The Map of Mathematics is the definitive guide to the subject.

34 Views· 12/13/22
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The entire field of mathematics is summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

SchoolTube highlights high-quality Math videos that showcase the foundational subject of Mathematics or ‘Math’. Mathematics (from Ancient Greek μάθημα; máthēma: ‘knowledge, study, learning) is an area of knowledge that includes such topics as numbers (arithmetic and number theory), formulas, and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis). Most mathematical activity involves the use of pure reason to discover or prove the properties of abstract objects, which consist of either abstraction from nature or—in modern mathematics—entities that are stipulated with certain properties, called axioms. A mathematical proof consists of a succession of applications of some deductive rules to already known results, including previously proved theorems, axioms, and (in the case of abstraction from nature) some basic properties that are considered true starting points of the theory under consideration. SchoolTube Math videos feature teachers academics, students, and publishing professionals sharing their knowledge and learning experiences.

The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.

#mathematics #DomainOfScience

If you would like to buy a poster of this map, they are available here:
North America:
Everywhere else:
French version:
Spanish Version:

I have also made a version available for educational use which you can find here:

To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!

1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).

2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.

3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.

4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it:

5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.

Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much.

Here are links to some of the sources I used in this video.

Summary of mathematics:
Earliest human counting:
First use of zero:
First use of negative numbers:
Renaissance science:
History of complex numbers:
Proof that pi is irrational:

Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.

Frontiers of Space:
Atomic Adventure:
Intergalactic Activity Book:
Solar System App:

Find me on twitter, instagram, and my website:

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