# Did great Mathematicians of the Past Leave Unsolved Problems Behind?
**URL:** https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646
**Category:** Factual Questions
**Created:** [October 5, 2004, 2:47pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646 "2004-10-05T14:47:45Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@ralph124c](https://boards.straightdope.com/u/ralph124c)
#### Post date: [October 5, 2004, 2:47pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/1 "2004-10-05T14:47:45Z")
I know that a mathematician solved Fermat’s Last Theorem a few years ago…are there other instances where a famous matematician of the past had given up on solving a problem? Suuposedly, some of ramanujan’s works are still puzzling to modern mathematicians…and Lagrange attempted to solve the three-body problem,(unsuccessfully).
So are modern math wizards still stumped by problems from 100-200 years ago? 🆒
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### Author:  [@ccwaterback](https://boards.straightdope.com/u/ccwaterback)
#### Post date: [October 5, 2004, 2:52pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/2 "2004-10-05T14:52:01Z")
Here’s one list:
[http://mathworld.wolfram.com/UnsolvedProblems.html](http://mathworld.wolfram.com/UnsolvedProblems.html)
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### Author:  [@BrotherCadfael](https://boards.straightdope.com/u/BrotherCadfael)
#### Post date: [October 5, 2004, 2:59pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/3 "2004-10-05T14:59:51Z")
By the way… what is the consensus on Fermat’s Marginal Note – the one where he says he “discovered a marvelous proof of this theorem, but the margin is too small to contain it”?
Is it at all likely that he did, in fact, have a valid proof of the theorem? Or was he just mistaken?
Given the difficulties that mathematicians have had over the last couple of centuries proving Fermat’s Last, it seems unlikely that Fermat himself actually accomplished the deed. But, mathematics being what it is, it’s just barely possible…
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### Author:  [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)
#### Post date: [October 5, 2004, 3:04pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/4 "2004-10-05T15:04:52Z")
As I understand it, there was a lot of hard work involved in putting the integral calculus on a firm logical foundation after Newton and Leibnitz got the ball rolling.
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### Author:  [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)
#### Post date: [October 5, 2004, 3:12pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/5 "2004-10-05T15:12:41Z")
> [@](#):
>
> By the way… what is the consensus on Fermat’s Marginal Note – the one where he says he “discovered a marvelous proof of this theorem, but the margin is too small to contain it”?
>
> Is it at all likely that he did, in fact, have a valid proof of the theorem? Or was he just mistaken?
>
> Given the difficulties that mathematicians have had over the last couple of centuries proving Fermat’s Last, it seems unlikely that Fermat himself actually accomplished the deed. But, mathematics being what it is, it’s just barely possible…
I think the general feeling is that he was mistaken. Therer have been a lot of times in the past couple of centuries when someone thought he’d solved the problem, only to be proven wrong yet again.
Of course, there’s another possibility, raised in one of my very first sigs:
“I give up. How _do_ you keep a mathematician busy for 350 years?”
```
--- Pierre de Fermat's friend
```
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### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [October 5, 2004, 3:25pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/6 "2004-10-05T15:25:12Z")
The Goldbach conjecture is the most interesting famous unsolved problem, given it’s age and how simple it is to understand.
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### Author:  [@The\_Llama](https://boards.straightdope.com/u/The_Llama)
#### Post date: [October 5, 2004, 3:38pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/7 "2004-10-05T15:38:45Z")
Fermat’s last theorem was solved, finally, by proving that it was false. Therefor, Fermat couldn’t have solved it inside or outside the margin.
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### Author:  [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)
#### Post date: [October 5, 2004, 3:52pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/8 "2004-10-05T15:52:37Z")
Nonsense. Andrew Wiles proved the truth of the theorem, although he did it by proving a far more inclusive theorem.
[http://mathworld.wolfram.com/FermatsLastTheorem.html](http://mathworld.wolfram.com/FermatsLastTheorem.html)
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### Author:  [@InvidiousCourgette](https://boards.straightdope.com/u/InvidiousCourgette)
#### Post date: [October 5, 2004, 4:00pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/9 "2004-10-05T16:00:13Z")
> [@The\_Llama](#):
>
> Fermat’s last theorem was solved, finally, by proving that it was false. Therefor, Fermat couldn’t have solved it inside or outside the margin.
