Timeline for "Family Tree" of Theorems
Current License: CC BY-SA 3.0
23 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2018 at 0:51 | answer | added | charles knight | timeline score: 2 | |
| Dec 11, 2017 at 0:29 | review | Close votes | |||
| Dec 11, 2017 at 10:00 | |||||
| Sep 10, 2016 at 7:50 | comment | added | Martin Sleziak | A question which seems to be related to this one has been posted recently: Is there a database for tracking the dependencies of mathematical theorems? | |
| S Sep 8, 2016 at 23:19 | history | suggested | Rodrigo de Azevedo |
Added tag to this question
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| Sep 8, 2016 at 22:45 | review | Suggested edits | |||
| S Sep 8, 2016 at 23:19 | |||||
| Jun 10, 2015 at 6:17 | comment | added | Manfred Weis | A family tree for the definitions in a mathematical theory might also be a good idea that maybe is easier to realize. | |
| Jun 9, 2015 at 23:11 | comment | added | Menachem | I see how this can become very tricky very quickly, and this is related to what Goldstern and Yoav are discussing -- of course we might have a proof that Theorem A implies Theorem B. That statement, which we might call Theorem C, does not actually depend on either Theorem A or B. So I guess that in some sense even edges might be nodes? This will be messy... | |
| Jun 9, 2015 at 20:12 | comment | added | Yoav Kallus | @Goldstern Fair. I would argue that in your particular example you cannot "use H to prove Z" since H "depends" on Z, but then we'll descend to an argument about terms. | |
| Jun 9, 2015 at 20:05 | comment | added | Goldstern | @YoavKallus Yes, but "Theorem H. Proof: follows from Z" and "Exercise: Show that Z immediately follows from H" is fine. Lazar asked for 'statements such as "Theorem A is used / can be used to prove Theorem B"'. | |
| Jun 9, 2015 at 20:00 | comment | added | Yoav Kallus | @Goldstern but if you read in a textbook "Theorem H. Proof: follows from Z □" then "Theorem Z. Proof: follows from H □", you would throw the book in garbage. | |
| Jun 9, 2015 at 19:55 | comment | added | Goldstern | I am not sure what you mean by "dependencies", and why cycles should be forbidden. You can prove Zorn's lemma Z from Hausdorff's maximality principle H; but H is an immediate consequence of the Teichmüller-Tukey lemma, which itself easily follows from Z. | |
| Jun 9, 2015 at 19:49 | comment | added | Jeff Strom | You could get a well-defined graph describing the relationships between the results in a particular (traditional) exposition (i.e., textbook). | |
| Jun 9, 2015 at 18:01 | history | edited | Menachem | CC BY-SA 3.0 |
added second paragraph
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| Jun 9, 2015 at 17:40 | answer | added | Fred Rohrer | timeline score: 5 | |
| Jun 9, 2015 at 17:08 | answer | added | François G. Dorais | timeline score: 12 | |
| Jun 9, 2015 at 17:04 | answer | added | Yoav Kallus | timeline score: 3 | |
| Jun 9, 2015 at 16:58 | comment | added | Menachem | And yes, I agree, directed. And hopefully acyclic :) | |
| Jun 9, 2015 at 16:57 | comment | added | Robert Israel | These dependencies are not unambiguous. There may be many different proofs of theorem $A$, some of which use theorem $B$, while others use theorem $C$, and still others prove $A$ first and derive $B$ and $C$ as corollaries. | |
| Jun 9, 2015 at 16:57 | comment | added | Menachem | Hmm, this is an interesting question -- I didn't think so much about the specifics. This question came to mind because I am thinking about a specific theorem, and was wondering whether it is built on another specific theorem. Of course I can track down and read the original paper, but it would be great if this sort of graph were available, and I could just "look it up". | |
| Jun 9, 2015 at 16:51 | comment | added | Joonas Ilmavirta | Would you like it to include a single theorem depending on several others in addition to simple $A\implies B$ branches? | |
| Jun 9, 2015 at 16:49 | comment | added | Yoav Kallus | directed acyclic graph, hopefully | |
| Jun 9, 2015 at 16:45 | review | First posts | |||
| Jun 9, 2015 at 16:51 | |||||
| Jun 9, 2015 at 16:42 | history | asked | Menachem | CC BY-SA 3.0 |