Reddit mentions of What Is Mathematics? An Elementary Approach to Ideas and Methods

maybe you mean What is Mathematics? by Courant and Robbins.

https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

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https://www.amazon.com/Mathematics-Form-Function-Saunders-MacLane/dp/1461293405/ref=sr_1_3?keywords=MacLane%2C+Saunders&qid=1555006726&s=books&sr=1-3 (unfortunately, very expensive)

You would probably like these two books:

• Geometry and the Imagination by David Hilbert and Stefan Cohn-Vossen.
  
  
• What is Mathematics? by Richard Courant.
  
  Neither of those are "popular math" books; the authors are famous mathematicians, and they explore various fields of mathematics without requiring too much advanced knowledge.

I really like What is Mathematics by Richard Courant. It's aimed at the lay person and I think a 13 year old would enjoy it. It's a book you can jump around in too.

Please take a look at What is mathematics by Courant, Robbins, Stewart. It is much leaner, yet it is accessible and was endorsed by Einstein:

"A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods."

This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.

General Stuff:
The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.

1. Mathematics: A very Short Introduction : A very good book, but also very short book about mathematics by Timothy Gowers, a Field medalist and overall awesome guy, gives you a feelling for what math is all about.
   
   
2. Concepts of Modern Mathematics: A really interesting book by Ian Stewart, it has more topics than the last book, it is also bigger though less formal than Gower's book. A gem.
   
   
3. What is Mathematics?: A classic that has aged well, it's more textbook like compared to the others, which is good because the best way to learn mathematics is by doing it. Read it.
   
   
4. An Infinitely Large Napkin: This is the most modern book in this list, it delves into a huge number of areas in mathematics and I don't think it should be read as a standalone, rather it should guide you through your studies.
   
   
5. The Princeton Companion to Mathematics: A humongous book detailing many areas of mathematics, its history and some interesting essays. Another book that should be read through your life.
   
   
6. Mathematical Discussions: Gowers taking a look at many interesting points along some mathematical fields.
   
   
7. Technion Linear Algebra Course - The first 14 lectures: Gets you wet in a few branches of maths.
   
   Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.
   
   
8. Linear Algebra Done Right: A pretty nice book to learn from, not as computational heavy as other Linear Algebra texts.
   
   
9. Linear Algebra: A book with a rather different approach compared to LADR, if you have time it would be interesting to use both. Also it delves into more topics than LADR.
   
   
10. Calculus Vol II : Apostols' beautiful book, deals with a lot of lin algebra and complements the other 2 books by having many exercises. Also it doubles as a advanced calculus book.
    
    
11. Khan Academy: Has a nice beginning LinAlg course.
    
    
12. Technion Linear Algebra Course: A really good linear algebra course, teaches it in a marvelous mathy way, instead of the engineering-driven things you find online.
    
    
13. 3Blue1Brown's Essence of Linear Algebra: Extra material, useful to get more intuition, beautifully done.
    
    Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.
    
    
14. Calculus: Tom Apostol's Calculus is a rigor-heavy book with an unorthodox order of topics and many exercises, so it is a baptism by fire. Really worth it if you have the time and energy to finish. It covers single variable and some multi-variable.
    
    
15. Calculus: Spivak's Calculus is also rigor-heavy by Calculus books standards, also worth it.
    
    
16. Calculus Vol II : Apostols' beautiful book, deals with many topics, finishing up the multivariable part, teaching a bunch of linalg and adding probability to the mix in the end.
    
    
17. MIT OCW: Many good lectures, including one course on single variable and another in multivariable calculus.
    
    Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.
    
    
18. Principle of Mathematical Analysis: Rudin's classic, still used by many. Has pretty much everything you will need to dive in.
    
    
19. Analysis I and Analysis II: Two marvelous books by Terence Tao, more problem-solving oriented.
    
    
20. Harvey Mudd's Analysis lectures: Some of the few lectures on Real Analysis you can find online.
    
    Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.
    
    
21. Abstract Algebra: Dummit and Foote's book, recommended by many and used in lots of courses, is pretty much an encyclopedia, containing many facts and theorems about structures.
    
