6 ms·

How have lack of travel and increased social isolation affected mathematics?

28 points by theafh 7y ago

vidanay 7y ago
Those books look like they'd all fit on $300 worth of shelving from IKEA. The library probably cost $800k to remodel.
- throwphoton 7y ago
  You could also fit a large assortment of gourmet meats into a stack of shoeboxes, but it's preferable to display them in a way that whets the observer's appetite.
  - dhosek 7y ago
    I don't know, I find a bunch of yellow-spined Springer texts to be appetizing just shelved together. I didn't realize the shelves weren't empty until I saw the top comment and went back to look.
- Smaug123 7y ago
  My reaction to the various pictures, for what it's worth, was "what a beautiful place - perhaps it needs more blackboards, but I would love to do maths there".
- dubya 7y ago
  I'm not sure how big Oberwolfach's library is, but the first pic looks more like a (somewhat fancy) journals/new acquisitions display than like primary storage.
lidHanteyk 7y ago
While folks might not be getting many papers done, the research has hardly stopped. There are many many maths seminars [0] moved online. [0] https://golem.ph.utexas.edu/category/2020/04/online_seminar_lists.html https://golem.ph.utexas.edu/category/2020/04/online_seminar_...
- williamstein 7y ago
  Indeed - Check out the amazing https://mathseminars.org/ https://mathseminars.org/
btrettel 7y ago
> “Mathematics used to be a much more individual activity,” Minsky said. “Maybe in the next year or so, we’ll be back to some solo projects.” Seems that most research used to be more individual. I'm not sure why research has shifted towards being collaboration-heavy and I don't think that this has necessarily improved the quality of science. In my experience, papers with many authors tend to be worse. (Could be field specific.) A few months ago I got reviews back for a paper I wrote which had only me as the author and one of the reviewers was suspicious of this and brought it up in the review. They didn't say what they were suspicious of but I'd guess that they assumed that the work couldn't have been done by an individual. I replied that the work was done one my own and anyone with a small contribution not worthy of authorship was mentioned in the acknowledgements. I'm still waiting to hear if that would satisfy the reviewer.
- nil-sec 7y ago
  Many current problems are simply too complex to be solved by a single person, often because it requires expertise from very different fields. High energy physics, biology and neuroscience come to mind. There is not a single person who understands all aspects of CERN. Likewise there isn’t a single person who understands how to 1. Build a large scale Electron microscope to acquire high res images of an entire brain 2. Analyze hundreds of terabytes of data to make these images usable and 3. Analyze the results which would require highly specific domain knowledge of neural circuits or other biological features of the system you are looking at. My experience is opposite to yours. You are lost as a lone researcher in many fields and the best papers these days are written by enormous collaborations.
  - redis_mlc 7y ago
    The topic is math, not building megamachines. I've been following the progress in number theory proofs for the past few years, and email and forums have worked fine.
    - nil-sec 7y ago
      The parent explicitly talks about science in general. There is a tendency of some (often of those outside of science) that feel like science is getting worse over time and nothing of value is found anymore. The parent seems to echo this sentiment and gives very shallow anecdotes to make his point. Still it is the top comment as of writing. It’s just plain wrong in my opinion.
albertshin 7y ago
If you're interested, there's a paper on a more "extreme" situation that mainly related to Soviet mathematics developing solely within USSR apart from the rest of the world (see the "Luzin affair"). The paper examines the aftermath. https://academic.oup.com/qje/article-abstract/127/3/1143/1921708?redirectedFrom=fulltext https://academic.oup.com/qje/article-abstract/127/3/1143/192...
- redis_mlc 7y ago
  Note: that's in an economics journal, "The Quarterly Journal of Economics". Not sure what, if anything, that has to do with math.
  - albertshin 7y ago
    Yes, it's one of the more reputable economics journals. Modern economics seeks to answer research questions (e.g. impact of research collaboration and global knowledge diffusion) using quasi-experimental settings (e.g. the unexpected fallout of the Luzin affair to mathematics research). Would be surprised to find this in a math journal if anything!
redis_mlc 7y ago
> No one I talked to had gotten much new math done. They were preoccupied with the news, distracted by kids at home, and pulled between online Zoom meetings. So, it's a time-management issue, nothing to do with math here.
mr_gibbins 7y ago
I have a genuine question, as someone with an interest in mathematics but alas, no natural ability in the area. Is there some kind of 'map' or list of mathematics areas, problems, etc. that professional mathematicians consult for ideas when conducting research? Likewise physics? It strikes me that we've collectively had at least 5,000 years of math-related research stretching back to ancient civilisations. Surely most discoveries have been made? How much more math ore is there to mine? When I read Richard Feynman claim (paraphrasing) that the joy of physics, math is the theoretical discovery of new knowledge without applications, I wonder where on earth today's mathematicians are looking for new ideas and discoveries? And how do they get research funding? As a CS researcher, funding is hard to come by if I don't propose a tangible product. When I say, e.g., let's re-examine the relational model and extend it, or do something interesting in AI, the question is always the same: what is the product? Mathematicians on the other hand never create a 'product', so I'm confused who, why and where they get their money? Lots of questions, I know, but I'm missing something here.
- miscPerson 7y ago
  I only really know about the company-sci touching parts, but — Mathematics didn’t have a strong notion of proof until the late 1800s/early 1900s. Contradictory “proofs” in calculus created a need for a more rigorous system of reasoning. (It took until the 1950s to formalize what an ‘infinitesimal’ is — but those were used in early calculus prior to limits.) That gave us electronic computers, as the effort to reduce proofs to things that could be mechanized bore fruit. Every program is a proof! Since then, the idea of proof and structuring mathematics has been radically redefined — introducing things like category theory and type theory as alternatives to set theory, while studying the impact of certain axioms and developing tools around “reverse mathematics”, which is fitting a set of axioms to the theorems you want to be true. Modern mathematics is working on the study of logic topology, extending our reasoning tools to deal with complexities around proving equality in the hopes we can automatically verify mathematics. These tools overlap heavily with AI research. The applications here are what you might guess: new AI methods, data analysis methods, verification of software, etc. The DOD has paid a fair bit to support that research into software verification, for instance. The NSF and others fund “big data” analysis. I’m less familiar with other parts of mathematics, but — The study of knot theory has impacts for physical sciences, from particle physics (anyons) to fluid dynamics. In particular, there’s some work to be done in higher order knot theory and computational knot theory (ie, how to be efficient). MSFT is building a quantum computer based on this — and has suggested that higher order knots might not require as expensive of hardware. In number theory, we still don’t know much about almost all real numbers. Things like Chaitins constant exist — and such uncomputable, normal numbers form the bulk of the reals — but we don’t really know how to get our hands on them. In less exotic research, elliptic curves are used in cryptography. There’s some work I don’t quite understand in building out a homomorphic encryption — where we can operate on encrypted data. In many areas, we’re still working through the algebra-geometry correspondence, which we got hints of 400 years ago but only formalized once topology and category theory were invented — and still are building tooling around. And there’s lots of areas I have no idea about — but I assume are being similarly productive. Ones that I know of, but can’t comment on: fractals, differential equations, bifurcation theory, and chaos theory.

