bio  website  ncatlab.org/nlab/show/… 

location  Adelaide, Australia  
age  31  
visits  member for  5 years, 9 months 
seen  6 hours ago  
stats  profile views  11,021 
Pure mathematician interested in category theory and foundations.
13h

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Why should we care about “higher infinities” outside of set theory?
Wooden > Woodin 
2d

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Which Lie algebra admit symplectic forms
Welcome to MO, Wolfgang! 
2d

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Why should we care about “higher infinities” outside of set theory?
You may also be interested in predicative mathematics: ncatlab.org/nlab/show/predicative+mathematics. It doesn't get rid of higher cardinalities, insomuch as this still makes sense, but does reject the notion of power set (still keeping, for instance, function sets more generally, but rejecting a subobject classfying set, which is classical mathematics is {0,1}) 
2d

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Geodesics on SO(3)
principle > principal 
2d

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Why should we care about “higher infinities” outside of set theory?
You may be interested in a foundation where one can form each of the finitely iterated power sets $P^n(\mathbb{N})$, but draw no conclusion about anything bigger. Then one is assured of having spaces of functions that turn up in analysis etc, starting from existing sets. See: arxiv.org/abs/1212.6543, and this question, phrased in terms of higher cardinalities arising from Replacement: mathoverflow.net/questions/208711/whoneedsreplacementanyway 
2d

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How to rewrite square root without exponents?
No${}{}{}{}{}{}$ 
2d

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Why should we care about “higher infinities” outside of set theory?
What's the cardinality of the space of operators on a separable Banach space? 
2d

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Detecting torsionclassified bundles by differential invariants
The above assumes that one can find a section of P over an open set with complement of zero measure, so that the integral can be done. 
Aug
26 
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Detecting torsionclassified bundles by differential invariants
The question in a nutshell is this: can I calculate a number from a connection that tells me about the classification of the underlying bundle by 'torsion' invariants? 
Aug
26 
awarded  Good Question 
Aug
26 
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How much of the ATLAS of finite groups is independently checked and/or computer verified?
Do you know any specific examples where there are no other sources to corroborate facts stated in the ATLAS? 
Aug
26 
revised 
Detecting torsionclassified bundles by differential invariants
added 72 characters in body 
Aug
26 
asked  Detecting torsionclassified bundles by differential invariants 
Aug
26 
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Representation ring of circle group over complex field
I suggest this question would be a better fit at math.stackexchange.com  here it's gathering votes to close. 
Aug
26 
awarded  Popular Question 
Aug
26 
revised 
How much of the ATLAS of finite groups is independently checked and/or computer verified?
Clarified question 
Aug
24 
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Soft Question: Relationships Between Moduli Space and Objects They Parametrize
Another example to keep in mind is the work of Mirzakhani, where dynamics on moduli spaces of Riemann surfaces tell us something about Riemann surfaces themselves. See eg mathoverflow.net/questions/199212/maryammirzakhanisworks 
Aug
24 
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How to compute (co)limits of enriched categories?
@user40276 for future reference, anything four years old or older on ScienceDirect in most if not all pure mathematics journals is free to read. Part of Elsevier trying to win back the hearts of mathematicians (you'll notice it's not true for as many journal in other fields, like theoretical physics, that have similar halflife for their papers). 
Aug
24 
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Probability and Statistics
Wrong website! Have a read of some other questions here... 
Aug
21 
awarded  Popular Question 