Timeline for What is the most useful non-existing object of your field?
Current License: CC BY-SA 3.0
7 events
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| Dec 31, 2014 at 12:33 | comment | added | jmc | I think this answer is not really in the spirit of the question. The question says many proofs by contradiction end with "we have built an object with such, such and such properties, which does not exist". Otherwise, besides $\mathbb{F}_{1}$, I think motives would definitely deserve a place in this list. Both $\mathbb{F}_{1}$ and motives (and also path integrals, as far as I can see) are really important guidelines, that help us develop theory, even though we do not know whether they exist. We surely hope they do exist. But such objects is not what this question is about… | |
| Oct 3, 2014 at 20:32 | comment | added | André Henriques | The sense in which it does not exist is that it has never been defined mathematically. Here, it's important to distinguish "define" and "compute". Physicists know how to compute (some) path integrals, but they don't know how to define them. Mathematicians, on the other hand, refuse to deal with concepts that havn't been defined. I should point out that there is mathematical work whose goal is to define path integrals (e.g. Glimm & Jaffee's book) but a lot of the path integrals considered by physicists fall outside the scope of that book. That being said, I'm really not an expert on all that. | |
| Oct 3, 2014 at 4:06 | comment | added | Ruslan | Hm, in what sense does it not exist? | |
| Sep 29, 2014 at 17:04 | comment | added | Peter Samuelson | Definitely too good not to mention! | |
| Sep 29, 2014 at 16:30 | comment | added | Todd Trimble | Neither is $\mathbb{F}_1$, but if we are liberal and admit such chimerical entities, then both are worthy of mention! | |
| S Sep 29, 2014 at 16:25 | history | answered | André Henriques | CC BY-SA 3.0 | |
| S Sep 29, 2014 at 16:25 | history | made wiki | Post Made Community Wiki by André Henriques |