Mathematics for Humanity: a Plan

I’m working with an organization that may eventually fund proposals to fund workshops for research groups working on “mathematics for humanity”. This would include math related to climate change, health, democracy, economics, AI, etc.

I can’t give details unless and until it solidifies.

However, it would help me to know a bunch of possible good proposals. Can you help me imagine some?

A good proposal needs:

• a clearly well-defined subject where mathematics is already helping humanity but could help more, together with

• a specific group of people who already have a track record of doing good work on this subject, and

• some evidence that having a workshop, maybe as long as 3 months, bringing together this group and other people, would help them do good things.

I’m saying this because I don’t want vague ideas like “oh it would be cool if a bunch of category theorists could figure out how to make social media better”.

I asked for suggestions on Mathstodon and got these so far:

figuring out how to better communicate risks and other statistical information,

developing ways to measure and combat gerrymandering,

improving machine learning to get more reliable, safe and clearly understandable systems,

studying tipping points and ‘tipping elements’ in the Earth’s climate system,

creating higher-quality open-access climate simulation software,

using operations research to disrupt human trafficking.

Each topic already has people already working on it, so these are good examples. Can you think of more, and point me to groups of people working on these things?


The International Centre for Mathematical Sciences is indeed going ahead with this plan! Read more about it here:

Mathematics for Humanity.

30 Responses to Mathematics for Humanity: a Plan

  1. Goff Smeets says:

    John, the project Math for Humanity is the umpteenth thinktanking for humanity. My proposal is to have a mathematical section on the dynamics of mathematical thinktanking. Go for it.

    • John Baez says:

      Give me a list of people working on this.

      • Goff Smeets says:

        John, there isn’t such a list. Mathematicans don’t reflect mathematically on what they’re doing for humanity. Economicist don’t reflect economicacally what their work does for humanity. Climatologists don’t reflect on the impact of their CO2 driven research on CO2 accumulation. So much for the epistemological elephant in the scientific room. There’s no list of people you’re asking for, not that I know of.

      • John Baez says:

        I was kidding: I didn’t expect such a list. But my post asked for lists of people, and you weren’t giving me one.

        The point of this blog post is not to initiate research that isn’t being done, no matter how great it would be. It’s to find groups of people already working on different aspects what you might call “mathematics for humanity” (the meaning of which I explained in the blog post), who might apply for funding to have a workshop.

  2. jo rem says:

    Math for humanity=applied mathematics.

  3. Another idea would be developing robust methods for bridging-based ranking in recommender systems.

    https://www.belfercenter.org/publication/bridging-based-ranking
    https://twitter.github.io/communitynotes/ranking-notes/

    There’s at least a couple of people working on this, and Twitter recently (pre-Musk) deployed the largest scale version of it with their Birdwatch / Community Notes feature, but there’s still a lot more work that needs doing.

    • John Baez says:

      Thanks! I love the idea of improving social media, since it seems crucial to well-functioning politics, so any successful mathematical efforts to do that would be exactly the sort of thing I’m looking for… but I know very little about this, so this is much appreciated.

  4. For helping to understand the magnitude and patterns of violations to human rights, Human Rights Data Analysis Group implements the cutting-edge in statistics and computation. Recently, Colombian teams at Truth Commission and at Special Jurisdiction for Peace were trained to do these kind of research. The director of this ONG is Patrick Ball, who leads this work along two years.

  5. Michael says:

    Are you familiar with the work of the QSIDE institute? They try to apply technical math/stat/data science knowledge to real social problems. Projects include analyzing gender discrepancies within the mathematical profession, studying racial disparities in sentencing data from criminal courts, and much more: https://qsideinstitute.org/

  6. This is related to the idea of making ML safe and reliable, but in a different spirit. There are quite a few logical and decision theory problems on how a system that has access to its own program would behave in an open environment. See the papers in https://intelligence.org/, in particular those about embedded agency https://arxiv.org/abs/1902.09469. This approach would be needed if we intend to have powerful general intelligence and we want to understand its behavior.

    Alternatively, there is the more applied approach of developing techniques to learn from human preferences (see https://humancompatible.ai/research), or make the learned representations more robust and generalizable (eg, via causal modeling perhaps).

    All of this is in the topic of making sure AGI is beneficial if we develop it: https://80000hours.org/problem-profiles/artificial-intelligence/

  7. nick says:

    There are still theoretical aspects of the coupled atmosphere-ocean system that need to be worked out (see, eg, https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019AV000129) and could benefit from a tighter collaboration between mathematicians and earth scientists.

    For example, Rick Salmon (SIO) has been bringing more geometry into fluid mechanics problems related to the ocean, and turbulence in general. Rick wrote up some lecture notes (http://www-pord.ucsd.edu/rsalmon/More.Lectures.pdf), see particularly chapters 6/7, that highlight some of these discussions (these notes are a few years old and some of these ideas have evolved). I can list specific problems these approaches could help with if that is deemed useful.

