# Fermat's Theorem **URL:** \ **Category:** Factual Questions\ **Created:** [May 24, 2011, 5:58am UTC](https://boards.straightdope.com/t/fermats-theorem/582989 "2011-05-24T05:58:23Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![statsman1982](https://avatars.discourse-cdn.com/v4/letter/s/e79b87/32.png) [@statsman1982](https://boards.straightdope.com/u/statsman1982)\ **Post date:** [May 25, 2011, 10:16pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/41 "2011-05-25T22:16:44Z")
> [@mla1](#): > > Fermat was very clever. i rate hime one of the greatest minds in the last 500 years. proving his theorem was difficult but have you guys ever looked at my Theorem? Armstrong’s last Theorem?:dubious: Why don’t you break it down for us? ---
**Author:** ![aruvqan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aruvqan/32/2891_2.png) [@aruvqan](https://boards.straightdope.com/u/aruvqan)\ **Post date:** [May 25, 2011, 10:33pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/42 "2011-05-25T22:33:24Z")
> [@Thudlow\_Boink](#): > > Yeah, I can easily understand why mathematicians might take umbrage at some of your comments, like: > I can think of at least two ways that you’re poking mathematicians with a stick here. > > (1) For literally millennia, mathematicians have resented it when people demand, “But what use is it?” as though truth had no inherent value. > > “Give that man a coin, since he must make a profit from what he learns!” - Euclid > > “Of what use is a newborn baby?” - attributed to various famous scientists > > (2) Belittling what you don’t understand. Your last line, especially, conveys the attitude that if _you_ can’t understand something, it must be esoteric mumbo-jumbo of interest to no one who isn’t hopelessly geeky. > > This is an attitude that plagues not only mathematicians but also artists, writers, musicians, etc. People try to read a complex novel or look at an abstract painting and, if it’s over their head, they conclude it must be overrated, worthless, elitist crap. > > * * * > > Now, as for how “a formula without a solution” could matter to anyone, consider this example of a theorem that’s similar to Fermat’s Last Theorem only much, much simpler: > > **The equation _a + b = c_ has no solutions for which a, b, and c are all odd numbers.** > > Could knowing this fact ever come in handy? Possibly. But, more importantly, if you can prove it—which means, if you can understand _why_ it’s true—you have a better understanding of how numbers work in general, and the approach or techniques you developed to prove it might be useful in proving more substantial things as well. Why I need to “prove” a thingy I can draw in 15 seconds does not make sense to me [geometry class] Just give me the damned drawing stuff and get off my back [can you tell I detested geometry because of my math tormenting teacher of 4th grade?] Not to mention that in general I have pretty much _never_ used 80% of all the math I had to try and force into my skull other than literally elementary school level stuff, and for anything else, I could always get a book and look up what I needed. So no, knowing math is not really handy to me in any hobby sort of way. Since apparently playing with equations seems to be hobby for pretty much anybody in mathematics that isn’t getting paid to scribble graffiti on chalkboards. And if it pleases you to play with equations, knock yourself out. If you want to read russian fiction, knock yourself out [Ill get some valium to put me to sleep instead] and enjoy the artwork. I tried to find out what was so important about a theorum, just to discover it really has no _real world_ importance. I can’t use it to calculate wet hull speed, or the amount of paint for my barn, or how many squirrels I can fit in my jetta’s trunk. It is great for spending time playing with numbers. I guess it is insulting to be questioned as to what use some batch of numbers is just to be dismissed as essentially a hobby that you can turn into a paper to get a degree at a university with. Most of us have a need to make a living, and need to make sure what we do can actually make a paycheck. ---
**Author:** ![Hypnagogic\_Jerk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hypnagogic_jerk/32/4252_2.png) [@Hypnagogic\_Jerk](https://boards.straightdope.com/u/Hypnagogic_Jerk)\ **Post date:** [May 25, 2011, 10:49pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/43 "2011-05-25T22:49:36Z")
Okay, so you don’t like pure math. Fair enough, I’m more of an applied guy as well anyway. Do you like music? Of what use is music? While musicians are fiddling with their guitars and keyboards, some of us have to work for a living, you know. Sheesh, I never knew some people were that hostile to math. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 25, 2011, 11:17pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/44 "2011-05-25T23:17:57Z")