28 points by theafh 7y ago

vidanay 7y ago

Those books look like they'd all fit on $300 worth of shelving from IKEA. The library probably cost $800k to remodel.

throwphoton 7y ago
You could also fit a large assortment of gourmet meats into a stack of shoeboxes, but it's preferable to display them in a way that whets the observer's appetite.
- dhosek 7y ago
  I don't know, I find a bunch of yellow-spined Springer texts to be appetizing just shelved together. I didn't realize the shelves weren't empty until I saw the top comment and went back to look.
Smaug123 7y ago
My reaction to the various pictures, for what it's worth, was "what a beautiful place - perhaps it needs more blackboards, but I would love to do maths there".
dubya 7y ago
I'm not sure how big Oberwolfach's library is, but the first pic looks more like a (somewhat fancy) journals/new acquisitions display than like primary storage.

lidHanteyk 7y ago

While folks might not be getting many papers done, the research has hardly stopped. There are many many maths seminars [0] moved online. [0] https://golem.ph.utexas.edu/category/2020/04/online_seminar_lists.html https://golem.ph.utexas.edu/category/2020/04/online_seminar_...

williamstein 7y ago
Indeed - Check out the amazing https://mathseminars.org/ https://mathseminars.org/

btrettel 7y ago

> “Mathematics used to be a much more individual activity,” Minsky said. “Maybe in the next year or so, we’ll be back to some solo projects.” Seems that most research used to be more individual. I'm not sure why research has shifted towards being collaboration-heavy and I don't think that this has necessarily improved the quality of science. In my experience, papers with many authors tend to be worse. (Could be field specific.) A few months ago I got reviews back for a paper I wrote which had only me as the author and one of the reviewers was suspicious of this and brought it up in the review. They didn't say what they were suspicious of but I'd guess that they assumed that the work couldn't have been done by an individual. I replied that the work was done one my own and anyone with a small contribution not worthy of authorship was mentioned in the acknowledgements. I'm still waiting to hear if that would satisfy the reviewer.

