Reputation
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
3 34 81
Impact
~330k people reached

Apr
27
awarded  Favorite Question
Apr
15
revised Morita equivalence base equivalence relation for discrete groups
added 3 characters in body
Apr
13
awarded  Popular Question
Apr
1
comment Proof synopsis collection
Or better yet: Every such operator is unitarily equivalent to a multiplication operator, and you can just write the resolution of such a thing as multiplications by characteristic functions.
Mar
31
awarded  Notable Question
Mar
31
comment Number theory and physics
(cont.) this said, the functional analytic approach he proposes is not mainstream (I'm not sure how Peter Sarnak would view it, e.g.). Nevertheless, Connes has expressed that he believes that the key to RH will require ideas from quantum field theory. A very high level reason why these ideas may be involved with number theory is that the positive real numbers with respect to multiplication is a so-called "noncommutative space"...a "quotient" by the subsemigroup of natural numbers is pathological (becomes a point, topologically) and so noncommutative geometry ideas are needed to study this.
Mar
31
comment Number theory and physics
I'm not prepared to give an answer of the quality the question requires, but Alain Connes finds an interesting connection between the classification of factors (which involves deep ideas connected with quantum statistical mechanics) and the Riemann Hypothesis: alainconnes.org/docs/imufinal.pdf
Mar
30
comment Expert, Intuitive, Organizing Analogies
It might be, depending on whether the game lays out the "gist" in a way that would be useful for actually constructing the theory, so that each piece of the game corresponds to a particular aspect of category theory, and so that the pieces fit together in an appropriate and illuminating way. (I'm not familiar with the game, so I'd be interested to see...)
Mar
30
comment Expert, Intuitive, Organizing Analogies
@Yemon: I will consider commenting on the other answers, but I'm at a bit of a loss regarding how to do this in a way that won't transmogrify this thread into a discussion. For brevity, I'll keep quiet for a while and hope people read the comments associated with this answer.
Mar
30
comment Expert, Intuitive, Organizing Analogies
of a mathematical theory. Roughly, what I'm looking for are maps to common sense experience that capture the basic structure of a strategy or technique with a large kernel, namely the definition-baggage of the abstract theory. Admittedly, this is probably mostly for mnemotechnic purposes.
Mar
30
comment Expert, Intuitive, Organizing Analogies
Although the discussion of categories is interesting, and the observation is a good one (I do believe that mathematical structure as expressed in categories precises the concept of mathematical analogy), what I am looking for are "structure preserving maps" from mathematics to the concrete world of human sensory experience, as an exploration of certain ways of stimulating native human thinking for organizing abstract techniques. The "cheese" examples I'm looking for are not a dime-a-dozen, as they should not be contrived and yet should encode and organize a lot of the technical structure
Mar
29
awarded  Good Question
Mar
29
awarded  Electorate
Mar
29
comment Expert, Intuitive, Organizing Analogies
@DanielMoskovich: I put an italicized paragraph after the original question, in order to try to tighten the question and screen the hairy ball answers...
Mar
29
revised Expert, Intuitive, Organizing Analogies
added 371 characters in body
Mar
28
comment Expert, Intuitive, Organizing Analogies
@DanielMoskovich: This is the reason I included the example, in hope that similar answers would be spurred by it. If you can think of a good edit to "tighten" the question, I'd welcome it!
Mar
23
revised Expert, Intuitive, Organizing Analogies
added 913 characters in body; edited title
Mar
23
comment Expert, Intuitive, Organizing Analogies
@Amir: It might, if you include the parts of the analogy in more or less precise detail. It certainly makes the result salient. Can you use it to remember the mathematics and reproduce an argument or strategy?
Mar
21
comment Expert, Intuitive, Organizing Analogies
@Amir: It may be that this question embeds in Bill Thurston's question, or perhaps that Bill Thurston could have provided a nice answer to this question. I find myself rather missing Bill Thurston right now...
Mar
21
awarded  Nice Question