12,001 reputation
436107
bio website ncatlab.org/nlab/show/…
location Adelaide, Australia
age 31
visits member for 5 years, 7 months
seen 24 mins ago

Pure mathematician interested in category theory and foundations.


45m
awarded  Good Question
2h
comment What conditions imply that a function over $\mathbb{Z}$ is a polynomial?
I think perhaps by the way it was phrased. If it were something like: "What conditions on a function imply that it is a polynomial, if I am only allowed to use its values on the integers?" Otherwise it looks like a total rookie question. It is best to specify what sort of function, and what the domain is. Is it defined on $\mathbb{R}$? $\mathbb{C}$? Is it smooth? Analytic? Merely continuous?
3h
comment Does projective imply flat?
Nice! (On a different note, did you do that thing you emailed me about? :-P)
5h
comment What is the reverse mathematical strength of the fundamental theorem of algebra?
Hmm, that's less satisfying than I thought. In particular, as people have pointed out (on tea.mathoverflow for instance) assuming the the mere (in the technical, HoTT, sense) existence of some Cauchy subsequence of an arbitrary sequence, let alone its consistency, is more than someone wanting strict logical hygiene may be willing to admit. Thanks for disabusing me of this misunderstanding :-)
12h
awarded  Popular Question
20h
comment What is the reverse mathematical strength of the fundamental theorem of algebra?
Sorry, @QiaochuYuan, forgot to mention you by name, to give you a notification, in the previous comment.
21h
comment What is the reverse mathematical strength of the fundamental theorem of algebra?
I would imagine first-order PA, although B-W is said to be equivalent to $ACA_0$ over $RCA_0$, and PA is the first-order fragment of $ACA_0$. So maybe B-W is not quite exactly equivalent to $Con(PA)$, but certainly implies it. I wish Friedman would write down his claim properly, so people have something to cite other than 'HF said this on fom, and we all know it to be true anyway...' Restricting to rational sequences in [0,1] probably is a little nicer than full B-W, but I don't know if it really helps.
21h
awarded  Nice Question
22h
awarded  Announcer
1d
accepted What is the reverse mathematical strength of the fundamental theorem of algebra?
1d
comment What is the reverse mathematical strength of the fundamental theorem of algebra?
Ah, thanks! I did wonder how one would get something so general as BW from something to do with polynomials.
1d
comment Is PA consistent? do we know it?
"(according to Harvey Friedman) actually much less than RCA0 is needed." Can someone ask him to please write this down/up? This is too interesting a result to lurk as claims in fom postings and as hearsay by others in other internet forums.
1d
asked What is the reverse mathematical strength of the fundamental theorem of algebra?
1d
comment Ways to prove the fundamental theorem of algebra
I would ask on the fom mailing list, but I got off it. So, maybe a new question here?
2d
comment How to write an abstract for a math paper?
@ToddTrimble I saw what you did there!
2d
comment Ways to prove the fundamental theorem of algebra
And there's your 100 upvotes!
2d
comment Ways to prove the fundamental theorem of algebra
I wonder if the reverse mathematical strength of FTA is the same as Bolzano-Weierstrass (in the sense that BW is necessary to prove FTA). This would make even stronger Friedman's point that BW over the rationals (a variant on 'every bounded sequence has a Cauchy subsequence') is equivalent to Con(PA), over some base theory.
Jun
26
comment Next steps on formal proof of classification of finite simple groups
@GeoffRobinson maybe a better term might be 'polish' (now I look it up, I was thinking more of the noun form, and then verbing that)
Jun
26
comment Is anything known about a ternary equivalent of groups?
There are abstract structures with ternary operations, for instance planar ternary rings. Given a quasifield, one can define a PTR from the two binary operations, namely T(a,b,c)=ab+c. In general, you might want to look at operads (much much more general!)
Jun
26
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
@AndréHenriques that I feel is a productive approach, as long as it it contained to addressing specifics, and not allowed to run on and on -- this isn't a forum for convincing people the published version is correct.