The Map of Mathematics: Animation Shows How All the Different Fields in Math Fit Together

Back in December, you hopefully thoroughly immersed yourself in The Map of Physics, an animated video–a visual aid for the modern age–that mapped out the field of physics, explaining all the connections between classical physics, quantum physics, and relativity.

You can’t do physics without math. Hence we now have The Map of Mathematics. Created by physicist Dominic Walliman, this new video explains “how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.” Watch the new video above. You can buy a poster of the map here. And you can download a version for educational use here.

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Comments (10)
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  • vluong says:

    Please make another version regarding Mathematics applied in Economics.

    Thank you & Best Regards,
    Luong Vu

  • Mladen says:

    Very good overview. However, did you not omit Functional analysis with its Hilbert space Projection theorem?

  • Elizabete says:

    Boa noite, gostaria de receber mais artigos vossos sobre matemática.

  • Lorraine grindstaff says:

    I haven’t a clue what any of this means but it is so awesome! But I do not have to understand it to appreciate it. EVERTHING is math!


    I am very impressed! Thank you so much!!!

  • Susanne Kestner says:

    Just beautiful!
    Thank you.

  • Melissa Cleland says:

    I really enjoyed the video and the connections made within the realm of math.

    I did notice an error about the earliest note of “zero.” Here’s a reference for the Maya who lived in Central America

    “…Perhaps we should note at this point that there was another civilisation which developed a place-value number system with a zero. This was the Maya people who lived in central America, occupying the area which today is southern Mexico, Guatemala, and northern Belize. This was an old civilisation but flourished particularly between 250 and 900. We know that by 665 they used a place-value number system to base 20 with a symbol for zero. However their use of zero goes back further than this and was in use before they introduced the place-valued number system. This is a remarkable achievement but sadly did not influence other peoples.”

    “Almost certainly the reason for base 20 arose from ancient people who counted on both their fingers and their toes. Although it was a base 20 system, called a vigesimal system, one can see how five plays a major role, again clearly relating to five fingers and toes. In fact it is worth noting that although the system is base 20 it only has three number symbols (perhaps the unit symbol arising from a pebble and the line symbol from a stick used in counting). Often people say how impossible it would be to have a number system to a large base since it would involve remembering so many special symbols. This shows how people are conditioned by the system they use and can only see variants of the number system in close analogy with the one with which they are familiar. Surprising and advanced features of the Mayan number system are the zero, denoted by a shell for reasons we cannot explain, and the positional nature of the system. However, the system was not a truly positional system as we shall now explain…”

    Thank you for time and interest.
    Melissa Cleland

  • Geoffrey Roulet says:

    This is an excellent overview. I was very pleased to see that you mentioned Gödel’s Incompleteness Theorems and the fact that mathematics is essentially a human construct. Mathematics is all too often presented as the model of “absolute truth”.

  • Punyavee says:

    This is impressive. Thanks for making a good overview of mathematics universe.

  • Astra says:

    Perhaps it would’ve been interesting to observe – and reflect upon – differences occurring when a mathematician draws a corresponding diagram, as compared to what D. Walliman, a physicist, did draw!

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