I read Simon Singh’s “Fermat’s Last Theorem” a few years back which describes in layman’s terms Wiles’s quest to prove the theorem. It explains that the proof
> [@](#):
>
> is a masterpiece of modern mathematics, which leads to the inevitable conclusion that Wiles’s proof of the Last Theorem is not the same as Fermat’s
> \
> …the Frenchman did not invent modular forms, the Taniyama-Shimura conjecture, Galois groups, and the Kolyvagin-Flasch method centuries before anyone else.
The theorem was, nonetheless, correct.
I hesitate to post this having [just said I will never again post in a mathematics thread](http://boards.straightdope.com/sdmb/showthread.php?p=5331312#post5331312).
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### Author:  [@The\_Llama](https://boards.straightdope.com/u/The_Llama)
#### Post date: [October 5, 2004, 4:09pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/10 "2004-10-05T16:09:21Z")
Yeah, he proved the Taniyama-Shimura first. Sucks, because one of those guys killed themselves because they couldn’t prove their own theorum. Anyway,I’ll have to ask my wife when she gets home, because she’s the math teacher. She told me that it was proved by Wiles to not work.
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### Author:  [@The\_Llama](https://boards.straightdope.com/u/The_Llama)
#### Post date: [October 5, 2004, 4:12pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/11 "2004-10-05T16:12:06Z")
OK, I’m obviously wrong. I had to have misunderstood what she said. Perhapse some part of the final outcome was determined by proving something else false. All of the interviews I’ve been checking with Wiles say it’s proved, but nothing about proving anything false. Sorry, I honestly held this to be what I knew.
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### Author:  [@Finagle](https://boards.straightdope.com/u/Finagle)
#### Post date: [October 5, 2004, 4:13pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/12 "2004-10-05T16:13:19Z")
> [@The\_Llama](#):
>
> Fermat’s last theorem was solved, finally, by proving that it was false. Therefor, Fermat couldn’t have solved it inside or outside the margin.
Need a cite on that one. This [site](http://www.mbay.net/~cgd/flt/fltmain.htm) seems to think that it was proved.
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### Author:  [@The\_Llama](https://boards.straightdope.com/u/The_Llama)
#### Post date: [October 5, 2004, 4:16pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/13 "2004-10-05T16:16:11Z")
I never said it wasn’t proved, just that in proving it, it was proved to be false. That’s the same as a proof of “it works.” I then went on to say, “my knowledge is false.” Proven by the others who preceded me.
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### Author:  [@chappachula](https://boards.straightdope.com/u/chappachula)
#### Post date: [October 5, 2004, 4:32pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/14 "2004-10-05T16:32:38Z")
But is Fermats theory considered a satisfactory solution?After all, whatever he wanted to write in the margin is still unknown to us.
I guess I’m askiing what drives the mathematicians–the discovery of a new mathematical fact, or the PROCESS of discovering it?
IF Wiles proved Fermat’s theorem using very modern techniques, are mathematicians satisfied by it? Or do they still consider Femat’s challenge unanswered, until it is proved using only 17th century techniques?.
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### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [October 5, 2004, 4:34pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/15 "2004-10-05T16:34:06Z")
A proof is a proof, and whatever Fermat wanted to write in the margin was almost certainly incorrect.
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### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [October 5, 2004, 4:37pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/16 "2004-10-05T16:37:30Z")
> [@BrotherCadfael](#):
>
> By the way… what is the consensus on Fermat’s Marginal Note – the one where he says he “discovered a marvelous proof of this theorem, but the margin is too small to contain it”?
>
> Is it at all likely that he did, in fact, have a valid proof of the theorem? Or was he just mistaken?
>
> Given the difficulties that mathematicians have had over the last couple of centuries proving Fermat’s Last, it seems unlikely that Fermat himself actually accomplished the deed. But, mathematics being what it is, it’s just barely possible…
I believe the majority, though not universal, opinion among mathematicians is that Fermat was mistaken. I’ve even seen reasonable speculations as to what the (flawed) proof was that Fermat _thought_ he had. It’s even plausible that Fermat himself realized his “proof” was incorrect but didn’t see the point in going back and changing a marginal note that he believed no one else might ever see.
