Todd Trimble
|
Registered User
|
|
|
1d |
comment |
Is there a contractible bounded homogeneous space? Yes, it has that kind of flavor. That still doesn't prevent me from finding it amazing. |
|
1d |
comment |
Is there a contractible bounded homogeneous space? That's really quite a remarkable result... |
|
2d |
comment |
Google question: In a country in which people only want boys Although Matthew has bowed out, I just want to say what a pleasure it is to read his comments generally, not only for their erudition but for their wonderful civility. Too bad not all comments under this question in particular are so civil... |
|
May 14 |
comment |
Proof of the weak Goldbach Conjecture As in party-pooper, I suppose (for those who don't know the English expression: someone who acts in a way to dampen enthusiasm). |
|
May 13 |
comment |
Unit sphere in R^\infty is contractible? I wouldn't worry about it -- let it stand. It seems like an interesting remark. Since some like me might not be too familiar with the Banach-Dieudonne theorem and its consequences, you might also consider fleshing this out a bit (I quickly googled and the statement I found applied to Banach spaces, which $\mathbb{R}^\infty$ is not, so it would help me personally to have a little more explanation). |
|
May 9 |
comment |
What is known about the area of the symmetric Pythagorean tree? @Gerard: such a pro tem explanation is good enough for me. It would be ridiculous to hold every MO question to the same standard (explain to me why I should care), and in my view many other questions that appear on MO are of even less intrinsic interest. I expect the problem is indeed challenging. People should work on it only if they feel like it. |
|
May 9 |
comment |
What is known about the area of the symmetric Pythagorean tree? I don't know, guys. The linked Wikipedia article seems to give a clear enough indication of what the (symmetric) Pythagorean tree is; just click on it if you want to know. If the question were slightly edited to "what is known about the area?" (beyond what is contained in the Wikipedia article or articles linked therein), then it wouldn't disqualify itself on the grounds of being an open problem, and probably about as acceptable as many other MO questions, although I agree with Deane that the response to Anton was really uncalled for (and could warrant a flag). If you don't like it, skip it. |
|
May 8 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? Thank you for this tremendous answer, Andrej! It practically made my day. |
|
May 8 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? @Amir: I am utterly confused about what actually happened at that discussion. I don't think anyone who wasn't there can really comment on that discussion, and certainly not on the basis of such a skeletal report. It might help if the discussion were videotaped and made public, so that you could point to specific moments of the discussion that trouble you, although it's my opinion that MathOverflow (and its particular functionalities) are in fact poorly adapted for such a discussion about a discussion. I have just entered a vote to close. |
|
May 7 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? I am aware of what was said in the OP. However, in view of the update, it's not clear to me that anyone's feelings were accurately recounted. We could have a real discussion if we could see something expressed in print, instead of getting information second-hand whose accuracy has been called into question. |
|
May 4 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? Thanks for clarifying your comment, trb456. I largely agree, but I thought the general discussion here was to be about mathematicians (e.g., the author of Theorems For a Price). I didn't mean to sound insulting by using the word 'academic', and I'm sorry if I did. |
|
May 4 |
comment |
Complete De Morgan algebra You should try googling. The Wikipedia article can help. |
|
May 3 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? Thanks to John Stillwell for providing a fuller quotation -- the final words are something that most mathematicians would agree with. And while he exaggerates when he says "all physicists", he's right that many (most?) physicists have such attitudes, perhaps even moreso in his day. |
|
May 3 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? Yes, a proof that certifies 99.999% likelihood of validity should itself be impeccable. I think Terry Tao was driving at something slightly different, about arguments being both correct but perhaps more crucially for the advancement of understanding, letting the high-level ideas shine through without being cluttered with details at a routine and professionally trivial level. But I agree that everyone, and I would include prodigies, has to go through these stages. That said, I feel as though some of this discussion is academic: which mathematicians nowadays publicly wish to get rid of rigor? |
|
May 3 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? It's completely fine to answer your own question. I set off the quotation of Atiyah to make it clear that it's his (and gave the source). I think also you should put your non-neutral comments here where they belong, not meta, where the discussion was about whether this question was appropriate for MO. |
|
May 3 |
revised |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? set off quotation and provided source |
|
May 3 |
comment |
How can we distinguish between frames and multiplicative lattices? Well, assuming I understand the definition of multiplicative lattice (encyclopediaofmath.org/index.php/…), frames are exactly multiplicative lattices in which every element is idempotent. |
|
May 3 |
accepted | Proof by contradiction in a topos |
|
May 2 |
revised |
Proof by contradiction in a topos edited body |
|
May 2 |
answered | Proof by contradiction in a topos |
|
May 1 |
revised |
For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? fixed a typo and added a few words |
|
May 1 |