    This might be too niche for the funding agency you are interfacing with, but as a scientist working on these problems, a tighter collaboration with mathematicians (which seems more accessible in Europe) seems like it would prove useful.

    • John Baez says:

      Thanks very much! This is not necessarily too niche. Something tightly focused that really gets something done is better, at least in my opinion, than a more gaseous workshop where people talk a lot and leave without accomplishing much.

      I hope I can get in touch if I need more details. Right now I’m casting a rather wide net.

    • Chapter 6 of the Rick Salmon notes features this parenthetical comment:

      “(See for example George Stokes’s uncomprehending review of a Reynolds paper in the book A Voyage Through
      Turbulence, p. 26.)”

      Fascinating advice therein.

    • This document and server http://www-pord.ucsd.edu/rsalmon/More.Lectures.pdf is no longer publicly available. Perhaps the author deemed it private and intended for only for class-work. In any case, I am working on large scale ocean and atmospheric behavior that applies some of these novel concepts.

  8. Michelle Gelfand at Stanford is studying culture and norms using computational models:
    https://www.michelegelfand.com/academic-culture

    Click to access de2017understanding.pdf

    Peter Turchin (univ. of Connecticut) is using mathematical models to study history:
    http://peterturchin.com/cliodynamics/
    https://www.science.org/doi/10.1126/sciadv.abn3517

    I know you’re already familiar with Safa Motesharrei and the HANDY model, which i think is related, as a research topic.

    A nice side outcome of this research is that shows how sciences (specifically math) and humanities can work together, enhancing their respective strengths.

    • John Baez says:

      Thanks, these are very helpful! And I’d sort of forgotten the HANDY model.

      There are other aspects of this big project, if it’s realized, that will have even more direct focus on mathematics and the humanities (as opposed to ‘humanity’).

  9. David Hewins says:

    In economics I advocate low debt capitalism. Socialism has many advocates but implementation has never worked. So imagine a topos containing one or more transaction spaces. Synchronic morphisms map current prices to current prices. Adjoints are arbitrage? Diachronic morphisms map prices transtemporally. Adjoints are investments? I hope we can work out the math maximizing competitive but friendly participation in this topos!

  10. Josh Tan says:

    We actually do some work applying compositional game theory to institutional design at Metagov, and are using it to build stuff like (smart) contract models. This is ultimately intended to support more democratic, decentralized, and equitable forms of governance, especially over open-source technology or other public goods.

  11. Bruce Smith says:

    Scott Aaronson’s latest blog post (a talk on AI Safety) seems relevant, and lists some examples of existing research that might fit in. You could comment there about this and probably get some more concrete suggestions.

    • John Baez says:

      Hi! Yes, I read Scott’s blog. So yes, I should email him and ask for suggestions. I am not eager to join his mosh pit of blog comments… right now on that same article people are talking about holocaust deniers and whether Trump is an antisemite.

      • Bruce Smith says:

        True, but they are not mixing those with the AI-related comments (so it’s easy to skip them, and no one will reply to you in a related way), and some of the AI-related comments are pretty interesting. The advantage of a comment over an email is that the commenters (including lurkers) collectively know a lot more good answers to your question that Scott alone does. Anyway it’s obviously your call — I won’t argue (beyond what I just did).

  12. enricouva says:

    Not to undermine the worthwhile efforts of your organization, I have to point out that mathematics already exists for humanity. Infinite applications aside, it is one of the best antidotes for a world in which instinct and emotion have too much say. :)

    • John Baez says:

      Mathematics already exists, but there is a lot of new mathematics to be created, and a lot of new applications of mathematics to be developed. That’s what the workshops are for.

  13. Mike McCracken says:

    Hi John,
    This may be more of a meta-project that would be informed by some/all of topics mentioned above:

    Developing contextual secondary and intro-college mathematics education that presents mathematics as a tool for humanity.

    It’s sad to work with so many bright college students that see mathematics (you know, with its focus on proving things and being sure that techniques are sound) as being at odds with progress in the sciences (where we like to play it fast and loose to crank out the papers). I had a conversation with a student today who is trying to decide between pursuing mathematics “or science”. I don’t think that this is a good way to frame a career choice.

    I think that this is being worked on by pockets of people here and there. Recent culture wars over (e.g.) high school textbooks applying math/data science to analyze (e.g.) racial/demographic discrimination or climate change have perhaps distracted from the real education need for these approaches.

    Many of the proposed topics are exciting, but this is a project that could prepare the new generations to adopt “mathematics for humanity” as the default, rather than a zany new idea.

    Thanks for doing this work.

  14. John Baez says:

    The Mathematics for Humanity project has started, and you can read more about it—and talk more about it!—here.

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