The Man Who Solved the World’s Most Famous Math Problem

[@Newsthink]

*What other videos would you like to watch?* Try brilliant.org/Newsthink/ for FREE for 30 days, and get 20% off your annual premium subscription

[@davidaIano]

may I request a video on the life and contributions of Edward Witten

[@dragoda]

Too much repr3sentation of suicide in your video. Stick to math. You made me sad. Re do the video without suicide mentions.

[@hansombrother1]

Hello, I studied math in college and I appreciate your explanation. I was very aware of this problem, but I am very amazed how the gentlemen solved the problem very recently. This was very historic. However I was expecting a bit more from your video. Could you please provide a few values for X,Y, Z, & N? Certainly when we consider a2 + b2 = c2 there are many values we can assign to a, b, & c , for example 3,4,5. What are some possible values for X,Y,Z, and N?

[@CheckmateSurvivor]

Please prove that we don't live on a spinning ball.

[@timothymcglynn1935]

Hi

[@Pioneer_DE]

Imagine being a suicidal Industrialist but being motivated to live by a maths problem.

[@quakerninja]

I am also suicidal but motivated by cheesecakes I don't think dead people can eat cake, so I guess I'm stuck here.

[@plasmaastronaut]

why doesn't incelTV / Rehab Room mention maths as a escape from inceldom?

[@DiegoTorres-kv7js]

@@plasmaastronaut because you can be the greatest mathematician in the world, but still not get pussy.

[@thefart]

@@plasmaastronaut you would still be an incel after math. Maybe not suicidal

[@ButchNews]

I'M ABOUT TO BE 80. ALL DAY PAIN IS NORMAL. I SAW A GRAFFITI WHICH SAID "ALWAYS HAVE SOMETHING TO LOOK FORWARD TO". I THOUGHT I DIDN'T EXCEPT I LOOKED FORWARD TO BEING DEAD AND LEAVING THE IDIOT HUMANS BEHIND ME FOREVER WOULD BE GOOD. BUT... TRYING TO SOLVE BASIC UNIVERSE PROBLEMS KEEPS ME GOING. LIKE ANYONE CARES.

[@DynestiGTI]

The amount of knowledge you need to even understand the proof is insane

[@drgetwrekt869]

indeed. thats also why the disconnect between average person and actual science is larger today than it was in the past. paradoxically.

[@RobertoCarlos-tn1iq]

yup. around the year einstein got his phd, you were expected to be competent in ALL of physics or ALL of mathematics. now, no chance.

[@television9233]

True, you would need a complete PhD's level of knowledge just to begin reading books/papers that would shed light on what the actual proof is.

[@calicoesblue4703]

💯💯💯😎

[@mikemondano3624]

@@television9233 A PhD would hardly cut it. Someone with a PhD in a different branch would be as perplexed as a non-mathematician. The subject is vast and a PhD implies focused interest, not broad knowledge.

[@kwith]

I've watched that original documentary and its amazing how emotional Andrew gets. You can see the passion for the problem in how he barely is able to get out the words "Nothing I ever do again will...." as he almost bursts into tears. I would say 99% of people would just say "umm..its just a math problem!". To him though, this represented the culmination of an entire lifetime of dedication that has finally been realized. A quote given by Simon Singh from what Piet Hein said: "Problems worthy of attack prove their worth by fighting back". That is this entire journey in a nutshell.

[@shibhanlalpandita6975]

Did he disprove the alleged theorem?

[@kwith]

@shibhanlalpandita6975 no he solved it and proved the theorem correct

[@ajzma]

Reminds me of another great quote: "you bite the fry, the fry bites back, my man"

[@PracticalAI_]

I think we are part of that 1%

[@nomennescio4242]

"Nothing I ever do again will...." will bring the same thrill, the same passion... (I will never be young enough again to find a task as monumental as this one and even if i find one I will not have the time to solve it) it is a bit (very) sad if he was thinkinng like that at that moment

[@ozymandias4488]

Everytime I listen to Wiles's work on Fermat's last theorem I get incredibly amazed by his passion and determination to complete the dream of his life. Truly a remarkable person

[@henson2k]

I'm surprised he kept his marriage

[@huzcer]

The book about it was very well publicized at the time. Can't see a book about maths doing as well nowadays

[@mikemondano3624]

He never did anything with Fermat's Last Theorem. He proved the modularity theorem for semistable elliptic curves. He left Fermat's part to others since the proof had become trivial.