comment |
For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? That's very nice! |
|
May 1 |
comment |
For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? Just to add to what Noah said: given a poset, meets and joins (if they exist) are uniquely determined by universal properties of cartesian product and coproduct (thinking of the poset as a category). Thus, $a \wedge b$ would be the unique element such that $x \leq a \wedge b$ iff $x \leq a$ and $x \leq b$. Negation can also be defined universally: $x \leq \neg a$ iff $x \wedge a \leq 0$ (where $0$ is the bottom element). |
|
May 1 |
comment |
For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? No, please don't delete. You can update the question if you like by referring to this information, and if you like you can use the html command "strike" which crosses out the bit you don't like but still leaves it visible. |
|
May 1 |
answered | For a monoid with zero $M$, how many additive operations on $M$ can there be making $M$ a ring? |
|
Apr 29 |
awarded | ● Enlightened |
|
Apr 29 |
awarded | ● Nice Answer |
|
Apr 26 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? Alright then, so I misread Asaf's comment. Stuff happens. I'm happy to remove my own comment, but I still encourage you (Paul) to improve your answer by explaining how it relates to the question. |
|
Apr 22 |
comment |
Another identity involving sums of (alternating) binomial coefficients. Thanks Suvrit; I didn't know that about him. |
|
Apr 22 |
comment |
Another identity involving sums of (alternating) binomial coefficients. Following on Aaron's comment: it sounds like you've already answered your own question! That is, assuming your solutions were correctly derived, you've already given a proof of the identity yourself. Did I misunderstand? Follow-up question: are you familiar with the usual techniques as set out in Concrete Mathematics by Graham, Knuth, and the last guy whose name I forget? (Otashnik or something) |
|
Apr 22 |
comment |
Giving $Top(X,Y)$ an appropriate topology Just a little note on local compactness. A lot of texts define this to mean a space such that every point has a compact neighborhood. But this often isn't as "convenient" (to use the word pointedly) as the stronger condition that every point has a basis of compact neighborhoods, which is essentially the interpolation property mentioned above. However, the conditions coincide if the space is assumed to be Hausdorff. |
|
Apr 21 |
comment |
Torsion product Tor^R_1(,) I strongly doubt this question will be reopened, but let me attempt to say something helpful. The specific places where there is confusion are where you attempt to invoke things like $\lim_{n \to \infty} Z_n \simeq Z$. If you were in my office with this question, I would challenge you just to explain exactly what you mean by those limit assertions, backing it up with precise definitions. I'm pretty sure that if you honestly do this by yourself or in a mathematician's office, your confusion will unravel. (But this is not the right venue for this exercise -- sorry.) |
|
Apr 21 |
comment |
Torsion product Tor^R_1(,) This site is geared essentially to professional mathematicians for their research interests, and so this question doesn't belong here. Moreover (to put it bluntly), the question is pure confusion. The best idea might be to work honestly through a basic text on homological algebra, if this material is something you need. |
|
Apr 20 |
comment |
An example of a beautiful proof that would be accessible at the high school level? @Quinn: in that case, I suggest trying to invent your own proof, and then make it as pretty as you possibly can. |
|
Apr 19 |
awarded | ● Enlightened |
|
Apr 19 |
awarded | ● Nice Answer |
|
Apr 19 |
comment |
Elementary proof for identity involving sums of binomials You're welcome! I actually rather enjoyed working it out. |
|
Apr 19 |
revised |
Elementary proof for identity involving sums of binomials edited body |
|
Apr 19 |
accepted | Elementary proof for identity involving sums of binomials |
|
Apr 19 |
revised |
Elementary proof for identity involving sums of binomials added 57 characters in body; added 14 characters in body |
|
Apr 19 |
answered | Elementary proof for identity involving sums of binomials |
|
Apr 18 |
comment |
Is there any nontrivial monad on the category of graphs? Don't worry; it took me a couple of minutes to think of this (having thought of and then discarding things like the complete graph which doesn't work). More important maybe is the general technique of using monoids in monoidal categories to cook up examples of monads. |
|
Apr 18 |
comment |
Is rigour just a ritual that most mathematicians wish to get rid of if they could? A ritual?! What a tendentious way of putting it, and I disagree with every fiber of my being. But naturally, there are different levels of proof which are appropriate to different occasions. There is a high level which can be a sentence or two between collaborating experts, which might be a paragraph or two in a seminar, which might be a few pages in a published journal, and which would be further expanded in a fully formal proof in Mizar. What is completely tossed out the window, however, is the idea that the presentation of proof can be a real art form. It should be what we live for. |
|
Apr 18 |
comment |
Most harmful heuristic? Ironically, I just had an example the other day (linear codes) where it wasn't completely clear to me what the correct notion of isomorphism should be!! So this is me answering my former (August 25 2012) self. |
|
Apr 18 |
accepted | Is there any nontrivial monad on the category of graphs? |
|
Apr 18 |
answered | Is there any nontrivial monad on the category of graphs? |
|
Apr 17 |
accepted | Does “induction” for a functor algebra imply it is initial? |
|
Apr 15 |
answered | What is “Data” involved in a mathematical construction? |
|
Apr 14 |
answered | Does “induction” for a functor algebra imply it is initial? |
|
Apr 10 |
answered | Fixed point theorems |