But it is this marginal note that made Fermat’s Last Theorem such a tantalizing problem. If you believed his claim to have a “marvelous proof,” it meant that the problem was solvable, and the solution was simple enough to be found by a lucky amateur without using all the mathematical equipment that has been developed since Fermat’s day. Even now that the problem has been solved, you’d still become world-famous if you could come up with a valid proof that might have been _Fermat’s_ proof.
As **ccwaterback** ’s link shows, there are plenty of unsolved problems in mathematics (including a number [no pun intended] of tantalizingly simple-sounding ones in number theory); but in none of them have we been assured that there is a “marvelous” solution out there just waiting to be found—or even necessarily any solution at all, since Godel showed that there are some things that just can’t be proved.
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### Author:  [@rfgdxm](https://boards.straightdope.com/u/rfgdxm)
#### Post date: [October 5, 2004, 4:53pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/17 "2004-10-05T16:53:16Z")
> [@Thudlow Boink](#):
>
> I believe the majority, though not universal, opinion among mathematicians is that Fermat was mistaken. I’ve even seen reasonable speculations as to what the (flawed) proof was that Fermat _thought_ he had. It’s even plausible that Fermat himself realized his “proof” was incorrect but didn’t see the point in going back and changing a marginal note that he believed no one else might ever see.
From what I understand, the current proof of Fermat’s Last Theorem uses math that wasn’t developed until after Fermat died. Thus, if Fermat had a proof, it must have been some other one. Odds seem very high Fermat was mistaken.
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### Author:  [@Mathochist](https://boards.straightdope.com/u/Mathochist)
#### Post date: [October 5, 2004, 5:15pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/18 "2004-10-05T17:15:18Z")
> [@ralph124c](#):
>
> are there other instances where a famous matematician of the past had given up on solving a problem?
First of all, Fermat didn’t give up. He died. I’d be surprised to find anywhere a mathematician explicitly giving up on a problem (except maybe whatever Grothendieck was working on before he moved).
There are a great many problems which have been stated by famous mathematicians but not solved. The Goldbach and Hardy-Littlewood conjectures in number theory, the Poincaré conjecture in topology (possibly now solved), the Riemann hypothesis in, well, everything.
Then, how do you mean famous? Do you mean math-famous or society-at-large-famous? Within any given field, any problem that’s known as an open problem has probably passed through the hands of a famous-in-the-field mathematician along the way.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [October 5, 2004, 7:53pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/19 "2004-10-05T19:53:41Z")
Fermat did end up proving his Theorem for the special cases of n=3 and n=4, and he may well have thought that the method he used for those two cases would generalize to all values of n. It didn’t. But as **Thudlow Boink** points out, the infamous margin note was not a published work, and he had no reason to suppose anyone else would read it, so there was no reason for him to make a retraction when he discovered it didn’t work. Heck, he might not have even remembered that he made the note in the first place… Do you remember all the notes you’ve scribbled in the margins of textbooks?
Incidentally, there are also problems in mathematics which have been resolved by being proven insoluable. Millenia of mathematicians tried to prove Euclid’s fifth postulate, before it was shown by Gauss and Riemann (I think; working from memory here) that geometries with alternative postulates were just as valid. Geometers dating from the ancient Greeks also strove at the problems of doubling the cube, squaring the circle, and trisecting the angle, but we now know that 2[sup]1/3 , pi, and sin(pi/6) are inconstructible numbers, meaning that those constructions are impossible. And the differential equations for the three-body problem are easy to find, but the solutions to those differential equations are known to be non-analytic, and can even be chaotic.
There are even some problems in mathematics which cannot be solved, but for which there is no way of knowing that they cannot be solved. I can’t give any definite examples here, of course, but many suspect that Goldbach’s conjecture may be such a problem.
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### Author:  [@Quartz](https://boards.straightdope.com/u/Quartz)
#### Post date: [October 5, 2004, 9:45pm UTC](https://boards.straightdope.com/t/did-great-mathematicians-of-the-past-leave-unsolved-problems-behind/267646/20 "2004-10-05T21:45:54Z")
IIRC Simon Singh’s book says that Fermat’s likely solution was the one worked on by Cauchy et al but disproved by Kummel - it supposed unique factorisation. But did Complex Numbers antedate Fermat?
Further, those who dismiss Fermat’s scribble would do well to remember the Dot Conjecture. It may well be that there’s a leap of logic that we’re all missing.
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