The Map of Mathematics: An Animated Video Shows How All the Different Fields in Math Fit Together

If you’re a reg­u­lar Open Cul­ture read­er, you have 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. Enjoy.

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Relat­ed Con­tent 

Jour­ney to the Cen­ter of a Tri­an­gle: Watch the 1977 Dig­i­tal Ani­ma­tion That Demys­ti­fies Geom­e­try

How the Ancient Greeks Shaped Mod­ern Math­e­mat­ics: A Short, Ani­mat­ed Intro­duc­tion

How to Defeat the US with Math: An Ani­mat­ed North Kore­an Pro­pa­gan­da Film for Kids

Free Online Math Cours­es, a sub­set of our col­lec­tion, 1,700 Free Online Cours­es from Top Uni­ver­si­ties

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Comments (11)
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  • Mike says:

    What an excel­lent job. I’ve shared this with my friends that teach math­e­mat­ics.

  • Clayton says:

    Can any­one know it all? re:math map

    Which sin­gle top­ic would be best to learn for gen­er­al knowl­edge?

  • Dave says:

    Am I the only one both­ered that the equa­tion at the begin­ning of the video is incor­rect?
    cosθ=O/A is not cor­rect is it? I remem­ber that being the equa­tion for tan­gent.

  • Eric Jefferson says:

    You say that you know all math­e­mat­ics that’s not true because if you did know all math­e­mat­ics you would know that you can’t do physics with­out math­e­mat­ics if you knew how to con­fig­ure and use …
    Right angle cal­cu­lus trigonom­e­try.

  • Eric Jefferson says:

    My reply came out incor­rect and it’s spelling I said that you can do physics with­out math­e­mat­ics you would have to know if you knew how to do and con­fig­ure :

    right ankle cal­cu­lus trigonom­e­try.

  • Muhammad says:

    I think you made a cou­ple of mis­takes in math­e­mat­i­cal his­to­ry, and I hope it is out of igno­rance. The zero was invent­ed by Arabs (not in India as you men­tioned). Even the num­bers which you use every day in your life are Ara­bic num­bers (1,2,3 ..) and I think you should know that. Alge­bra which a major com­po­nent in math­e­mat­ics was devel­oped by the Arab schol­ar “Jaber Bin Haiyan”, which was named after him. The word “Algorithm”came after the math­e­mat­i­cal schol­ar “Alkhawariz­mi.” Yes, he was not an Arab, but made his con­tri­bu­tion dur­ing the Ara­bic civ­i­liza­tion, which he was a mem­ber of. Albert Ein­stein was orig­i­nal­ly Ger­man, but his con­tri­bu­tion is attrib­uted to Amer­i­ca sine he moved to USA. I do not trust “sci­en­tists” when they are biased.

  • Abdul Kareem says:

    Math­e­mat­ics start from basic

  • Airean says:

    These ear­ly count­ing sys­tems only saw the zero as a placeholder—not a num­ber with its own unique val­ue or prop­er­ties. A full grasp of zero’s impor­tance would not arrive until the sev­enth cen­tu­ry A.D. in India. There, the math­e­mati­cian Brah­magup­ta and oth­ers used small dots under num­bers to show a zero place­hold­er, but they also viewed the zero as hav­ing a null val­ue, called “sun­ya.” Brah­magup­ta was also the first to show that sub­tract­ing a num­ber from itself results in zero.

    From India, the zero made its way to Chi­na and back to the Mid­dle East, where it was tak­en up by the math­e­mati­cian Mohammed ibn-Musa al-Khowariz­mi around 773. It was al-Khowariz­mi who first syn­the­sized Indi­an arith­metic and showed how the zero could func­tion in alge­bra­ic equa­tions, and by the ninth cen­tu­ry the zero had entered the Ara­bic numer­al sys­tem in a form resem­bling the oval shape we use today

  • Miles Fidelman says:

    This is phe­nom­e­nal.

    A great his­tor­i­cal per­spec­tive on how math devel­oped over time.

    What might make a nice fol­low-on is a “learn­ing path” — a sur­vey cur­ricu­lum (read­ing list) that goes from “foun­da­tions” through the entire field (at a high lev­el) based on how the con­cepts flow from each oth­er, now that we know all this stuff.

  • Mark says:

    The first ever use of zero we have dis­cov­ered, was Indi­an.
    Whilst the word alge­bra is Ara­bic, the first record­ed use is Baby­lon­ian.

    I did­n’t both­er check­ing the rest. Source: his­to­ry of maths dot org.

  • MohammedsFeet says:

    Arabs did so much for civ­i­liza­tion before the onset of the Mooslum scourge. It was Mo Ham Mood him­self that rede­fined the Arab peo­ple and made them worse off unfor­tu­nate­ly. As an Arab, I whole­heart­ed­ly denounce the false prophet and am bet­ter for it. The whole world would be.

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