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age 24
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Second-year graduate student at Stanford University.

Interests tend to center around differential geometry.

For now, I plan on being far more active on math.stackexchange.com


Feb
17
awarded  Nice Question
Dec
28
comment When is a Riemannian metric equivalent to the flat metric on $\mathbb R^n$?
Deane: "I don't believe I've ever seen this result used for anything." If you're referencing Cartan's Theorem (the local version of Cartan-Ambrose-Hicks), then I believe it can be used to prove that any Riemannian manifold with $\nabla R = 0$ is locally isometric to a symmetric space.
Sep
30
awarded  Caucus
Feb
24
comment Awfully sophisticated proof for simple facts
And here I was thinking the standard proof was just the Integral Test for series convergence.
Jan
22
awarded  Nice Answer
Jan
12
comment How to respond to “I was never much good at maths at school.”
It's interesting. Pretty much everyone I know would agree that it's not a good thing when elementary school teachers tell their students that they didn't like math, either. And yet I can think of more than a handful of those same people (grad students and professors) who would have no problem telling their calculus classes that they don't like calculus, or that it's not "real" math somehow...
Dec
12
comment “Softness” vs “rigidity” in Geometry
Funny, I would've said that when doing geometry, you either fall into algebra or analysis. In fact, it seems to me that the more "rigid" your geometry is, the more likely you are to fall into one of the sides. By contrast, "softer" geometries can rely on topology.
Nov
28
comment Fundamental motivation for several complex variables
That's fair. In truth, I'm still rather ignorant about harmonic functions and their properties. I don't mean to suggest that reason (1) is the only reason one would care about them, but simply that it's a primary reason that I do (again, given my ignorance).
Nov
28
answered Fundamental motivation for several complex variables
Nov
26
awarded  Civic Duty
Oct
11
comment How to escape the inclination to be a universalist or: How to learn to stop worrying and do some research.
"Maybe the bred desire that you mention is (or is related to) the emphasis on 'theory building'. Yes, theory building is great, but I personally see it through the lens of problem solving." Okay, but what if one is far more interested in theory building than problem solving, or if theory-building IS the lens by which one views things?
Mar
22
awarded  Popular Question
Jun
29
comment How to respond to “I was never much good at maths at school.”
"What makes some of you think the 'math' people learned in school is 'not real'?" Just for that one line I would upvote your comment ten times if I could. For me it is extremely refreshing to hear a professional mathematician question that line. Thank you for that.
May
2
awarded  Nice Answer
Apr
5
comment How should one present curl and divergence in an undergraduate multivariable calculus class?
To be pedantic, I think technically it's $\text{curl} = \sharp \circ \ast \circ d \circ \flat$, but no matter.
Apr
4
awarded  Necromancer
Mar
25
awarded  Notable Question
Dec
17
awarded  Yearling
Oct
28
comment Meaning of \Subset notation
I have seen $A \Subset B$ mean that the (topological) closure of $A$ is contained in $B$, but I'm sure there are plenty of other uses as well. Could you perhaps provide some context?
Oct
5
comment Memorizing theorems
+1 for the first sentence. Memorization is certainly not a substitute for understanding -- and really, who would ever claim that it is? -- but it's sometimes just so useful! Especially in areas like real analysis where theorems can have multiple hypotheses and omitting even one of them can render the theorem false (think Dini's Theorem), sometimes it just saves time and stress to sit down one day and memorize it. Also, the "modes of convergence" diagram is wonderful.