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answered Double-layer potentials on Riemannian manifolds
Feb
4
comment Your favorite surprising connections in Mathematics
There is some subtlety in making the tensor-product associativity be the complete answer... for the topological vector space end of the analogy. Too technical, and maybe not immediately interesting, but P. Cartier's 1973/4 Sem. Bourb. talk/article explains how certain technical points (at a later "perfect" extreme the Dixmier-Malliavin theorem) make heuristics into theorems in such regards. Maybe the fact that the heuristics are "obvious" makes the actual surprise less?
Feb
4
comment Your favorite surprising connections in Mathematics
Yes! This is a fundamental "surprise". :)
Feb
4
comment Your favorite surprising connections in Mathematics
You are completely correct, that this is in some way an astonishing thing. The downvotes are an expression of the absence of this astonishment from the official account of things... So, by accident, it is not surprising that you'd get downvotes. But I think you are perfectly correct...
Feb
2
comment Question about the Reimann Zeta Function
@silversurfer, right. Also, if you're wanting to Google around, the spelling is "Riemann", and in English "analytic continuation".
Jan
29
comment What is the mathematical significance of the IHES logo?
... and, just for context, I think that in those years the ideas of "catastrophe theory" and "classification of singularities" were newish, had great cachet, and we know what that might lead to, PR-wise. :)
Jan
29
comment What is the mathematical significance of the IHES logo?
@JohnVoight, yes, I think some correct choices have to be made "at infinity" to make this be a literal trefoil. Due to some personal interests long ago, somehow it appears "immediate" to me that this thing is "in that ballpark". Perhaps the question is why an asymmetry was apparently deliberately chosen, in contrast to the potential/natural symmetrical version almost always chosen in those old art-situations. Sure, a repeating pattern needs more symmetry... and a one-off might seem to want asymmetry.
Jan
28
answered What is the mathematical significance of the IHES logo?
Jan
22
comment Reducibility of a variety
Ping? Viktor! I had thought of you... and I don't know where you are... geographically... :) I had thought you were in luxuriously rural-bucolic Oswego, but their pages don't reflect your presence... I did look around, but could find no better way to say hello than this...
Jan
22
comment Examples where physical heuristics led to incorrect answers?
Alekk, would it be ok to edit your language to change "proved wrong" and such, to something else? "Wrong" is a bit charged... and, in fact, I think does not convey the dramatic tension in these situations. That is, colloquial "wrong" is (often) very different from genuine scientific "wrong". And so on...
Jan
20
comment inverse Fouier transform from partial Fourier transform
One could use Cauchy's integral formulas as a more robust way to evaluate derivatives at a basepoint. Still, you'd need arbitrarily many to get arbitrarily good precision for the Fourier transform.
Jan
20
comment inverse Fouier transform from partial Fourier transform
How about using Cauchy's integral formulas to evaluate the power series coefficients (... derivatives)? Somewhat more robust than direct numerical methods to evaluate derivatives...
Jan
19
comment How do i show that:$\prod\frac{p^2+1}{p^2-1}=\frac{5}{2}$ without using properties of Riemann zeta function?
@zeraouliarafik, but, of course, this might be very difficult, or in some sense impossible! :)
Jan
19
comment How do i show that:$\prod\frac{p^2+1}{p^2-1}=\frac{5}{2}$ without using properties of Riemann zeta function?
@zeraouliarafik, don't worry, in some sense this was a perfectly-answerable question for this site: it is certainly true that standard methods give the result, but asking to avoid analytic methods is a potentially interesting question about the combinatorics of cancellation/telescoping. Noam E. happened to recall at least the one prior occurrence, etc. Bingo. :)
Jan
19
comment Everyday, real-life applications of mathematical concepts, and human intuition vs mathematical analysis
Would be better to delete the second paragraph entirely, I think: "human intuition" and "rigorous mathematical analysis" is not a legitimate or genuine dichotomy, in the first place, and, as @DouglasZare comments, is a caricature.
Jan
15
comment Scaling of distributions
Good, physical counter-example.
Jan
9
awarded  Nice Answer
Jan
8
answered Analytic continuation of intertwining operator
Jan
8
answered Reference request: normalization of intertwining operators for GL(2, C)
Jan
7
comment When can a locally compact group be approximated by discrete subgroups?
So now that @YCor's scholarship has "grounded" the question... we can hopefully-usefully restrict the question to a regime where the outcome is positive for the immediate purposes? Clarification?