Timeline for When have we lost a body of mathematics because errors were found?
Current License: CC BY-SA 3.0
36 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2020 at 2:21 | answer | added | Phil Harmsworth | timeline score: 3 | |
| May 11, 2016 at 2:03 | comment | added | Yemon Choi | @LSpice The OP mathoverflow.net/users/15516/edmund-harriss is, at time of writing, "last seen Sep 6 '14" | |
| May 11, 2016 at 1:55 | comment | added | LSpice | Since the issue seems to come up repeatedly in answers (despite @YemonChoi's heroic efforts), would you mind making a further edit to clarify that you mean 'lost' not in the sense of "unable to be found" ("the lost work of …"), but rather in the sense of "realised not to be true" (something more like "lost innocence")—unless that isn't what you mean, in which case a clarification to that effect would probably be appropriate? | |
| May 10, 2016 at 19:37 | history | edited | Yemon Choi | CC BY-SA 3.0 |
reworded title to make the intent clearer (see the blogpost being linked to)
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| May 10, 2016 at 15:58 | answer | added | Dima Pasechnik | timeline score: 0 | |
| Dec 16, 2012 at 16:13 | answer | added | Todd Trimble | timeline score: 25 | |
| Dec 16, 2012 at 15:26 | answer | added | Rodrigo A. Pérez | timeline score: 40 | |
| May 14, 2012 at 5:34 | comment | added | Colin Reid | @Henry: In a similar vein, I have heard the fear expressed that the last generation of experts on the proof of the Classification of Finite Simple Groups will die out and posterity will never recover the current level of insight into CFSG, because it will be too much effort for too little reward for newcomers to reach this level of expertise. | |
| May 14, 2012 at 1:19 | comment | added | Edmund Harriss | @Misha Thanks for that. Will look up that paper. | |
| May 13, 2012 at 21:25 | comment | added | Misha | @Edmund: Actually, the first correct proof appeared in M. Kapovich, J. Millson, Universality theorem for configuration spaces of planar linkages, Topology, Vol. 41 (2002), no. 6, p. 1051--1107. | |
| May 12, 2012 at 22:37 | answer | added | none | timeline score: 17 | |
| May 10, 2012 at 13:38 | answer | added | Eugene | timeline score: 1 | |
| May 10, 2012 at 13:02 | comment | added | Abdelmalek Abdesselam | @Daniel: I don't understand what you mean by "it was that numerical...practical applications". 19th century invariant theory was not about doing numerical calculations. Also, it was an endeavor in pure mathematics. Practical applications were not at the top of the agenda. | |
| May 10, 2012 at 8:41 | answer | added | Per Manne | timeline score: 30 | |
| May 10, 2012 at 7:53 | answer | added | Charles Matthews | timeline score: 17 | |
| May 10, 2012 at 4:57 | comment | added | Edmund Harriss | @Henry Sadly the decay is not a new thing. For example the role that Coxeter played in protecting many results in Geometry, or the nineteeth century interest in the geometry of linkages that is now being rediscovered. A nice example of this is Kempe's result that any bounded region of an algebraic curve can be made by a linkage. Though in this case the decay is being reversed as O'Rourke and Demaine give (the first correct) proof in amazon.com/Geometric-Folding-Algorithms-Linkages-Polyhedra/dp/… | |
| May 10, 2012 at 4:42 | comment | added | Edmund Harriss | @Terry and @Eric Gematria is a neat example, certainly built on foundations we now feel are unfounded. The actual mathematics built on top of it, however, some combinatorics is still valid. So perhaps this is actually evidence the other way that good mathematics CAN be built on the weakest of foundations. | |
| May 10, 2012 at 4:25 | comment | added | Henry Cohn | According to cecm.sfu.ca/organics/covering/html/node4.html, "We have reached the point of decay in some areas. Richard Askey has observed that Gregory Chudnovsky knows things about hypergeometric functions that no one has understood since Riemann and that, with Chudnovsky's eventual passing, no one is likely to understand again." I've wondered what this refers to, but I've never asked Askey whether this quote is accurate or what he meant. | |
| May 10, 2012 at 4:19 | answer | added | Kristal Cantwell | timeline score: 21 | |
