Mirco Mannucci
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Registered User
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I do not believe in natural numbers, yet I reject no math, not even the most outrageously large cardinals.
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Jan 13 |
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A General Framework for Ramsey Theory ? Aaron, yes, Motzkin 's mantra is exactly why Ramsey's theory is such a huge contribution to our understanding of the world. I gave you my like, because you gave some philosophical context to my question. However, what I am after here is: how can I make a general formal framework for this theory? Martin's answer goes some way in that direction.... |
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Jan 13 |
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A General Framework for Ramsey Theory ? perhaps the best starting point to provide such a framework. But I would be happy with something else, as long as it makes formal the general (and generic statement) I have put in bold. |
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Jan 13 |
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A General Framework for Ramsey Theory ? Martin, thanks for the ref! As for the motivation behind, well, what I do need is this: Ramsey's result is not just a beautiful piece of math, which it certainly is, but a true REVOLUTION in math (and in fact, it literally originated an entire industry with no end in sight). What is more, it is a very DEEP result, which has a philosophical interest, namely the discovery that order can emerge out of chaos just by sheer numbers.. anyway, my point is: WHAT EXACTLY IS RAMSEY'S THEORY? what is its general framework? I do not necessarily think this framework should be categorical, only cat theory is |
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Jan 13 |
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A General Framework for Ramsey Theory ? David, yes you should mention them ! In fact, I was thinking of what Joyal did for general combinatorics with the Theory of Species, as perhaps a possible baseline for what I ask for here |
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Jan 13 |
asked | A General Framework for Ramsey Theory ? |
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Jan 11 |
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New grand projects in contemporary math finite realm than what we ever dreamed so far. I reiterate that your answer is especially dear to my heart, because I am certain that in the years to come we will see much more of that. The complexity (and beauty) of the finite realm (particularly finite graphs, finite categories, etc) will literally astound us |
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Jan 11 |
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New grand projects in contemporary math Tim, thanks for this add-on. This result by HF not only does not bother me, but actually is music to my ears! My philosophical position could be summarized in two main tenets: 1) all math objects are configuration of syntactic games (included the "natural numbers") 2) the apparent dichotomy finite-infinite is contextual. Now, 1) allows me to avoid restrictions of any sorts as far as which axiomatic system I can play with (of course, just like ordinary games, someone likes bridge and someone likes poker). 2) tells me basically this: there is infinitely (sorry the pun) more in the so-called |
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Jan 6 |
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small hyperworlds ? Yes Joseph, this talk looks like something right up my alley. And so do the other links. Thanks! |
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Jan 6 |
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small hyperworlds ? added 857 characters in body |
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Jan 5 |
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small hyperworlds ? deleted 94 characters in body; deleted 7 characters in body |
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Jan 5 |
asked | small hyperworlds ? |
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Jan 5 |
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New grand projects in contemporary math @suvrit Well, the caps were meant to be noticed, and sure enough they were! :) I agree that it was a bit rough, but it provoked the intended effect, namely to push people to be more informative in their answers. I am glad though that quid polished it up. |
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Jan 4 |
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New grand projects in contemporary math Dirk, Fascinating! But can you say a bit more about the motivating problems behind it? And how this method made them more tractable? |
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Jan 4 |
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New grand projects in contemporary math Thanks Timothy, this is really spectacular stuff! I confess (shame on me!) that up to 10 minutes ago I did not even know what a minor of a graph is.... But after your great answer, I checked the wiki and found out a whole fascinating universe there. For instance, to someone like me that cringes at the word infinity, it comes as a happy surprise the Friedman, Robertson & Seymour 's theorem that is the finitistic version of the above. I have the feeling that this is exactly one of these paradigm shifting events I was looking for, and that we will see much more along similar lines |
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Jan 2 |
awarded | ● Notable Question |
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Jan 2 |
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New grand projects in contemporary math very interesting and well presented answer Kevin, KUDOS! somehow I feel that one of the next breakthroughs will be in new math tools to manage and get insights from large data sets, so I look forward especially to dig into your number 2 above |
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Jan 2 |
awarded | ● Favorite Question |
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Jan 1 |
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New grand projects in contemporary math this is a MO question on tropical math which also addresses why this new field is very relevant (I have found especially fascinating the perspective of looking at the tropical semi-ring as a "classical limit"): mathoverflow.net/questions/83624/… |
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Jan 1 |
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New grand projects in contemporary math This is the kind of answer I was hoping for: something I knew absolutely nothing about and also very informative! Fascinating new field...I will most definitely check it out. Thanks Yuichiro! PS also thanks to the commentators, who brought in new material. Kudos to all |
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Jan 1 |
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New grand projects in contemporary math Yes Adeel. This is perhaps the only answer I know something about. Lurie's program is in fact an extension and continuation of Grothendieck's ideas, but it brings in new fire, and also unifies a large amount of research. A grand effort indeed! |
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Dec 31 |
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New grand projects in contemporary math no, it is not too far, and moreover I have not mentioned "pure" math as a constraint. You got my vote |
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Dec 31 |
awarded | ● Popular Question |
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Dec 31 |
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New grand projects in contemporary math deleted 3 characters in body |
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Dec 31 |
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New grand projects in contemporary math added 1237 characters in body |
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Dec 31 |
awarded | ● Good Question |
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Dec 30 |
awarded | ● Nice Question |
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Dec 30 |
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New grand projects in contemporary math dear unknown, excellent! |
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Dec 30 |
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New grand projects in contemporary math dear quid, I have no issues if you folks decide to close it down, and I do understand your misgivings about possible arguments on what is important and what not. But fact is, there have always been and there will always be leading trends in math and sciences, and the only thing I am after here is a set of honest answers: why not letting working mathematicians talk about what is important right now in their great field? If people will feel differently about what is relevant, so be it. All the best, Mirco |
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Dec 30 |
asked | New grand projects in contemporary math |
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Dec 23 |
awarded | ● Nice Answer |