> [@aruvqan](#): > > I tried to find out what was so important about a theorum, just to discover it really has no _real world_ importance. I can’t use it to calculate wet hull speed, or the amount of paint for my barn, or how many squirrels I can fit in my jetta’s trunk. It is great for spending time playing with numbers. I guess it is insulting to be questioned as to what use some batch of numbers is just to be dismissed as essentially a hobby that you can turn into a paper to get a degree at a university with. Most of us have a need to make a living, and need to make sure what we do can actually make a paycheck. Mathematicians need to make sure what they do can actually make a paycheck too, of course; it just so happens that there are people willing to pay them for what they do. If you have a problem with that, take it up with the people who pay mathematicians; presumably, they can explain to you their motives for doing so. I note you enjoy reading the “Girl Who” novels. Hey, if you want to read that stuff, knock yourself out. But one might ask what use some batch of fictional sentences is; you can’t use it to calculate wet hull speed, or paint a barn, or cure cancer. That Stieg Larsson really lucked out there, managing to eke out a living from that writing hobby of his. What, may I ask, do you do for a living? ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [May 26, 2011, 3:06pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/45 "2011-05-26T15:06:31Z")
To address the OP, I know much less about this subject than most (perhaps all) of the other posters in this thread, but I can highly recommend “Fermat’s Last Theorem” by Simon Singh for a very interesting, readable, and comprehensive treatment of the subject. ---
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [May 26, 2011, 5:18pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/46 "2011-05-26T17:18:25Z")
I _think_ part of the solution has to do with F(x)=x^(1/x)… …that is, plot the “x”-th root of x on log graph paper. [http://graph.seriesmathstudy.com/](http://graph.seriesmathstudy.com/) note: not a log graph but bear with me:rolleyes: Starting at the origin…at 0…the graph curves up through x=1, starts flattening out at x=2, peaks at x=e, and slowly curves back down to y=1 as x goes to infinity. At 0 there is a graphic incontinuity (cant divide by 0) thus A^0+b^0=c^0 dosen’t work (1+1 =/ 1) 1 works (elementary arithmetic) a^1+b^1=c^1…1+2=3 2 works (pythagoras) 9+16=25 3 and integers above dosen’t work because, unlike 1 and 2, the slope of the curve is decreasing. I’d wager if e was an integer, it would work. BTW, what interesting stuff can be found where (a^e)+(b^e)=(c^e)? ---
**Author:** ![Snickers](https://avatars.discourse-cdn.com/v4/letter/s/5daacb/32.png) [@Snickers](https://boards.straightdope.com/u/Snickers)\ **Post date:** [May 26, 2011, 5:38pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/47 "2011-05-26T17:38:02Z")
> [@Thudlow\_Boink](#): > > Yeah, I can easily understand why mathematicians might take umbrage at some of your comments, like: > I can think of at least two ways that you’re poking mathematicians with a stick here. > > (1) For literally millennia, mathematicians have resented it when people demand, “But what use is it?” as though truth had no inherent value. > > “Give that man a coin, since he must make a profit from what he learns!” - Euclid > > “Of what use is a newborn baby?” - attributed to various famous scientists > > (2) Belittling what you don’t understand. Your last line, especially, conveys the attitude that if _you_ can’t understand something, it must be esoteric mumbo-jumbo of interest to no one who isn’t hopelessly geeky. > > This is an attitude that plagues not only mathematicians but also artists, writers, musicians, etc. People try to read a complex novel or look at an abstract painting and, if it’s over their head, they conclude it must be overrated, worthless, elitist crap. \*Very \*well said, my **Boink** y friend. And precisely why I can never watch The Big Bang Theory. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 26, 2011, 5:45pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/48 "2011-05-26T17:45:29Z")
Re: **Enola Straight** : This suggests you believe a^n + b^n = c^n does not have any solutions where a, b, and c are positive integers and n is a real number \> e. But that conjecture is false: 4^n + 4^n - 5^n is positive when n = 3 and negative when n = 4; accordingly, there is some n inbetween 3 and 4 (and thus larger than e) such that 4^n + 4^n = 5^n. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 26, 2011, 6:17pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/49 "2011-05-26T18:17:45Z")
Quoth **aruvqan** : > [@](#): > > I tried to find out what was so important about a theorum, just to discover it really has no _real world_ importance. > … > Most of us have a need to make a living, Of what use is living? Serious question, there. Some might argue that our purpose in life is to understand the world. If putting bread on the table is important, it’s only because it enables us to live long enough to understand more things. Look at it this way, and pure mathematics becomes one of the most practical pursuits of all, since it leads directly to fulfilling life’s purpose, instead of just indirectly like almost all other fields. ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 6:48pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/50 "2011-05-26T18:48:18Z")
