#math beginner resources

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.