nil-sec 7y ago
Many current problems are simply too complex to be solved by a single person, often because it requires expertise from very different fields. High energy physics, biology and neuroscience come to mind. There is not a single person who understands all aspects of CERN. Likewise there isn’t a single person who understands how to 1. Build a large scale Electron microscope to acquire high res images of an entire brain 2. Analyze hundreds of terabytes of data to make these images usable and 3. Analyze the results which would require highly specific domain knowledge of neural circuits or other biological features of the system you are looking at. My experience is opposite to yours. You are lost as a lone researcher in many fields and the best papers these days are written by enormous collaborations.
- redis_mlc 7y ago
  The topic is math, not building megamachines. I've been following the progress in number theory proofs for the past few years, and email and forums have worked fine.
  - nil-sec 7y ago
    The parent explicitly talks about science in general. There is a tendency of some (often of those outside of science) that feel like science is getting worse over time and nothing of value is found anymore. The parent seems to echo this sentiment and gives very shallow anecdotes to make his point. Still it is the top comment as of writing. It’s just plain wrong in my opinion.

albertshin 7y ago

If you're interested, there's a paper on a more "extreme" situation that mainly related to Soviet mathematics developing solely within USSR apart from the rest of the world (see the "Luzin affair"). The paper examines the aftermath. https://academic.oup.com/qje/article-abstract/127/3/1143/1921708?redirectedFrom=fulltext https://academic.oup.com/qje/article-abstract/127/3/1143/192...

redis_mlc 7y ago
Note: that's in an economics journal, "The Quarterly Journal of Economics". Not sure what, if anything, that has to do with math.
- albertshin 7y ago
  Yes, it's one of the more reputable economics journals. Modern economics seeks to answer research questions (e.g. impact of research collaboration and global knowledge diffusion) using quasi-experimental settings (e.g. the unexpected fallout of the Luzin affair to mathematics research). Would be surprised to find this in a math journal if anything!

redis_mlc 7y ago

> No one I talked to had gotten much new math done. They were preoccupied with the news, distracted by kids at home, and pulled between online Zoom meetings. So, it's a time-management issue, nothing to do with math here.

mr_gibbins 7y ago

I have a genuine question, as someone with an interest in mathematics but alas, no natural ability in the area. Is there some kind of 'map' or list of mathematics areas, problems, etc. that professional mathematicians consult for ideas when conducting research? Likewise physics? It strikes me that we've collectively had at least 5,000 years of math-related research stretching back to ancient civilisations. Surely most discoveries have been made? How much more math ore is there to mine? When I read Richard Feynman claim (paraphrasing) that the joy of physics, math is the theoretical discovery of new knowledge without applications, I wonder where on earth today's mathematicians are looking for new ideas and discoveries? And how do they get research funding? As a CS researcher, funding is hard to come by if I don't propose a tangible product. When I say, e.g., let's re-examine the relational model and extend it, or do something interesting in AI, the question is always the same: what is the product? Mathematicians on the other hand never create a 'product', so I'm confused who, why and where they get their money? Lots of questions, I know, but I'm missing something here.

miscPerson 7y ago
I only really know about the company-sci touching parts, but — Mathematics didn’t have a strong notion of proof until the late 1800s/early 1900s. Contradictory “proofs” in calculus created a need for a more rigorous system of reasoning. (It took until the 1950s to formalize what an ‘infinitesimal’ is — but those were used in early calculus prior to limits.) That gave us electronic computers, as the effort to reduce proofs to things that could be mechanized bore fruit. Every program is a proof! Since then, the idea of proof and structuring mathematics has been radically redefined — introducing things like category theory and type theory as alternatives to set theory, while studying the impact of certain axioms and developing tools around “reverse mathematics”, which is fitting a set of axioms to the theorems you want to be true. Modern mathematics is working on the study of logic topology, extending our reasoning tools to deal with complexities around proving equality in the hopes we can automatically verify mathematics. These tools overlap heavily with AI research. The applications here are what you might guess: new AI methods, data analysis methods, verification of software, etc. The DOD has paid a fair bit to support that research into software verification, for instance. The NSF and others fund “big data” analysis. I’m less familiar with other parts of mathematics, but — The study of knot theory has impacts for physical sciences, from particle physics (anyons) to fluid dynamics. In particular, there’s some work to be done in higher order knot theory and computational knot theory (ie, how to be efficient). MSFT is building a quantum computer based on this — and has suggested that higher order knots might not require as expensive of hardware. In number theory, we still don’t know much about almost all real numbers. Things like Chaitins constant exist — and such uncomputable, normal numbers form the bulk of the reals — but we don’t really know how to get our hands on them. In less exotic research, elliptic curves are used in cryptography. There’s some work I don’t quite understand in building out a homomorphic encryption — where we can operate on encrypted data. In many areas, we’re still working through the algebra-geometry correspondence, which we got hints of 400 years ago but only formalized once topology and category theory were invented — and still are building tooling around. And there’s lots of areas I have no idea about — but I assume are being similarly productive. Ones that I know of, but can’t comment on: fractals, differential equations, bifurcation theory, and chaos theory.