Timeline for How to explain to an engineer what algebraic geometry is?
Current License: CC BY-SA 4.0
46 events
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| Apr 15 at 20:55 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Oct 20, 2020 at 10:57 | comment | added | Qfwfq | @Geva Yashfe: "it is not self evident to an outside observer that AG is not some collective waste of time", that's why I asked the question. Curiously, one probably wouldn't have this problem with number theory, which is itself pretty abstract. --- "relatively small number of external applications", yes the practical applications usually give reassurance, but my question was more about how to convey that AG is intellectually "plausible", perhaps inevitable, rather than practically useful (the latter could be a different interesting question, that probably already exists in this site). | |
| Oct 19, 2020 at 23:04 | comment | added | Geva Yashfe | it is not self evident to an outside observer that AG is not some collective waste of time, especially to one shown difficult, abstract ideas, and a relatively small number of external applications which don't visibly justify over a century of work by the mathematical community. | |
| Oct 19, 2020 at 23:03 | comment | added | Geva Yashfe | Some participants here seem to think it's not difficult to give examples that engineers are satisfied by, or at least find reasonable, and that it is self evident that there is a point to studying algebraic geometry. But when some new user came here about a day ago and (admittedly, misusing the website) gave an answer which expressed skepticism, this answer was downvoted and then deleted. I think we should have rather taken him/her seriously and left the answer even though it was out of place: ...(to be continued) | |
| Oct 19, 2020 at 13:45 | comment | added | Christian Chapman | this engineer you have imagined seems to have a pretty impoverished mind | |
| Sep 2, 2020 at 22:05 | answer | added | Hollis Williams | timeline score: 3 | |
| Aug 18, 2020 at 19:04 | comment | added | Andrés E. Caicedo | twitter.com/littmath/status/1295167214455332866 | |
| Aug 18, 2020 at 18:04 | comment | added | Qfwfq | I never said engineers are perplexed with complex numbers; but with complex geometry yes, I think they would be. You're going to say I don't have statistics about that. Fair enough, I don't have statistics about that, but I reason out of analogy: people tend to perceive things they aren't used to as exotic. For example for me it's anything over $\mathbb Z$ or over a number field. | |
| Aug 18, 2020 at 17:59 | answer | added | Michael | timeline score: 6 | |
| Aug 18, 2020 at 17:48 | comment | added | Michael | A side note: engineers are perfectly comfortable with complex numbers, so they won't get perplexed at all. Things like Fourier transforms (naturally, with complex coefficients) are bread and butter for many EEs. | |
| Aug 18, 2020 at 9:35 | answer | added | J W | timeline score: 3 | |
| Aug 17, 2020 at 18:45 | comment | added | Tim Campion | A thought too half-baked for an answer: There's a whole industry of applied algebraic geometry. I don't know anything about it, but I have the impression that Grobner basis methods and something called "homotopy continuation" are used to solve algebraic systems for applications like robot motion planning. I'm sure that a little bit of reading on stuff like this would reveal that the global perspective provided by classical algebraic geometry is important for shedding light on how to do things like this in better ways than just "crunching through some algebra". | |
| Aug 17, 2020 at 17:42 | comment | added | Hollis Williams | If you look back earlier in the comments it seems like someone else pointed it out 2 years ago, so I think you should edited it before now anyway. | |
| Aug 17, 2020 at 16:23 | history | edited | Qfwfq | CC BY-SA 4.0 |
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| Aug 17, 2020 at 16:22 | comment | added | Qfwfq | (...) As for the complex numbers, I assume the average engineer is not exposed to complex geometry (as opposed to, say, 1 variable complex analysis) so might find it a bit exotic. Also, in the sense of the OP, complex alg. geometry is "easier" than the real one, so in hindsight that phrasing it not so patronizing after all. But I'll edit the word "intimidated" out, just to avoid giving that impression. | |
| Aug 17, 2020 at 16:18 | comment | added | Qfwfq | @Hollis Williams: In fact I have not instinctively gone for "her" at all. I just chose to adhere to the new trend of using "she" as a neutral pronoun, usually used to counterbalance the traditional "he" for the neutral (or to counterbalance the traditional expectation that an engineer had to be a male). (...) | |
| Aug 17, 2020 at 14:43 | comment | added | Hollis Williams | ''Here she's starting to feel a bit intimidated: why complex numbers and not just reals? But she can feel comfortable again once you tell her it's because you want to have available all the geometry there is, without hiding anything - she can think of roots of one-variable polynomials: in (x−1)(x2+1) the real solutions are not all there is etcetera.'' Some of this question is coming across as very patronising. Why have you instinctively gone for 'she' and saying 'she' is intimidated and 'not sure' about complex numbers? | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Apr 8, 2019 at 11:40 | review | Close votes | |||
| Apr 8, 2019 at 18:43 | |||||
| Apr 8, 2019 at 9:42 | answer | added | Al-Amrani | timeline score: 3 | |
| Nov 19, 2018 at 0:27 | answer | added | Joseph O'Rourke | timeline score: 23 | |
