[math-fun] Publishing new proofs of old results
Rich made the following comment re Science.
From: rcs@xmission.com d) Confirming studies are not normally publishable.
Q: How does Mathematics treat papers which are new proofs of old results? We all know about Euler & Gauss & multiple proofs, but how are modern mathematicians treated in the published literature when they attempt to publish new proofs of old results? Has anyone counted the percentage of published math papers of new proofs/old results? BTW, I strongly disagree with Boltzmann's comment re "leaving elegance to the tailors"; part of the progress of modern math/science is to convert PhD thesis results into undergraduate homework or lab exercises. This is the only way to condense the incredible amount of material that a budding mathematician/scientist must learn before getting into new territory.
Q: How does Mathematics treat papers which are new proofs of old results?
It depends on how different the techniques are. My memory (which I am unable to confirm by web searching) says that in 1957 someone named Reed proved that differentiable = analytic in the complex domain without using the Cauchy integral theorem. People had been trying to do it for years without success and that was considered very significant. I also believe that a lot of algebraic topology in mid 20th Century was an attempt to get known geometric results by purely algebraic techniques. Whit
On Wed, Oct 30, 2013 at 9:16 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Rich made the following comment re Science.
From: rcs@xmission.com d) Confirming studies are not normally publishable.
Q: How does Mathematics treat papers which are new proofs of old results?
We all know about Euler & Gauss & multiple proofs, but how are modern mathematicians treated in the published literature when they attempt to publish new proofs of old results?
Has anyone counted the percentage of published math papers of new proofs/old results?
I think that wouldn't be easy to do. However, a quick search of MathSciNet putting "new proof*" in the title search box, one gets 1263 hits from Halava, Vesa; Harju, Tero; New proof for the undecidability of the circular PCP. *Acta Inform.* 50 (2013), no. 5-6, 331–341. to Bolza, Oskar New proof of a theorem of Osgood's in the calculus of variations. *Trans. Amer. Math. Soc.* 2 (1901), no. 4, 422–427.
Has anyone counted the percentage of published math papers of new proofs/old results?
That strikes me as very hard to even define. Many papers include a re-proof of some existing fact, to reduce dependence on checking references, to demonstrate a different approach, or just in ignorance of previous work. But I don't think you'd want to count something as a new proof/old result paper just because lemma 42 had been published in the Proceedings of the Odessa Mathematical Society thirty years ago. Conversely, a reproof of existing results will almost always involve proving new lemmata. So to make this determination you need to decide what a 'main result' is, or perhaps give fractional credit. But even that would require determining whether two proofs or theorems are equivalent, which is not at all obvious... Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Oct 30, 2013 at 9:16 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Rich made the following comment re Science.
From: rcs@xmission.com d) Confirming studies are not normally publishable.
Q: How does Mathematics treat papers which are new proofs of old results?
We all know about Euler & Gauss & multiple proofs, but how are modern mathematicians treated in the published literature when they attempt to publish new proofs of old results?
Has anyone counted the percentage of published math papers of new proofs/old results?
BTW, I strongly disagree with Boltzmann's comment re "leaving elegance to the tailors"; part of the progress of modern math/science is to convert PhD thesis results into undergraduate homework or lab exercises. This is the only way to condense the incredible amount of material that a budding mathematician/scientist must learn before getting into new territory.
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The MAA's Monthly often publishes new proofs of old results. Often it's clear that the new proof is an improvement. Other times I'm not sure why it gets published. --Dan On 2013-10-30, at 9:49 AM, Charles Greathouse wrote:
Has anyone counted the percentage of published math papers of new proofs/old results?
participants (5)
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Charles Greathouse -
Dan Asimov -
Henry Baker -
W. Edwin Clark -
Whitfield Diffie