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.

If you would like to sign up for Open Culture’s free email newslet­ter, please find it here. Or fol­low our posts on Threads, Face­book, BlueSky or Mastodon. If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Relat­ed Con­tent:

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

Free Math Text­books

Math­e­mat­ics Made Vis­i­ble: The Extra­or­di­nary Math­e­mat­i­cal Art of M.C. Esch­er

Cit­i­zen Maths: A Free Online Course That Teach­es Adults the Math They Missed in High School

by | Permalink | Comments (10) |

Sup­port Open Cul­ture

We’re hop­ing to rely on our loy­al read­ers rather than errat­ic ads. To sup­port Open Cul­ture’s edu­ca­tion­al mis­sion, please con­sid­er mak­ing a dona­tion. We accept Pay­Pal, Ven­mo (@openculture), Patre­on and Cryp­to! Please find all options here. We thank you!

Comments (10)
You can skip to the end and leave a response. Pinging is currently not allowed.
  • 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!

Leave a Reply

Open Culture was founded by Dan Colman.