    
22. Harvard's Abstract Algebra Course: A great course on Abstract Algebra that uses D&F as its textbook, really worth your time.
    
    
23. Algebra: Chapter 0: I haven't used this book yet, though from what I gathered it is both a category theory book and an Algebra book, or rather it is a very different way of teaching Algebra. Many say it's worth it, others (half-jokingly I guess?) accuse it of being abstract nonsense. Probably better used after learning from the D&F and Harvard's course.
    
    There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.

Try What is Mathematics?, by Courant & Robbins. It's a good overview of mathematics beyond the elementary level you've completed. Another good book like that is Geometry and the Imagination, by Hilbert & Cohn-Vesson.

Try this book for help with understanding Algebra. My uncle had left a copy at my grandparents house, and I picked it up when I was there when I was in the third grade (we were working on multiplication and division). I made a perfect score in the state tests for Algebra 1, Algebra 2, Geometry, and Trigonometry.

I read this book in high school, and it really helped me figure out how to think about breaking down more complex problems.

This book made math very clear for me as well.

I think these books may help you because you could do the math he read to you. These books helps give you an understanding of what is actually happening. Foe example, most people do not understand that multiplication is nothing more than extended addition, until you explain it to them. If you can think about the problems and understand what the problem is saying, it will be easier to figure out. I did a lot of math in my head that would have taken several pages to write it out the way I did it, but if you wrote it the way they expect would only take a few lines.

I am very happy for you for finally finding someone who knew what was going on with you. I had a similar problem in elementary school, but my parents did not trust the school and had me tested on their own. They decided that I had a "social communication disorder, kind of like a really weak autism" (This is what my parents ended up telling me anyway). The school thought I was "developmentally challenged" ("borderline retarded" was the phrase that was bandied about) but when my parents had my IQ tested, it was a 141, which is not quite what was expected, they decided that the problems were elsewhere.

One thing that is very important in math is that if you do not understand, you can go back and work on fundamentals and build up your foundation, and the more advanced stuff will be easier.

Good luck, and I believe you really are an adept writer. What you wrote grabbed my interest and was compelling.

"What is Mathematics ? An elementary approach to Ideas and methods ( 2nd Edition) by Richard Courant (Author), Herbert Robbins (Author), Ian Stewart (Editor) "

I'm not sure I understand your concern, but if you struggle with math, it may help to start with coding. It can make things a little more concrete. You might try code academy, a coding bootcamp, or MIT open courseware.

An Emory prof has a great intro stats course online: https://www.youtube.com/user/RenegadeThinking

Linear algebra is the foundation of the most widely used branch of stats. This book teaches it by coding example. It's full of interesting practical applications (there's a coursera course to go with it): https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991/ref=sr_1_1?ie=UTF8&qid=1469533241&sr=8-1&keywords=coding+the+matrix

Once you start to feel comfortable, this book offers a great (albeit dense) introduction to mathematics. It used to be used in freshman gen ed math courses, but sadly, American unis decided that actually doing math/logic isn't a priority anymore: https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=sr_1_1?ie=UTF8&qid=1469533516&sr=8-1&keywords=what+is+mathematics

As far as watching, I've seen pretty much every special available online (they're easy to google in forums, as there's not many of them). The best one, hands down, is BBC's The Story of Maths.

As far as books, I'm currently reading A History of Mathematics, which is great but he does pack a lot in every page, so it's no light reading. And I am also reading Courant's What is Mathematics?, which is turning out to be just about my favorite math books ever. It's not exactly History, it's... well, it's a bit of everything. It's certainly in a league of its own.

Even though the latter is more heavy in the math, somehow Courant manages to make it so fun the pages just fly out of your fingers, and before you know it, you've been sitting two hours reading the thing.

These are a couple of nice old books about mathematical thinking:

• What is Mathematics? by Courant, Robbins, and Stewart
  
• How to Solve It by Polya

You might want to try "What is Mathematics?" by R.Courant and H.Robbins. The book is written for people new to the field of theoretical mathematics and is intended for those who wish to develop a solid foundation on the topic.

