Timeline for Theorems with many proofs
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| May 8, 2022 at 7:20 | review | Close votes | |||
| May 9, 2022 at 6:45 | |||||
| May 5, 2022 at 14:03 | comment | added | Wojowu | Around a year after posting of this question a different, similar one was posted, which gained a lot more traction: mathoverflow.net/q/401493/30186 | |
| May 5, 2022 at 11:48 | answer | added | Chris Sangwin | timeline score: 2 | |
| Sep 16, 2020 at 15:39 | comment | added | Joseph O'Rourke | 183 proofs! Meštrović, Romeo. "Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2017) and another new proof." arXiv:1202.3670 (2012). arXiv abstract. | |
| Aug 20, 2020 at 9:54 | comment | added | HJRW | @GerryMyerson: sure, many of the examples in the comments are newer. I meant the ones listed in the question. | |
| Aug 19, 2020 at 13:17 | comment | added | Gerry Myerson | @HJRW the Wagon paper about tiling a rectangle, I believe the result is considerably less than 200 years old. | |
| Aug 18, 2020 at 16:07 | comment | added | Joseph O'Rourke | @AaronMeyerowitz: Nice Grünbaum quote! | |
| Aug 18, 2020 at 10:20 | comment | added | HJRW | The example theorems all have one thing in common, which makes it far more likely that they will have many proofs: they are OLD. (Euler's formula is by far the newest of them, but even that is over 200 years old.) I would be surprised to learn of a >200-year-old theorem with fewer than, say, five proofs. | |
| Aug 18, 2020 at 5:58 | comment | added | Gerry Myerson | I don't have an answer, but two more examples: Robin Chapman collected $14$ proofs of $\zeta(2)=\pi^2/6$ at empslocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf And $14$ is a good number – Stan Wagon won a prize for "Fourteen proofs of a result about tiling a rectangle." maa.org/programs/maa-awards/writing-awards/… | |
| Aug 18, 2020 at 5:39 | comment | added | Aaron Meyerowitz | There are a plethora of proofs that there are $n^{n-2}$ trees on $n$ labelled points. I'd say an common feature of most such theorems is to be easy understand, hard enough to be challenging but not so hard as to be unapproachable. Then other criteria come into play, | |
| Aug 18, 2020 at 5:31 | comment | added | Aaron Meyerowitz | I don't think Lakatos' thesis was that the proof of V-E+F=2 holds for "polyhedra" was difficult to get right. It was the determining of what should be considered a polyhedron (for these purposes, not toroidal ones, for example) . GrunBaum said: ""The Original Sin in the theory of polyhedra goes back to Euclid, and through Kepler, Poinsot, Cauchy and many others ... at each stage ... the writers failed to define what are the polyhedra". | |
| Aug 18, 2020 at 0:48 | comment | added | Will Sawin | The claim that two things are not equal (or variants of it) often has many fundamentally different proofs. This is because two things that are not equal are usually equal for many reasons - i.e. two integers are not equal because they are unequal mod $2$, unequal mod $3$, etc. Usually for an equality, there will be similarities between different proofs, and you can argue about whether they are really the same proof. | |
| Aug 18, 2020 at 0:36 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Aug 18, 2020 at 0:33 | history | edited | Nate Eldredge |
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| Aug 18, 2020 at 0:20 | comment | added | M.G. | Another prominent example is quadratic reciprocity. Does the fundamental theorem of algebra count? | |
| Aug 18, 2020 at 0:07 | history | asked | Joseph O'Rourke | CC BY-SA 4.0 |