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After doing nearly all the coursework for a Ph.D. in math, I then did all the coursework for a Ph.D. in statistics and completed that degree.
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Probabilistic statement on matrix ranks
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1d

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Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
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Jan 14 
awarded  Popular Question 
Dec 11 
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A sumofdeterminants identity
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Dec 10 
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A sumofdeterminants identity
I should have torn my brain away from the geometry question I was thinking about and thought: obviously this is algebra. Wondering about the geometric meaning in higher dimensions, of the choice of $\pm$ in each term was actually the main thing on my mind, and I haven't really done much with that yet. In dimension $2$ there are cases where one obviously wants to subtract, rather than add, the area of a triangle, and that's taken care of by the fact that the determinant is negative in those cases. 
Dec 10 
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A sumofdeterminants identity
$\ldots$ and lots of triviallyprovableevenifnontriviallyconsequential identities are named after someone who lived usually before 1800 (but I think maybe determinants were not widely known until some time after that?) so we still have the question of whether this might be one of those, or whether it is only "trivially consequential" and so not worth doing that for. 
Dec 10 
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A sumofdeterminants identity
$\ldots$ which just goes to show that algebra is efficacious; I should have shifted mental gears and thought of using it $\ldots$ 
Dec 10 
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A sumofdeterminants identity
@RichardStanley : Could be  I was thinking about geometry, not algebra. 
Dec 10 
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A sumofdeterminants identity
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Dec 10 
asked  A sumofdeterminants identity 
Nov 10 
awarded  Popular Question 
Nov 10 
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Arctangents and the golden ratio
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Sep 30 
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Do these properties characterize differentiation?
I wonder what nice sets of conditions that include shiftequivariance are satisfied only by differentiation? 
Sep 30 
awarded  Explainer 
Sep 24 
awarded  Autobiographer 
Jul 20 
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When is the earliest large prime gap also the latest large prime gap?
What do you mean by saying that the lim sup of the relative size is decreasing? The relative size is $(p_{n+1}p_n)/p_n$. That is a sequence, and it has a lim sup, and its lim sup is a number, not a sequence. What would it mean to say a number is decreasing? (And I'll be very surprised if you tell me the lim sup is not $0$.) 
Jul 20 
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Positively invariant set
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Jul 20 
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When is the earliest large prime gap also the latest large prime gap?
I notice that mathoverflow has no "prime gaps" tag. Stackexchange has that. Should that be created? 
Jul 20 
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When is the earliest large prime gap also the latest large prime gap?
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Jul 20 
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When is the earliest large prime gap also the latest large prime gap?
@TheMaskedAvenger : I'm not seeing that your comment actually answers the questions. If I'm not mistaken, in the case of $113$, where the relative gap size, $(127113)/113=14/113\approx 0.12389\ldots$ is bigger than any that occurs later. I have to suspect that "bigger than average" means bigger than some "average" that decreases as $n$ grows. 