Timeline for The interrelationship problem of modern mathematics – How to deal with it in first year graduate courses?
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33 events
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| Oct 16, 2023 at 13:52 | comment | added | Michael Hardy | "Is the old model of keeping the subdisciplines of mathematics separate in coursework for the sake of focus obsolete?" The word "obsolete" seems to mean it was a good thing at some time in the past. Whether that is true seems unclear. | |
| Sep 8, 2023 at 16:04 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Sep 8, 2023 at 15:12 | answer | added | Timothy Chow | timeline score: 5 | |
| Aug 31, 2021 at 4:32 | review | Close votes | |||
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| Dec 11, 2017 at 4:53 | review | Close votes | |||
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| Oct 12, 2017 at 3:16 | review | Close votes | |||
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| Apr 16, 2010 at 18:46 | comment | added | The Mathemagician | Apprieciated,Joel. I dunno if I'll have time this semester,but next semester,while waiting for my PHD application to be processed-I should have time for many things.I'll put it on my to-do list if you're still running the course. | |
| Apr 16, 2010 at 12:25 | comment | added | Joel David Hamkins | Well, my invitation to you stands. | |
| Apr 16, 2010 at 4:36 | comment | added | The Mathemagician | @Joel continued:I'm simply saying most mainstream mathematicians seem to change the subject when foundational questions come up because it's a thicket of metaphysics most aren't really comfortable with the same way they're comfortable with Lesbegue measures and sheaves.I personally think this is unfortunate because they have a great deal to learn from "foundational" mathematics like axiomatic set theory,logic and constructive category theory. | |
| Apr 16, 2010 at 4:36 | comment | added | The Mathemagician | @Joel-I've been a student of both Elliott Mendelson and Saul Kripke and I was a philosophy major in a former life.So trust me-you don't have to convince me about the importance of your field. | |
| Apr 16, 2010 at 0:54 | comment | added | Joel David Hamkins | About "controversial": That is surely a minority view (and possibly an offensive one as well), held I imagine only by someone with little exposure to what math logic is. Since you are here in New York, I would invite you to join my intro logic course at the CUNY Graduate Center (e.g. this semester), and I doubt afterwards that you would give any credence to such a view. | |
| Apr 15, 2010 at 22:51 | comment | added | The Mathemagician | Well,it ATTEMPTS to be broader then the average cirricula,Joel.My point is that the inertia of reputation and the resulting influence of the dominating faculty probably hinders this a lot more then it sounds at the department webpage with describes the program. By controversial I mean many mathematicians aren't comfortable calling it math. Philosophical questions are rather hard to avoid when dealing with this subject unless we just play with the symbols and follow the rules without thinking. Which I am definitely not in favor of. | |
| Apr 15, 2010 at 21:05 | comment | added | Joel David Hamkins | Andrew, I don't actually find the status of set theory or mathematical logic as mathematics to be controversial. Rather, I was objecting to the characterization of the Columbia program as holistic, when I would describe it more as focused. In your comments, however, you now seem to regard it as specialized, so perhaps we agree after all? | |
| Apr 15, 2010 at 18:05 | comment | added | The Mathemagician | @Joel concluded: Interestingly,the City University Of New York Graduate Center is now rated one of the top programs for Logic And Foundations in PHILOSOPHY.And a lot of that has to do with one man being here:Saul Kripke. So WHO'S on staff has a profound influence not only on the program itself,but it's prestige.And the prestige factor I suspect is largely to blame for the specialization. | |
| Apr 15, 2010 at 18:02 | comment | added | The Mathemagician | @ Joel continued: Sadly,top schools like Columbia further complicate the issue we're discussing by tailoring thier programs by the research areas of thier star faculty to the exclusion of all else.For example,for many years,Stanford was known for it's algebra and algebraic geometry researchers to the exclusion of all else-to the point they didn't offer a point set topology course or a standard number theory course. It seems the higher up you go on the academic food chain,the more specialized the programs get as dictated by thier faculty."Balanced" programs seem to be becoming rare. | |
| Apr 15, 2010 at 17:58 | comment | added | The Mathemagician | @Joel: Well,Joel,as I'm sure you're aware,the status of logic and set theory as mathematic per se is somewhat controversial.By it's very nature,it borders on philosophical terrain. (I personally think that makes it even MORE relevant,not less. What's the point of any domain of human understanding if it doesn't question it's own foundations?I think these questions if anything are even more important for mathematics since it appears to be a paradoxical enterprise:A man made structure with deep ties to the natural world.But I digress.) | |
| Apr 15, 2010 at 13:24 | comment | added | Joel David Hamkins | Andrew, you mention what you describe as the holistic approach of Columbia University, which is surely a great university. Nevertheless, from my perspective there are major omissions: in the math department there they have essentially no research in mathematical logic or set theory. Strange. (They do have Haim Gaifman over in Philosophy, but do not have him teach in mathematics.) So it seems not wholly holistic. | |
| S Apr 15, 2010 at 4:13 | vote | accept | The Mathemagician | ||
| Apr 15, 2010 at 4:13 | vote | accept | The Mathemagician | ||
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| S Apr 15, 2010 at 4:13 | vote | accept | The Mathemagician | ||
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| Apr 15, 2010 at 4:13 | vote | accept | The Mathemagician | ||
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| Apr 15, 2010 at 3:41 | comment | added | The Mathemagician | math.uchicago.edu/~may/327/General.pdf | |
| Apr 14, 2010 at 22:58 | comment | added | Kevin H. Lin | Where online are Peter May's comments? | |
| Apr 14, 2010 at 22:43 | answer | added | Alexander Woo | timeline score: 25 | |
| Apr 14, 2010 at 18:49 | answer | added | Steven Gubkin | timeline score: 5 | |
| Apr 14, 2010 at 18:17 | history | made wiki | Post Made Community Wiki by Anton Geraschenko | ||
| Apr 14, 2010 at 18:01 | answer | added | Mikael Vejdemo-Johansson | timeline score: 6 | |
| Apr 14, 2010 at 17:52 | comment | added | B. Bischof | It appears Jonas has taken care of the paragraph request. | |
| Apr 14, 2010 at 17:51 | comment | added | B. Bischof | First, I should say I am interested in this question so I upvoted it. I also tend to agree with Nicolas, that a brief tangent into the connecting field is a good way to handle this. (Also essentially the response of KConrad). However, as far as the question. You should edit it to include some paragraph breaks, it is frustrating to read in its current form. Further, I don't like your title, as I don't see this as a "problem" but an "advantage"! Connections in mathematics are a good thing, even if it makes teaching a bit more tricky. | |
| Apr 14, 2010 at 17:50 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
formatting, tags
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| Apr 14, 2010 at 17:47 | answer | added | KConrad | timeline score: 17 | |
| Apr 14, 2010 at 17:40 | comment | added | Nicolas Ford | I took that particular course from Peter May last year when I was at Chicago, and I definitely got the same vibe from him that you seem to have gotten from whatever you read. His solution to the issue struck me as a good one, which was to keep the course focused on the algebra, but mention the connections to other fields when they came up without letting it dominate the class. I'm pretty inexperienced as a mathematician, but it strikes me that a lot of the divisions between fields still make sense; there definitely are "algebraic methods" and "analytic methods", and they're different. | |
| Apr 14, 2010 at 17:24 | history | asked | The Mathemagician | CC BY-SA 2.5 |