I had started college as an engineer, switched to English, and now work as an ESL instructor. However, my love of math never died (despite my university professors' best attempts). So, I picked up that book a little while ago. It's a good read (albeit a dense one), and it covers a little bit of what you have listed.

[Amazon link here] (http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192)

Edit: some words

Like justrasputin says, there usually is quite a lot of work to be done before you start to really see the beauty everyone refers to. I'd like to suggest a few book about mathematics, written by mathematicians that explicitly try to capture the beauty -

By Marcus Du Sautoy (A group theorist at oxford)

1. Symmetry
   
2. The Music of the Primes
   
   By G.H. Hardy,
   
3. A Mathematician's Apology
   
   Also, a good collection of seminal works -
   God Created the Integers
   
   And a nice starter -
   What is Mathematics
   
   Good luck and don't give up!

This may not exactly be an answer to your question but I would recommend buying this book: https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

It's not quite a textbook nor it is a pop-sci book for the layperson. The blurb on the front says " "A lucid representation of the fundamental concepts and methods of the whole field of mathematics." - Albert Einstein"

In and of itself it is not a complete curriculum. It doesn't have anything about linear algebra for example but you could learn a lot of mathematics from it. It would be accessible to a reasonably intelligent and interested high-schooler, it touches on a variety of topics you may see in an undergraduate mathematics degree and it is a great introduction to thinking about mathematics in a slightly more creative and rigorous way. In fact I would say this book changed my life and I don't think I'm the only one. I'm not sure if i would be pursuing a degree in math if I had never encountered it. Also it's pretty cheap.

If you're still getting a handle on how to manipulate fractions and stuff like that you might not be ready for it but you will be soon enough.

I just bought this, and I'm waiting for it to be shipped. I heard it is life-changing.

Try to find entry points that interest you personally, and from there the next steps will be natural. Most books that get into the nitty-gritty assume you're in school for it and not directly motivated, at least up to early university level, so this is harder than it should be. But a few suggestions aimed at the self-motivated: Lockhart Measurement, Gelfand Algebra, 3blue1brown's videos, Calculus Made Easy, Courant & Robbins What Is Mathematics?. (I guess the last one's a bit tougher to get into.)

For physics, Thinking Physics seems great, based on the first quarter or so (as far as I've read).

Aleksandrov, Kolmogorov, Lavrent'ev. http://amzn.com/0486409163. Foundations to applicationsl.

Courant, Robbins, Stewart. http://amzn.com/0195105192. Tour of mathematics.

Aside from The Princeton Companion to Mathematics, you might like to check out What Is Mathematics? An Elementary Approach to Ideas and Methods by Courant and Robbins, and Mathematics: Its Content, Methods and Meaning by three Russian authors including Kolmogorov.

Seriously this may be a great coming-of-age title for you: Infinite Jest.
Also since you got your first job check out The Wall Street Journal's Guide to Starting Your Financial Life. If you haven't yet appreciated math, I would suggest you do so as you're going to need it for any decent job these days. Detach yourself from Fallacious Thought.

From Richard Courant's "What is Mathematics", page 35, a constructive method is suggested.

What Is Mathematics?: An Elementary Approach to Ideas and Methods

"Succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods." Journal of Philosophy

https://www.amazon.ca/What-Mathematics-Elementary-Approach-Methods/dp/0195105192

I recommend going through some of the lessons on Brilliant, and here is Brilliant's quick exposition on the set of complex numbers.

I don't know what a softer explanation would entail exactly, but I would offer you the alternative perspective that the representation of complex numbers as two real numbers a+ib for the real numbers a and b is extremely useful because of the interpretation of the extension of the one dimensional real number line into the two dimensional complex plane.

Also, I recommend reading on a simple exposition of complex numbers from Richard Courant's "What is Mathematics".

Be brave, start with http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

Assuming you're at around high school level you might like this: What Is Mathematics?

I haven't read it yet, but Richard Courant's What is Mathematics? has been highly recommended to me.