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I am interested in collecting a list of research papers with a mainly mathematical focus that appeared in high-reputation general science journals without a dedicated mathematics section. This would include things like Nature or Science, but exlcude, for example, PNAS.

By a "papers with a mainly mathematical focus" I mean publications whose purpose is the announcement/description/proof of a new mathematical method or result, rather than the mere use of (sophisticated) mathematical techniques to solve a scientific problem from another discipline.

I would imagine that often such papers are complemented by a publication in a more traditional mathematical venue that expands on technical details maybe omitted in the general science journal, and it would be nice to collect those as well to see how the two publications differ from each other.

I vaguely remember coming across one or two of such papers in the past, but I cannot find them anymore and cannot, therefore, give an example of what I am looking for.

I would be grateful if someone could convert this question to Community Wiki mode, I seem to be unable to find the right check-box.

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  • $\begingroup$ Isn't that so common that we couldn't list them all? If not, one I recall is about the Padé-Laplace method for recognizing sums of exponentials. ncbi.nlm.nih.gov/pmc/articles/PMC1280453 $\endgroup$ – Douglas Zare Sep 13 '14 at 10:58
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    $\begingroup$ Thanks for your comment @DouglasZare. I agree this is quite common in journals catering for disciplines adjacent to mathematics, such as physics or computer science. This is why I restricted the question to science journals publishing papers from all scientific disciplines and broadly perceived to be of high reputation. If that is still too broad I am happy to restrict the question to Nature and Science explicitly. $\endgroup$ – Eckhard Sep 13 '14 at 11:08
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    $\begingroup$ Oh, I didn't read "general science" as "publishing papers from all scientific disciplines." That greatly restricts the set of periodicals you are allowing, so there wouldn't be as many articles. To be clear, since Cell doesn't publish seismology articles, a paper there on a new mathematical method wouldn't be of interest to you? $\endgroup$ – Douglas Zare Sep 13 '14 at 12:47
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    $\begingroup$ Perhaps you were thinking of the Nature article "Designing tie knots by random walks"? $\endgroup$ – Joel Reyes Noche Sep 15 '14 at 3:17
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I guess you have already tried this, but just in case, you can search the publishers' websites. For example, here's all research and review papers under the "Mathematics and Computing" category in Nature Publishing Group's journals:

http://www.nature.com/subjects/mathematics-and-computing#research-and-reviews

You can refine the search by choosing narrower subjects such as Applied Mathematics.

For Science, go to http://www.sciencemag.org/cgi/collection/comp_math and then choose "Original Research" from the "Refine By Section" menu.

If computing doesn't count as mathematical research by your definition, I don't know how to narrow down the search results from here. But there seem to be only 50 or so articles in Science. So, it shouldn't be too difficult to locate the paper(s) you had in mind.

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  • $\begingroup$ For convenience, here are all papers in the Applied Mathematics category in Nature alone (i.e., no papers in other journals of the same publisher are included in case you don't think journals like Scientific Reports are high-reputation general science journals) nature.com/nature/archive/… It's just only 3 papers, and I'm not sure if they count as math papers by your criteria, though... $\endgroup$ – Yuichiro Fujiwara Sep 14 '14 at 5:59
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MathSciNet is another obvious resource. I just tried this myself and found that typing "Science" in the "Journal" search box does not have the desired effect; instead, I had to go to the Journals tab, type "Science" there, and scroll through until I found the desired journal.

I am not sure that I found any examples of what you are looking for, but here are a couple of candidates that may at least let you state more clearly what you want.

  1. Expository articles by Dana Mackenzie on major mathematical results (e.g., the Poincare conjecture).

  2. Checkers is solved by Schaeffer et al. This is in some sense a purely mathematical result but it is more of a milestone in computing than a mathematical advance per se.

  3. Explosive percolation in random networks by Achlioptas et al. To me this seems to be pretty clearly a probability theory paper, but the main purpose of the paper is to announce a conjecture and present supporting numerical evidence, rather than to announce a proved theorem.

  4. Various papers about quantum computing and quantum error correction. Despite the word "quantum," several of these are basically purely mathematical results, although some might argue that they belong to computer science rather than mathematics per se.

In general, I do not think that mathematicians treat Nature or Science as an appropriate venue to make a research announcement of a purely mathematical result whose technical details appear elsewhere (no matter how "generally interesting" the result is), so if that is really what you're after then I think there will be very few examples.

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Try PNAS papers in section Mathematics (returns 2308 results, but some are cross-discipinary). In the early days there were a lot of pure mathematics papers listed under just 'Mathematics' (e.g. Hardy-Littlewood!). But these days they seem to be listed under Mathematics and Physical Sciences, for instance Morrison-Walker, Griffin-Ono-Rolen and Conway-Jiao-Torquato (actually Ken Ono seems to have published a bunch of stuff there...). This search however picks up a lot of stuff that you wanted to rule out, "use of (sophisticated) mathematical techniques to solve a scientific problem from another discipline."

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    $\begingroup$ OP specifically excludes PNAS in the 1st paragraph of the question. $\endgroup$ – Gerry Myerson May 17 '15 at 23:53
  • $\begingroup$ @Gerry well I never. +1 for you! It does sit under the heading 'Physical sciences' - a slight lie - but with subheading 'Mathematics'. I note with interest that a mere three more mathematics papers have been published since I wrote this answer. Not exactly a flood... $\endgroup$ – David Roberts May 18 '15 at 0:46
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Not sure whether it qualifies, but here it goes: the journal Los Alamos Science, published between 1980 and 2005. The mathematics category contains some applied mathematics papers (numerical analyisis, statistics, etc.). Especially interesting is the issue dedicated to Ulam, with sort of survey articles by Graham, Mycielski, and others.

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Evans function and Fredholm determinants by Issa Karambal, Simon J. A. Malham is in Proc. R. Soc. A., February 2015 Volume: 471 Issue: 2174.

Proceedings of the Royal Society A does not have a dedicated mathematics section. It features plenty of applied mathematics papers and mathematical physics papers of course, but interestingly, sometimes also pure research mathematics.

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