Hello! for the longest time I've thought that I'm just "not good" at math, and that I'm just a creative type or something, but for the past few years I've been trying to brute-force my way through math drills and stuff to improve because I want to go into a STEM field. I've found that it doesn't work. I have, however, gained a kind of Stockholm syndrome for math, and I find myself wanting to know *more*. I feel like I'm missing out on something way beyond myself but idk where to even find that. So here i am. Asking a blog on tumblr for the secret math knowledge. If you have any resources that i could read about math that isn't just "here's how to do this" i would really appreciate it!!!
First of all, complete props to you for giving something that doesn't initially appeal to you, in this case, maths, a chance. Mathematics can be frustrating and even annoying, being an oftentimes nit-picky field. You can quickly realize that these are also the traits that grant the satisfaction and euphoria of mathematics. So don't forget to be proud of yourself for not disregarding mathematics as a whole and actually giving it a go.
Second of all, creativity is very necessary for maths. It is a shame that the educational system doesn't do maths justice (A Mathematician's Lament by Paul Lockhart is exactly about this). Mathematics is presented as something mechanical, force-feeding formulas and having students repeat them to find adequate results. That is not a fair portrayal of mathematics.
Different people will have different conceptions of what the learning of mathematics is or should be - I mean, for god's sake, mathematics hasn't even been defined properly and one expects people to know what to do with it. I can only tell you what I conceptualize mathematics, and its learning, to be. For me, mathematics is the boring work of examining multiple results and cases of the same formulas, it is the finding of patterns and attempting generalizations, it's the excited scribbles of formulas and the necessity of looking at a particular scenario from multiple perspectives. Most likely, the generalizations won't come easily, a minus sign will be forgotten making the following calculations obsolete, an approach to a problem will prove fruitless, and laborious work will be done only to find out there was a specific theorem that would have shortened the whole process. Patience is required for maths, and hopefully, you can now see that creativity is too, there is no shortcut to knowing where to look or what technique to utilize. As is the case with most worthwhile pursuits, and as you know from experience, mathematics is endlessly frustrating, but that also means it is endlessly fun.
Now, I do not have any secret math knowledge (or do I), what I can do is present you with some things that fascinate me and have led me to love mathematics as much as I do, outside of the conventional mathematics curriculum.
Maths really comes down to practice, practice, practice... as many other things. I heavily encourage you to start playing around with mathematics a little bit. Olympiad mathematics kind of do that, (I, very conveniently, have a lot of posts about that.) as do many other math competitions. Maybe try out some exercises from your national olympiad and, with no judgment, because this is just to have fun, play around a bit. Disregarding the conventional maths you know, test out your logic, laugh at mistakes and losses of time, and feel that happy rush when a conjecture you reach, or part of it, is correct.
In terms of the resources, I opted for a mix of funny math history moments and some actual mathematics, in no particular order. Prepare for confusion. ↓
0. How Mathematics is enjoyable
No better way to start than with the reasons mathematicians decided to dedicate a good portion of their lives to the subject, or why some people just enjoy mathematics. This is something that greatly interests me, I always love to see people’s passion for their interests, hence this post, where you’ll find many people’s reasons for enjoying mathematics.
Andrew Wiles answers “What does it feel like to do maths?” - (video) - Andrew Wiles is a mathematician who proved the theorem which had been taunting mathematicians for centuries, famously known for being the subject of the third point of this same post, explains peoples’ distaste for maths and his own experience with the subject.
YouTube Stories: Learning Mathematics with Wootube by Eddie Woo - (video) - Eddie Woo is a wonderful mathematics educator as well, who videotapes his lessons (available on Youtube). This serves as an introduction to him and his channel.
Mathematics is the sense you never knew you had by Eddie Woo - (video) - In his TEDx Talk, Eddie starts by explaining his distaste for maths in his school years, mentioning his low scores and lack of interest, and how, despite this, he ended up as a maths teacher.
Reddit asks: “Why do you love maths?” - Another compilation of people’s explanations for their mathematical interest. Wholesome content ahead.
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1. Intro to a new perspective on mathematics
Taming, claiming and reframing the beast that is mathematics by Vinay Kathotia - Small article related to the portrayal of mathematics by most and by mathematicians themselves.
On proof and progress in mathematics by William P. Thurston - Mentioned in the previous article, 17-page
Anyone Can Be a Math Person Once They Know the Best Learning Techniques by Po-Shen Loh - (video)
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√2 . The Pythagorean Cult
I’m sure you’re aware of Pythagoras and his fetish for right triangles, but do you know about his weird cult? That’s right, Pythagoras was the founder of Pythagoreanism, a cult based on the teachings and beliefs held by him and his followers, the Pythagoreans. - very original naming ik.
Here’s and article about them. A really popular myth related them is the throwing of Hippasus into the sea as a punishment for “believing” (i guess) in irrational numbers.
The unreasonable man by Vinay Kathotia, further explores the irrationality of the square root of 2, allegedly identified by Hippasus, providing some proofs of it.
Proof: √2 is irrational by Khan Academy (video) - Because Khan Academy rarely misses.
The Madness of Pythagoras by Kayla Mahoney - Did you know Pythagoras refused to eat fava beams, because he claimed they contained the souls of the dead? Now you do, and there’s no going back >:).
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2. The base tools of mathematics
Introduction to Mathematical Thinking by Alexandru Buium - Pretty self-explanatory title, simplistic and general apprach to mathematics starting with the essential, logic.
