## What is Mathematics?

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In this video I talk about an amazing book written by two legendary mathematicians. The book is called “What is Mathematics?” and it was written by Richard Courant and Herbert Robbins. I talk about various sections in this book and spend a lot of time talking about the Mathematical Analysis of Infinity. We discuss why there are just as many numbers in (0, 1) as there are real numbers. We also discuss why the rational numbers are countable and the real numbers are uncountable. I also go over the proof that (0,1) is uncountable(it’s a beautiful proof by contradiction). Other topics explored in this video include continued fractions, deformations in topology, etc. This book covers A LOT of mathematics and I only briefly touch on some of the topics in this video.

This is the book on amazon: https://amzn.to/3u7Ye4G
The pencils I use in the video: https://amzn.to/3yr5MCs
The paper I use in the video: https://amzn.to/3QLferc

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Thank you:)

Kainat Asgari says:

From India! I'm enjoying your videos although I'm a little weak in English but still I'm able to understand You ❤️

Renato Beraldo says:

what is the precalculus book that you recommend ?

Science For Dreamers says:

Man even has a great praise from Albert Einstein, and that's my man!

Snared _ says:

5:00 Ew I really don't like the word "Biunique" here. It sounds like Biunique implies unique, but clearly that map is not unique. I like saying we have a <bijective> correspondence between Z and 2Z instead.

Science For Dreamers says:

Amazing astounding super!

Guilherme Fonseca-Statter says:

Have you ever heard about «Fundamental Principles of Mathematics» by Bento de Jesus Caraça?…

Mark Kosmowski says:

Your videos are inspiring me to looking into a master in math. Thank you.

Brian Drake says:

"Finding facts by using facts is maths." -brian padrick drake

Pronto says:

I guess this is a new take on 'audio books'?

Neil Pickup's wifes boyfriend says:

Okay, but who is mathematics?

Devrost says:

we need more books that actually focus on the thing they teach and not on filling the pages with exercises. another problem many school books have is that it is 90% talk without real informations or informations about the 100+ years of history that nobody wants to know when he is trying to "understand" maths or another subject.

Kathleen McKenzie says:

no, no, no,…. 11:11 x on left is a variable but x on right is supposed to be an actual number. this is like proving 0 = 1.

Kathleen McKenzie says:

what is the big bang theory? I disagree with a lot of math. 6:38 that's not a number line

James G says:

There is nothing quite like Mathematics.

Lamb Of Khorne says:

A language. Too easy.

H says:

Jonathan Popham says:

I started watching your channel in my community college precalculus class and now I've been accepted to study my BS in Mathematics at Indiana University this fall and I'm so excited. Math has been very helpful in my work as a software engineer and computer scientist. I will be reading this book! Thanks again, the math student community appreciates your support and benediction.

Green Focus says:

I read some where that mathematics was derived from the Greek "mathesis" which means "purifying the soul" and largely relates the process and rituals relating to the mind. Most of the biblican and academic terminologies like theology, theory, thesis, mathesis and mathematics are interrelated.

Joel Dick says:

You weren't laying in bed. You were lying in bed.

passarinho says:

It's so nice to see people being enthusiastic about math because all I hear from people my age and younger is that they hate math with a passion.
I'm 20, finishing the second year of computer engineering, and in the process of ditching my major for a degree in math instead. After 2 years of only caring about the calculus classes I finally realized what I truly want to learn, so I'm taking notes of all the books recommended in the comments to get me started. It's nice to feel like I'm on the right path for a change