Mathematics in the 21st Century

I’m giving a talk in the Topos Institute Colloquium on Thursday March 25, 2021 at 18:00 UTC. That’s 11:00 am Pacific Time.

I’ll say a bit about the developments we might expect if mathematicians could live happily in an ivory tower and never come down for the rest of the century. But my real focus will be on how math will interact with the world outside mathematics.

Mathematics in the 21st Century

Abstract. The climate crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that no physical quantity can grow exponentially forever. This transformation may affect mathematics—and be affected by it—just as dramatically as the agricultural and industrial revolutions. After a review of the problems, we discuss how mathematicians can help make this transformation a bit easier, and some ways in which mathematics may change.

You can see my slides here, and click on links in dark brown for more information. You can watch the talk on YouTube here, either live or recorded later:

You can also watch the talk live on Zoom. Only Zoom lets you ask questions. The password for Zoom can be found on the Topos Institute Colloquium website.

15 Responses to Mathematics in the 21st Century

  1. allenknutson says:

    Do you have more planned in the series? Literature in the 21st century, Geology, etc.? Anyway see you then!

  2. Anna Knörr says:

    “how math will interact with the world outside mathematics”… Will you build a category of mathematicians? :p

  3. I’m giving a talk in the Topos Institute Colloquium on Thursday March 25, 2021 at 18:00 UTC. I believe that’s 11:00 am Pacific Time.

    The time-zone difference between London and California is 8. That would make it 10 o‘clock in the morning in California. However, IIRC the States have already switched to daylight-saving time, but Europe hasn‘t. So that would make it 11 o‘clock in the Pacific time zone.

    Note that Europe switches this coming weekend, then it will be back to 8 hours difference instead of 7, at least to local DST in Europe if not to UTC.

    A couple of decades ago, the UK switched to and from DST at different dates than the Continent. I wonder if that will return after Brexit?

    The EU recently decided (via a very undemocratic process) to abolish switching to and from DST. While I agree that it would be good to abolish switching to and from DST, that wasn‘t the way to do it. However, they didn‘t abolish DST, only the switching, and left it up to each country if they want to be permanently on DST or permanently on normal time, That is just plain stupid.

    One might think that it wouldn‘t matter, at least if one agrees that DST isn’t needed, and the default should be normal time. However, countries in the far west or far east of Europe which are in the time zone as most of Europe but should really be in another use the switch to ameliorate it being really dark in the morning in winter or really too light in the summer. They wouldn‘t have that problem if they were in the correct time zone. While it might make sense for countries with a long border to be in the same time zone even if they shouldn‘t (in which case they have a long north-south extent, so have variation for that reason anyway), in many cases it is just a desire to be in the same time zone with most of Europe. (In the case of Spain, Hitler and Mussolini wanted to be in the same time zone.)

    • John Baez says:

      Philip wrote:

      The time-zone difference between London and California is 8. That would make it 10 o‘clock in the morning in California. However, IIRC the States have already switched to daylight-saving time, but Europe hasn‘t. So that would make it 11 o‘clock in the Pacific time zone.

      Right. That’s the calculation I did, and the organizers have now confirmed it.

  4. Keith Harbaugh says:

    John, regarding your comment
    (“The challenge starts in kindergarten.”)
    on improving mathematical education,
    I have two questions:

    Are there one or several blogs or websites that you feel are useful on this subject?
    Your various activities have of course addressed various generally advanced aspects of this.
    But I would like to see you write a post here dedicated to K-12 math education.
    In particular, an expandable, editable post (starting perhaps merely as a placeholder) to which you could add ideas and thoughts as they come to you, as they surely will.
    And, of course, people could add comments.

    • John Baez says:

      I don’t know enough about K-12 math education to write a blog article on this, and I don’t read blogs about math education. Maybe I should start by thinking about this a bit more. (I feel I already have too many projects going–and not enough time to do most of them!)

      I feel math teaching is often badly done, and I’ve written up some advice on how to do it better:

      How to teach stuff.

      I have a feeling professional educators live in a different universe than I do, because they say a lot of complicated stuff, but rarely this stuff.

      • Keith Harbaugh says:

        Here’s one idea.
        There is an adjoint triple between (the integers Z) and (the reals R): ceiling, inclusion, floor.
        Illustrate this in 0-D (i.e. first-order logic), 1-D, and 2-D (2-categorical) diagrams.

        Both Z and R have various familiar structures, plus, times, max, min.
        Discuss the extent to which the parts of the adjoint triple preserve those structures.
        Mention the words and phrases that generalize all this.

        The point is to exemplify general “abstract” concepts in a simple, concrete, familiar setting.

  5. Keith Harbaugh says:

    There at about 13:00 in the revised video

    you mention the study of commutative monoids in an arbitrary SMC (symmetic monoidal category) as a generalization of commutative algebra.
    Could you suggest references for that generalization?
    Thanks.

    • John Baez says:

      The generalization of algebraic geometry to commutative monoids in a symmetric monoidal category is discussed here:

      • Bertrand Toen, Michel Vaquie, Under Spec Z.

      This paper will also give you a chance to practice your French!

      My slides include a link to Jacob Lurie’s paper where he generalizes this to symmetric monoidal (∞,1)-categories. That may be easier or harder than French.

      • Keith Harbaugh says:

        Thanks! I tried listening to the names you verbalized after that comment, but couldn’t make them out (Tune?). Seeing them in writing (with a link even!) does the trick.

        And thanks very much for your many contributions to communicating math, physics, and environmental issues!

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