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Why might André Weil have named Carl Ludwig Siegel the greatest mathematician of the 20th century?
I once heard from someone who claims to have been present that Weil in fact hesitated before naming Siegel, and that when he was asked "And who is the second greatest?", Weil replied without hesitation "Myself, of course". I have no idea whether any of this is accurate, and of course even if it's accurate I have no idea in what tone, and with what nonverbal expressions, the answer was delivered, which could make all the difference in how it should be interpreted. 
Aug
18 
comment 
Does every projective A/Imodule come from A?
Notice that your exact sequence (some version of which does exist per Mariano's answer) is far from sufficient to establish your claim. Surjectivity of $K_0(X)\rightarrow K_0(Z)$ is far from sufficient to establish that every $Z$projective lifts to $X$. 
Aug
14 
comment 
Meaning of $[A,B]$ when $A$, $B$ are selfadjoint
Actually, the paper you link to (in the answer you link to) denotes the nonstandard Lie bracket $(A,B)$, not $[A,B]$. 
Aug
11 
comment 
Meaning of $[A,B]$ when $A$, $B$ are selfadjoint
@RobertBryant: This sounds like it is probably the answer I'm looking for  though, because there are two possible nonstandard usages, I'd still like to know whether one is generally preferred to the other. 
Aug
11 
comment 
Meaning of $[A,B]$ when $A$, $B$ are selfadjoint
@RobertBryant: Thanks for this  but I'm not sure it answers the question. In a math paper, is it less confusing to use $[A,B]$ for the commutator, or for the Lie bracket, or ought one not use this notation at all? 
Aug
11 
asked  Meaning of $[A,B]$ when $A$, $B$ are selfadjoint 
Jul
23 
revised 
Worst case difference in rank by columnrow swapping
added 184 characters in body 
Jul
23 
comment 
Worst case difference in rank by columnrow swapping
@BrendanMcKay: Actually, I'm back to not being sure what "swapping" means, so the operation might be as in my comment or as above. Fortunately, the above argument works either way. I've included an edit to mention this. 
Jul
23 
revised 
Worst case difference in rank by columnrow swapping
edited body 
Jul
23 
revised 
Worst case difference in rank by columnrow swapping
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Jul
22 
comment 
Worst case difference in rank by columnrow swapping
I've deleted my last comment, which was nonsense. 
Jul
9 
revised 
the true reason of the incompleteness of formal systems
added 610 characters in body 
Jul
9 
comment 
Worst case difference in rank by columnrow swapping
@BrendanMcKay: The operation seems to be $$\pmatrix{A&B\cr C&D\cr}\mapsto \pmatrix {A&C^T\cr B^T&D\cr}$$ where $A$ and $D$ are square matrices (perhaps of different sizes), $C$ and $D$ are rectangular of appropriate sizes, and the upper$T$ denotes the transpose. 
Jul
9 
revised 
Worst case difference in rank by columnrow swapping
added 107 characters in body 
Jul
9 
revised 
Worst case difference in rank by columnrow swapping
added 17 characters in body 
Jul
9 
answered  Worst case difference in rank by columnrow swapping 
Jul
7 
awarded  Good Answer 
Jul
5 
comment 
Which journals publish research announcements?
@SergeiAkbarov: A "research announcement" is a short communication without complete proofs. 
Jul
5 
comment 
Worst case difference in rank by columnrow swapping
Ah. I see that you've changed your example to respond to my last comment, but without bothering to mention or acknowledge it. 
Jul
5 
comment 
Worst case difference in rank by columnrow swapping
Your example adds to my confusion. If $S_i$ is the operation that "swaps" the $i$th row and column, and if I understand what "swap" means, then it seems that the $S_i$ commute with each other. But your example suggests that the results of applying $S_iS_j$ and $S_jS_i$ are different. So I'm back to believing that I don't know what "swap" means. 