinking and reason, not numbers

I burnt my maths books at 16 and didn't do any math after that until I was 30. Then I took Real Analysis as part of a PhD course. I was more mature, and I discovered I enjoyed the different approach. So (a) don't assume you haven't changed and (b) find the parts of math you like best, and start there.

I went back to university. I wouldn't have had the motivation to do this outside of the structured environment of academia and, critically, the pressure of exams and grades that come with school. A huge amount of my motivation comes from the fear of "getting a bad grade". Without the fear of a bad grade, I definitely would have given up learning math as soon as I got bored.

It would be a good idea to investigate the belief you have that you are "terrible at math". What does that mean, exactly? Are you bad at computation? Do you forget rules? Are there gaps in your knowledge which are preventing you from accumulating more advanced concepts?

Learning math is like learning any natural language. For example, I'm "bad at Russian" because I have devoted all of 6 hours in my life to learning Russian and there are profound gaps in my understanding of Russian writing and grammar.

But I don't believe I am intrinsically incapable of learning Russian. The reality is that I've simply not put the effort into it.

It's truly the same with math. I am personally quite bad at computation by hand. It's exhausting, I often make careless errors, and I find computational problems by hand to be very boring. But that doesn't mean I'm bad at math! I've simply not invested much effort into improving my skill at computation by hand. I'm not terrible at proofs, for example; and the reason for this is that I find them interesting, and have devoted extra time and effort into learning how to write them. The heart of math isn't computation (which I'm not strong at), but proof and abstraction (which I am strong at, only because abstraction is interesting to me).

So really investigate your belief system regarding your capacity for mathematics. It's unlikely you are innately bad at it. Maybe you have knowledge gaps or you, like me, are not innately skilled at computation. But there are strategies you can employ to improve both.

being bad at something is the first step to being good at something

-adventure time

> it is never too late to learn math.

Unfortunately your experience is atypical. I have seen a few people trying to learn math late(ish) in life, but I haven’t seen a single one succeeding. I am not claiming it is impossible, because I thing everything is possible, it’s just that I haven’t seen it done.

Congrats to you for beating the odds. It is quite a singular achievement.

Did those people go to university or try to learn on their own? I absolutely would not have been able to learn upper mathematics outside of the structure (and intrinsic pressure!) of an academic environment. I would never have had the motivation or persistence on my own. Even within an academic system, generating the motivation to persist is a daily struggle, but a lot of my identity is around "being a good student", so that really works in my favor to counteract the difficulty of being a non-traditional student.

This learning adventure has been very, very hard. But it is possible.

Because if I can do it, seriously anyone motivated can. I was the epitome of "bad math student".

My precalc teacher in high school actually discouraged me from going on to calculus (I took his advice and took trig, not calculus, in senior year of high school), and I decided during that meeting that I would never take a math class again.

As an adult, I really take umbrage with that lack of faith. I wish someone had told me that math is not any harder than learning a new language (something I was very good at).

It would have given me courage and helped me see math as not some kind of untouchable, elite pursuit, but just a learnable skill set like any other.

If you don’t mind sharing, I’m curious what your first degree was in and what you think you got out of studying that subject?

> “…it is never too late to learn math.”

Thank you for sharing your experience. I feel the same.

I tried to

DOAH! ...I was saying, I tried to learn some useful Calculus back when I was doing Macromedia Flash a hundred years ago, and just could not get through it using academic resources. Too generic.

Fast forward and I came back to math for Python projects. And by this time youtube and authors like Khan Academy are making learning materials which let you enter in the middle and work your way in whichever direction suits your goals.

But what changed me from "I'm not good at math, so I hate math" to loving it was history of mathematics--the stories of the really interesting problems, and insights into the structure, theories of mathematics. I stopped thinking of math as a black box, and started to see its beauty and simplicity.

Thank you for this post. I am in my 40s and have a similar approach.

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