Fermat’s theorem is the equivalent of someone knowing how to subtract but not add. The problem is then the theorem isn’t complete it isn’t a universal law as such. It deals with a finite set. Armstrong’s Conjecture I came up this year solves this problem. ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 6:56pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/51 "2011-05-26T18:56:40Z")
Break it down and have you steal it? What the conjecture does is remove the limitration of adding two. So you can add the same number of exponents in a relation with the size of the exponent. the relation is always is always equal or less than a certain number. I can’t prove this theory as I don’t even understand half what you guys say. But just imagine if something like that was true? Would you give it up before you can publish it? I’m convinced it is. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 26, 2011, 7:38pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/52 "2011-05-26T19:38:56Z")
> [@mla1](#): > > I can’t prove this theory as I don’t even understand half what you guys say. Oh, to be able to understand half… ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 7:40pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/53 "2011-05-26T19:40:44Z")
when you were 16 had you developed any universal exponenet laws? Had you expanded on any theory? ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [May 26, 2011, 7:46pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/54 "2011-05-26T19:46:17Z")
If you don’t have a formal math education, what makes you so sure somebody hasn’t already come up with your theorem and proven it? ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 7:48pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/55 "2011-05-26T19:48:01Z")
Google. But I’m not its happened to me with square numbers. I asked my maths teachers and they said they have never seen it before. How would you prove an expansion on fermat ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 7:49pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/56 "2011-05-26T19:49:12Z")
i do receive a formal maths education ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [May 26, 2011, 7:49pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/57 "2011-05-26T19:49:28Z")
Why don’t you start by telling us exactly what your conjecture/theorem/whatever is? (Also, is English your native language?) ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [May 26, 2011, 7:51pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/58 "2011-05-26T19:51:08Z")
Given that you can’t even explain your theorem in comprehensible English, the likelihood of finding a discussion on it with a cursory Google search seems low. Have you searched any scholarly literature? And just because your math teacher hasn’t seen something, does that prove that it’s original? Do you have any idea how much original material is published in fields like number theory every year? ---
**Author:** ![mla1](https://avatars.discourse-cdn.com/v4/letter/m/c0e974/32.png) [@mla1](https://boards.straightdope.com/u/mla1)\ **Post date:** [May 26, 2011, 7:55pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/59 "2011-05-26T19:55:49Z")
Ok. The theory involves the amount a^2 + a2^2 = b^2 It is the ratio of the numbers needed and the exponent value. NO it doesn’t prove that it isn’t original but the mere fact that I was able to whether or not it has been makes it brilliant. Have you ever seen an expansion on fermat? So just because my english isn’t brilliant doesn’t mean my mind isn’t. I am brilliant. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [May 26, 2011, 8:05pm UTC](https://boards.straightdope.com/t/fermats-theorem/582989/60 "2011-05-26T20:05:16Z")
> [@mla1](#): > > I asked my maths teachers and they said they have never seen it before. No offense, but I see this at least once a month (usually more often, actually) on a different site. We get high school students who submit “original” math ideas that their teachers have never seen. Usually, it’s a fundamental algebra or number theory result that is taught in undergraduate math courses. Sometimes, it’s something that should be seen in high school. It’s incredibly rare that a truly original result is offered, and even then, usually the ‘proof’ that is included is horribly flawed. None of this is to say that high school math teachers are worthless. Many, if not most, do a reasonable job of teaching basic math. But it shouldn’t be assumed they have extensive, or even adequate, knowledge of any mathematics beyond what is required by curricula. [Previous page](https://boards.straightdope.com/t/fermats-theorem/582989.md?page=2) [Next page](https://boards.straightdope.com/t/fermats-theorem/582989.md?page=4)