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As Yves Meyer was getting ready to publish a detailed mathematical proof that he had spent months working on, he decided do a final search of the existing literature. In the reference list of one of the papers he had just peer-reviewed, he noticed what he describes as a "bizarre" paper published in 1959 by Andrew Paul Guinand. Upon further investigation, he was shocked to discover that Guinand had formulated the exact same proof to solve the same problem that Meyer had been working on, though the solution had remained deeply buried and completely forgotten.
Meyer, a Professor Emeritus at the École Normale Supérieure de Cachan, accordingly revised and published his paper [DOI: 10.1073/pnas.1600685113], which appeared just a few weeks ago in the Proceedings of the National Academy of Sciences. In his work, he proves that there is not just one, but many Poisson summation formulas, using a simpler solution than was previously known.
Meyer—who has spent his career making fundamental contributions to wavelet theory and number theory, and recently won the Gauss Prize—explains that at first he was somewhat embarrassed that someone else had made the same discovery many decades earlier. However, he also interprets the experience as an example of a more universal pattern: that all of human discovery builds on what comes before.
"Suddenly I understood what I have been steadily doing in my scientific life," Meyer told Phys.org. "I was transmitting a heritage. Today I can express my gratitude to Guinand, who was a great person, both as a human being and as a mathematician."
That's a tale to strike terror into the heart of every grad student...
(Score: 2) by bitstream on Saturday March 26 2016, @10:00PM
Is there any work such that one can search documents etc using Math formulas like MathML etc can express? or perhaps LaTeX? Not just that the names of the tags occurs in the searched document. But that the formula itself is a match?
Say I want to search "x^3 + 5y'' = z(cos 2x)". Currently the search engines will tell me that millions of pages mention cosines and that x is a too short term to search for etc.... *bangs head*
I hope someone "oogles" all those hidden away papers on dead trees that is succumbing to entropy, mold, moisture and evil administrators.
(Score: 0) by Anonymous Coward on Saturday March 26 2016, @10:36PM
what you're looking for is a handbook of differential equations, similar in function to this one http://people.math.sfu.ca/~cbm/aands/. [math.sfu.ca]
wolfram alpha will in fact work as a handbook of this sort, probably better than most things you can buy (well, other than wolfram's mathematica itself probably).
although I don't actually know if mathematica gives you the citation when it pops out a formula... (I haven't actually used mathematica more than a couple of times)
(Score: 2) by bitstream on Sunday March 27 2016, @06:45AM
Nice handbook. But what my thought was more along the line of that you type a formula and the search engine will tell you if that expression exist anywhere and that it is both formula and math aware. Perhaps equating sin(x+pi/2) with cos(x) and so on.
Finding out if your equations already exists on a physical paper in any university anywhere is tough. Even if one scan the papers. Is it possible to even do OCR to formula in an automated way that don't mess it up too often?
(Score: 3, Informative) by deimtee on Sunday March 27 2016, @12:36AM
Ten years ago you could have typed "x^3 + 5y'' = z(cos 2x)" into google and the quotation marks on the start and end would have meant find an exact match to the bit in between.
(Pointing out here that the middle quote is actually a double apostrophe, I didn't notice until I copied and pasted the formula).
Worked great, and did exactly what you want. So it can be done.
It doesn't work anymore though, now you get a bunch of ads, and "did you mean this" shit. Apparently being useful isn't profitable.
No problem is insoluble, but at Ksp = 2.943×10−25 Mercury Sulphide comes close.
(Score: 2) by bitstream on Sunday March 27 2016, @06:28AM
Yep, something was lost. But evaluating math formulas has not been a thing that search engines ever did really.
"World-Wide Web Worm" of 1993 handled perl regular-expression according to documents. Obviously the one that would be seriously needed now ;)
(Score: 2) by deimtee on Sunday March 27 2016, @09:10AM
It wasn't about evaluating it. That is exactly what you don't want. You now cannot search for an exact string.
Even if you jump through all the hoops to get to the "verbatim" mode, it doesn't really search for matching strings.
No problem is insoluble, but at Ksp = 2.943×10−25 Mercury Sulphide comes close.
(Score: 2) by bitstream on Sunday March 27 2016, @09:54AM
I'll suspect it's cheaper to split all documents into words, index them and search that way. But it of course removes any granularity. Most (l)users probably won't miss them. But it makes the search engine like a McDonalds outlet. You get feed but it's crap and have long term effects..