[@calicoesblue4703]

@@mikemondano3624Newsthink, needs to make a Video about Gregory Perelman.

[@mikemondano3624]

@@calicoesblue4703 Yes, but without his cooperation, no doubt.

[@MichaelPiz]

I don't think Andrew's proof would fit in the margin.

[@johnbauman4005]

Since the techniques employed by Wiles had not yet been discovered it makes one wonder what Fermat's approach might have been, and if perhaps it may have errors he did not initially detect. Or maybe he was just messing with us.

[@MichaelPiz]

@@johnbauman4005 I think the latter. I bet he was a real prankster.

[@robertunderwood1011]

@@MichaelPiz I think he was sincere, but mistaken and whatever proof he might’ve had would’ve been found to have errors had published it

[@michaelblankenau6598]

I think the challenge should be to now find a proof that actually would fit in the margin .

[@ernestsmith3581]

​@@johnbauman4005Fermat's proof would certainly have been geometric in the Ancient Greek tradition, but extended with his unique primordial form of calculus (Method of Infinite Descent). Perhaps he only proved to cubic (as Euler) or perhaps really did have it worked out in his head. The world will never know, but we have many wonderful new branches of mathematics (such as Fractional Dimensions) which emerged because of Fermat's highlighting of the problem.

[@T1000mileman]

I think Andrew is the right guy to tackle the mystery of the frequent disappearance of socks from my dryer.

[@postblitz]

Racoon theory could explain it.

[@XiangLiu-z7d]

@@postblitz Try getting rid of the dryer first.

[@keithrobinson2941]

Don't you know? The socks don't disappear....They are time travelling to the future. One day they will reappear in your dryer, or possibly in someone else's dryer. And I have a proof for this; but, unfortunately, I can't fit it in the margin.

[@aluisious]

@@keithrobinson2941 Funny and all, but the other day I wondered if deja vu is caused by events in your waking life matching up with dreams, which implies your dreams could sometime be anticipating future events. We don't understand our perception of time, or how dreaming works, or how thinking works, so...?? Maybe your socks and your dreams are in the same place.

[@gbreslin6635]

It is the true uncertainty principle 😁

[@lanzer22]

And here I am trying to solve the mystery of why my steak is always overcooked.

[@Newsthink]

Heat is too high

[@johnbauman4005]

​@@NewsthinkAnd/or left on too long! Alternative scenario root cause theory: rudeness to the waitstaff.

[@lanzer22]

@@johnbauman4005 heh I like the second theory :) Definitely a problem that should t take a lifetime to solve :)

[@dfs-comedy]

Don't cube the meat; there's no solution for that. A square meal is OK, though.

[@vincentmarotta9800]

Not a mathematical proof, but here's everything I know about cooking the "perfect" steak: 1. You can use butter, but it's preferable you use avocado oil. Mixing might be an eloquent solution. Avocado oil has a high "burn point" meaning you can heat the oil hotter than most. This allows for good charring on the outside, and a moist delicious inside. 2. Have a butcher cut your steak 1.5" thick. Thick steak allows for nice charred tasty outside, but perfectly cooked inside. 3. Get an instant read temp thermometer. When the inside of your steak reaches between 125-135F, instantly remove it from the grill and let it "rest" uncovered for about 10 minutes. This will make a good Medium Rare. 4. Let steak get to room temp. Pre-layer the steak in avocado oil. Apply generous salt and pepper, and that's it. Seasoning anything else on a good Ribeye steak is a sin. Bring some avocado oil to lightly drizzle during cooking to re-introduce a layer of moistness. 5. Preheat grill between 300-350F. Honestly once the oil starts to catch fire, the inside temp will rise high, but regardless as long as you keep an eye on the internal temp, you should be fine. 5. First cook on side 1 at 45 degree angle. Cook for 2 minutes. Then rotate on side 1 another 45 degrees. Cook for another 2 minutes. 6. Now flip the steak to side 2 at 45 degree angle. Cook for 2 minutes. Rotate on side 2 another 45 degrees. Cook for another 2 minutes. 7. Check internal temp occasionally. Once it reaches 125-135F, remove and let it rest for 10 minutes. This allows the steak's fibers to loosen again, not only making the steak more tender, but also absorbing back some of the juices (by the way, do not drain juices off plate if you see it right after cooking). I hope this helps. Delicious steak every time.