| May 10, 2012 at 3:56 | comment | added | Eric Tressler | @Terry: I still see numerology around, especially in California. Then again, I don't go out of my way to avoid it; I really enjoyed Underwood Dudley's "Mathematical Cranks". I think (hope) it doesn't count, though. | |
| May 10, 2012 at 3:35 | comment | added | Terry Tao | Would gematria count? | |
| May 10, 2012 at 3:23 | comment | added | Brendan McKay | A lot of classical Greek mathematics is only known to us via Arabic translations (so it was "lost" to Europeans for centuries) and some classical mathematical works referred to in others have been lost altogether. Of course it is rather unlikely that any original mathematics in those works has not since been rediscovered. | |
| May 10, 2012 at 2:12 | history | edited | Edmund Harriss | CC BY-SA 3.0 |
added 135 characters in body
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| May 10, 2012 at 2:06 | history | edited | Edmund Harriss | CC BY-SA 3.0 |
added 427 characters in body
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| May 10, 2012 at 0:06 | comment | added | Daniel Moskovich | This sounds like a different phenomenon from the one that you are refering to (is it?), but Indian Mathematics, Chinese Mathematics, Babylonian Mathematics, etc. were effectively "lost" (at least in large part), and have only recently been partially "rediscovered" as "archeology". More recently, 19th century invariant theory. It wasn't that they were false; it was that numerical methods became less valuable for these problems, because general methods were discovered, or else the calculations didn't draw enough attention because of lack of practical applications. | |
| May 9, 2012 at 23:59 | comment | added | David Roberts♦ | I would phrase the question 'Have we had to lose any mathematics?' (or "mathematics", or "theorems") There is probably some ancient Greek stuff that we know about but don't have (we have actually actually lost it, and not on purpose), but this is not what you are asking about. | |
| May 9, 2012 at 23:13 | comment | added | J.J. Green | Didn't something along these lines happen to Italian algebraic geometry in the 1930s? see en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry for example | |
| May 9, 2012 at 23:05 | comment | added | Felix Goldberg | But trisection have never been really accepted as valid, have they? Maybe a better example would be proofs of Euclid's fifth postulate. As I understand, they were being "improved" throughout the ages until the whole enterprise imploded. | |
| May 9, 2012 at 23:02 | comment | added | Gerhard Paseman | In which case, there are several instances of such theories that continually reappear, e.g. trisecting the angle using compass and straightedge alone. They aren't lost, unfortunately. Gerhard "Ask Me About System Design" Paseman, 2012.05.09 | |
| May 9, 2012 at 23:00 | comment | added | Felix Goldberg | en.wikipedia.org/wiki/Obsolete_scientific_theory makes no mention of mathematics... | |
| May 9, 2012 at 22:50 | comment | added | Gerry Myerson | I take the question to be, is there a mathematical equivalent of the phlogiston theory of combustion? | |
| May 9, 2012 at 22:47 | comment | added | Felix Goldberg | I think the OP might have meant a case when a whole field has been invalidated. I can't recall such a case. | |
| May 9, 2012 at 22:34 | comment | added | Asaf Karagila♦ | I had some mathematics in my pocket the other day, but I seemed to have lost it. Perhaps it is just buried in the mess of my desk... | |
| May 9, 2012 at 22:23 | comment | added | Henry Cohn | What counts as "anything"? Certainly incorrect theorems have been published. Sometimes they were unimportant, but occasionally they have been genuinely interesting and important results that could not be salvaged once the mistake was identified. Does that count as lost mathematics? I think there's a whole continuum here, from isolated errors to fundamental flaws in large parts of mathematics. I don't know of any really large-scale examples. | |
| May 9, 2012 at 22:03 | comment | added | Gerhard Paseman | If we had truly lost it, can you expect us to know enough about it to tell you? Gerhard "Still Looking For A Proof" Paseman, 2012.05.09 | |
| May 9, 2012 at 21:52 | history | asked | Edmund Harriss | CC BY-SA 3.0 |