
How have lack of travel and increased social isolation affected mathematics? - theafh
https://www.quantamagazine.org/how-has-coronavirus-affected-mathematics-20200428/
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btrettel
> “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
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
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
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.

~~~
btrettel
I didn't argue that science is getting worse in general and that nothing
valuable is being done now, and that's not what I believe. I could see how
someone could infer the former from the number of authors per paper increasing
and me thinking that papers with many authors tend to be worse. My experience,
at I said, could be field specific. (I work in fluid dynamics.) My view is
more that science has never been particularly well done as a whole, though
some recent things like the reproducibility crisis in social science and
verification and validation in engineering have been promising.

That some projects require a large amount of expertise that no single person
is likely to have is true. But there are disadvantages to having more authors
as well, e.g., "design by committee" immediately comes to mind. And I don't
think a majority of current projects require expertise that no individual
could have to an extent that would explain why collaboration is expected in
science. Ultimately I think a mix of the two would be ideal for science in
general, with a larger contribution from individuals than is seen at present.

Also: If my example is a shallow anecdote than your CERN example is as well. I
don't have hard data on any of this and you didn't mention any either. I'd be
happy to look at any hard data that exists, but I don't know if there is any.

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redis_mlc
> 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.

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mr_gibbins
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.

~~~
GaussBonnet
Background in pure math here. Generally researchers learn about what problems
are fashionable as they talk to others in the field. As a PhD student, your
advisor should give you ideas for problems to work on. Solutions to old
problems tend to open up new lines of inquiry. It's a potentially infinite
process, with the only limit being the capacity of the human mind.

The odd perfect number problem has been unsolved for thousands of years:

[https://en.wikipedia.org/wiki/Perfect_number](https://en.wikipedia.org/wiki/Perfect_number)

Why would anyone want to know the answer to this problem? The truth is that
the motivation for most pure math research is purely aesthetic. You could also
ask arts or english departments "How can you apply your paintings or
novels?!?". Some mathematicians (mostly geometers and topologists) are
inspired by problems in physics, but most aren't. In truth you never know what
structure or theorem might have some future application; number theory was
totally "useless" until modern cryptography made (some of) it useful.

For just a tiny taste of one small area of modern math, I dare you to click on
any of the links here:

[https://en.wikipedia.org/wiki/Floer_homology](https://en.wikipedia.org/wiki/Floer_homology)

We are flush with structures to investigate. The idea that "most discoveries
have been made" is nonsensical in a domain where the discoveries to be made
are literally infinite. To give a hint as to the infinite nature of
mathematical inquiry, you probably are familiar with the idea of a function
mapping a number to another number. A good deal of modern math is involved
with much higher order functions; we can have functions that map functions to
numbers, functions to functions, functions to spaces, and so on and so on. And
then we can consider functions between those functions (and so on). Category
theory is an attempt to give a framework to some of these "meta" relations. It
should be obvious there is no limit to these structures and no limit to the
number of problems one could pose about them.

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albertshin
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/127/3/1143/192...](https://academic.oup.com/qje/article-
abstract/127/3/1143/1921708?redirectedFrom=fulltext)

~~~
redis_mlc
Note: that's in an economics journal, "The Quarterly Journal of Economics".
Not sure what, if anything, that has to do with math.

~~~
albertshin
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!

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lidHanteyk
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_...](https://golem.ph.utexas.edu/category/2020/04/online_seminar_lists.html)

~~~
williamstein
Indeed - Check out the amazing
[https://mathseminars.org/](https://mathseminars.org/)

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vidanay
Those books look like they'd all fit on $300 worth of shelving from IKEA.

The library probably cost $800k to remodel.

~~~
throwphoton
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
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.