| Nov 19, 2018 at 0:01 | comment | added | Alexander Woo | I don't think it's helpful to try to hide that mathematicians are interested in theory for its own sake. Once the engineer understands that most algebraic geometry is motivated by curiosity, not applications, then they have the proper frame of mind to understand a description of the subject. Otherwise, they are unhelpfully stuck trying to understand your description in terms of potential applications. The engineer can't understand that algebraic geometry is about qualitative descriptions because they can't believe it because they don't see applications for qualitative descriptions. | |
| Nov 18, 2018 at 21:17 | answer | added | forget this | timeline score: 13 | |
| Oct 27, 2018 at 20:25 | answer | added | Timothy Chow | timeline score: 19 | |
| Oct 24, 2018 at 15:08 | comment | added | Viktor Vaughn | David Cox has a really nice article called What Is the Role of Algebra in Applied Mathematics? in which he begins with a problem in geometric modeling and shows how it leads to resultants, free resolutions, and the Hilbert-Burch Theorem. He then goes on to discuss a few other problems in economics and computer algebra. | |
| Oct 24, 2018 at 10:25 | comment | added | Qfwfq | @polfosol: yes, that's indeed a good idea (though the question was more about giving an idea of what AG is about than convincing of its usefulness in applications) | |
| Oct 24, 2018 at 10:23 | comment | added | polfosol | I am an engineer and I have to say that IMHO, the most convincing argument about usefulness and necessity of algebraic geometry was the beauty of elliptic curve cryptography. | |
| Oct 23, 2018 at 20:40 | answer | added | Mark Wildon | timeline score: 6 | |
| Oct 23, 2018 at 20:06 | comment | added | davidbak | Not sure I get why the engineer suddenly gets intimidated by the introduction of complex coefficients. Just because they use j and not I doesn't mean they don't understand the use and/or value of complex numbers. | |
| Oct 23, 2018 at 17:41 | answer | added | Rohit Chatterjee | timeline score: 5 | |
| Oct 23, 2018 at 14:38 | answer | added | Steven Landsburg | timeline score: 23 | |
| Oct 23, 2018 at 14:38 | comment | added | Al-Amrani | The more motivating , and more practical , way to understand and study algebraic geometry , is elimination theory (inertia forms (Trägheitsformen) , resultants, resultant-ideals , discriminants ...). | |
| Oct 23, 2018 at 13:45 | review | Close votes | |||
| Oct 24, 2018 at 1:55 | |||||
| Oct 23, 2018 at 10:25 | answer | added | Donu Arapura | timeline score: 33 | |
| Oct 23, 2018 at 8:00 | answer | added | Ben McKay | timeline score: 30 | |
| Oct 23, 2018 at 6:01 | comment | added | AHusain | Along the line's of @ZachTeitler comment, What is Numerical Algebraic Geometry | |
| Oct 23, 2018 at 5:17 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added the (ag.algebraic-geometry) tag
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| Oct 22, 2018 at 23:25 | comment | added | Somatic Custard | @ArunDebray With all respect to Mumford, his great expertise in the practice of algebraic geometry did not carry over to expertise in the explanation of algebraic geometry to non-mathematicians. It seems like his idea of a non-mathematician is someone who has at the very least a college degree or graduate degree in math or physics, but may not professionally practice math. | |
| Oct 22, 2018 at 23:04 | comment | added | Zach Teitler | Why do you think that algebraic geometers don't try to find the solutions? Maybe some (maybe most) algebraic geometers don't. But there are really a lot of algebraic geometers who work on computational algebraic geometry, and study solution sets. Names here include Bernd Sturmfels, David Cox, Elizabeth Allman, Andrew Sommese, Seth Sullivant, Jonathan Hauenstein... Saying algebraic geometry "doesn't care at all", even with "mostly" there, just seems incorrect, sorry. | |
| Oct 22, 2018 at 22:48 | comment | added | Arun Debray | Mumford has an interesting blog post, "Can one explain schemes to biologists?" Its context is very different, but it still says something useful about bringing algebraic geometry to non-mathematicians. | |
| Oct 22, 2018 at 22:40 | comment | added | Gerhard Paseman | Ask the engineer questions. Find out what they really want to know about it. If they want intellectual stimulation, given them a problem that is easy to solve with AG, and a similar one that is not. If they want applications, tell them about motion planning in robotics, systems in economics, and other things that show its actual as well as potential uses. Gerhard "Makes Explaining To Myself Easy" Paseman, 2018.10.22. | |
| Oct 22, 2018 at 21:59 | comment | added | François Brunault | One should at least try to give some geometric motivation (in other words, why it is called "geometry") and the fruitful interplay between algebra and geometry. | |
| Oct 22, 2018 at 21:58 | comment | added | Qfwfq | @Kevin Casto: I see your point, and I agree. But still, one might think that we're just studying things qualitatively because we're not able to do better, and that the final goal would be to.. ya know, actually solve stuff. | |
| Oct 22, 2018 at 21:55 | comment | added | Kevin Casto | To start, I might tell them that algebraic geometry lets us say qualitative things about solutions to equations even if it's intractable to find them quantitatively. For example, the fact that for curves, if it's genus 0 it has a dense set of rational points, genus 1 has f.g. set of rational points, and genus 2 has a finite number of rational points -- that's more arithmetic, but the point stands. I might compare this to the way dynamics can say qualitative things about solutions to differential equations, even when they can't be quantitatively solved, which might be more in their wheelhouse | |
| Oct 22, 2018 at 21:37 | history | edited | Qfwfq | CC BY-SA 4.0 |
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| Oct 22, 2018 at 21:33 | history | asked | Qfwfq | CC BY-SA 4.0 |