The Five-fold Path to Mathematical Wisdom by Vinay Kathotia - Article about five different approaches to mathematical problems/representations.
How to think like a Mathematician by Kevin Houston - Really useful book, starts with certain study skills and develops to the logic involved in mathematical thinking, explains theorems, definitions and proofs! Highly reccomend.
How to Think Like a Mathematician by Eugenia Cheng - (video)
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3. "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain."
Yup, this is about Fermat’s Last Theorem, which took 350 years to be proven.
I’m guessing you’ve come across some jokes about it, how could one not. Essentially, in the 1630′s, our man Pierre de Fermat jotted down the conjecture (fight me, no proof no theorem) that states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2, along with the sentence "I have a truly marvelous demonstration of this proposition that this margin is too narrow to contain.". The paper which contained this was only found after his death, and, as far as we know, he never got around to actually writing the proof. Because of this, we call this statement Fermat’s Last Theorem.
Andrew Wiles was who ended up proving Fermat’s Last Theorem, in 1993, after six years of working secretly on the problem. (Imagine your dirty little secret being working on revolutionizing an entire field of study, what a guy honestly.)
Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas [1993] - Documentary about the theorem and its proof, as told by Andrew Wiles himself.
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4. Functions
Honestly functions are just a very needed side of mathematics that can be applied to pretty much everything. You’ll find them in your average mathematics curriculum and in your everyday life, if you know where to look.
Introduction to functions
Introduction to Mathematical Reasoning - Numbers, Sets and Functions by Peter J. Eccles
Functions in the Real World - Education World
- This is definitely a more theoretical part of the list, I am sure you’ve encountered functions before and the resources you have musn’t be terrible. Look into these if you find the necessity, but again the “math secret” really is practice. They can be interesting reads though.
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5. Möbius strips and Klein bottles
The wondrous world of ✨one-sided objects✨. Learn about these cool looking objects and the field they originated, topology.
The Mathematical Madness of Möbius Strips and Other One-Sided Objects by David Gunderman and Richard Gunderman
Intro to Topology by Alex Küronya - Decently advanced maths, I don’t know what level of maths you’re learning, but honestly only read this if you have a pretty thorough backgroung in maths and you’re enrolled/very interested in the field.
Möbius Strip - Cool graphics, cooler maths.
Klein Bottles on Numberphile - Because Numberphile never misses.
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6. The Chicken McNugget Theorem
Yes, you did read that right, No, this is by far not the only theorem with a weirdly funny name*. This theorem derives from a 1800′s math problem.
Explanation of the theorem by Xavier Lien
Chicken McNugget Theorem - Art of Problem Solving
Another explanation, if needed by Mike Beneschan
*Proof: Reddit asks: “ What's the funniest theorem name you know? ” - Literally a gold mine, read this.
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7. Godël’s incompleteness
One of the essential works of Modern Logic. His theorems destroyed the search for a mathematical theory of everything, at the mere age of 25.
Gödel’s Incompleteness Theorems - Stanford Encyclopedia of Philosophy
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem by Marcus du Sautoy @ Ted-Ed (video)
How Gödel’s Proof Works - Quanta Magazine
Gödel: His Tragic Life Story by Aimee Lamoureux - (TW: Sensitive themes)
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8. Mathematics is an art, actually
I’ve seen many people stray away from the sciences because they’re “creatives” or “arts people”. Hopefully you’ve gotten at least a glimpse of the creativity needed in mathematics - if you didn’t, that is totally on me and I’m sorry.
I don’t doubt that you may be a “creative type”. We actually need creatives, more than anything, in this field. I thought the perspective of mathematics as an art mignt be a good ending note.
Why Math is an Art, Not a Science by Peter Flom
Why the history of maths is also the history of art by Alex Bellos - He also wrote the book “Alex’s Adventures in Numberland”, which I own and have read. It’s a pretty sweet book, it has my stamp of approval if you’re interested.
Math and Movies (Animation at Pixar) - Numberphile - On the mathematics behind the art of animation.
Art and Math: Aesthetics of Calculations by Rute Ferreira (DailyArt Magazine)
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Besides this I’m also leaving a list of youtubers/authors that are worth looking into. :)
∞. General resources:
Math-related Youtube:
Numberphile - Have different concepts explained to you in a seemingly personal and almost always funny manner.
3Blue1Brown - Maths explanations paired with excellent visual representation of the concepts.
Reducible - As they put it “Reducing problems to their simplest form.”. Also paired with really good animations.
Websites:
Art of Problem Solving
Blogs/Articles:
Cantor’s Paradise - I’ve linked a few articles published there throghout this post. Essentially, different authors publish math articles in this online space, varied and generally well-written about topics.
Alex Bellos for The Guardian - Puzzles and mathematical articles.
Mathblr Blogs - Check the notes of this post to find a lot of them.
Games:
Nerdle - Math Wordle
(...) - Please reccomend more resources below, I’m not the most well-versed on these subjects.
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Hopefully, you now find maths a little sweeter, funnier, or comprehensible. As with most things, people lead math discovery, and there’s absolutely no reason you’d be unable to be part of that group.
Mathematical problem-solving is something really frustrating but also immensely fun and rewarding. Please look into it, be it olympiads or general problems you find online, don’t take yourself too seriously and have fun with maths! Mathematics doesn’t judge, people do. I wish you well on your math journey! Hopefully, you’ll love it.
P.S: Feel free to add to this post with any math stuff you think is interesting. The more, the merrier!