[@frankteunissen6118]

The reason that Wiles kept his work on Fermat’s Last Theorem secret wasn’t that he feared others might steal his thunder. The reason was that by the mid-20th century trying to prove the theorem was something that drew in cranks and crackpots. No serious mathematician worked on Fermat’s theorem if he valued his reputation in the world of mathematicians.

[@darcash1738]

What’s the context behind that

[@piepiedog1]

I believe Wiles himself said that he kept it a secret because he thought people might scoop the proof out from under him given that they knew his field of expertise and thus might be able to make some assumptions about his approach. I think it's unlikely they would think he had slid into crackpottery, but rather the opposite; if _Wiles_ was seriously working on a proof, he must have realized something important. I could be wrong about it being him who said this, but it does seem the most likely reason.

[@darcash1738]

I see-so mostly the crazy math dudes would try to solve it at that point, but if they were to see that the Big Dog Wiles were working on it, then they would find out that it wasn’t merely a fool’s errand anymore

[@XCC23]

@@piepiedog1 Well, it's more that there was no way of really working at it for a long time. Taniyama and Shimura stated what's now known as the modularity theorem in the fifties, but at the time, it was just a conjecture. Through the work of Frey, Serre and Ribet in the late 80s, it was shown that the modularity conjecture, if true, would directly imply Fermat's last theorem. So it was really first in 1989 with Ribet's proof of the epsilon conjecture that the path Wiles took to prove Fermat's last theorem actually existed. So it's really more that Wiles happened to be the man with the dedication, the correct research area and the timing to be working in that field when the path opened up.

[@Comonad]

The new crackpot fascination is solving Collatz conjecture or Riemann hypothesis, like moths to a flame.

[@Jazzwr]

I felt that!.. when he broke into tears 💪

[@Shreysoldier]

When they paused I thought he was laughing 😭

[@extreme4180]

@@Shreysoldier ig he was laughing , it was a laugh and tears of success

[@stevenvanhulle7242]

That fragment is at the beginning of a BBC Horizon documentary on FLT, created by John Lynch and Simon Singh. The documentary was the basis for Singh's book. "Captivating": adjective. Said of a 45 minute documentary which fascinates even though you don't understand a word of the mathematics it's about.

[@rtarbinar]

I got misty when I saw that! He looked into the deepest secrets of the universe and saw the face of "God" (Spinoza/Einstein/Hawking version, of course)

[@londomolari5715]

Sadly, because of its age restriction, Andrew could not win a FIelds Medal, but they did give him a special award.

[@mikemondano3624]

He wouldn't have gotten a Fields Medal anyway for that proof. He'd need a greater body of work.

[@aleksandarloncar2914]

He got the Abel Prize, which is more important

[@cracknblast8247]

Mike Mondano that was a good one. Andrew Wiles would have easily won the Fields Medal. If you think otherwise you need to check his work again or reflect on yourself because delulu is not the solulu

[@laurent-ym2jw]

May be a reason that Abel price arrive .... no more reason of age restriction (at beginning I think it was to avoid : given for all he's work at the age of 90 years old) ?

[@pholdway5801]

How much?

[@schrodingerscat1863]

The most extraordinary thing about this proof is that it builds on the work of so many others pulling it all together to prove Fermat's last theorem. The documentary on this is a very good watch, really gives a flavour of the amount of work involved and how much it meant to him.

[@caseyclausen2627]

Really good music from Penguin Cafe Orchestra as well.

[@domnanzwandor]

Never underestimate the determination of a 10 year old.

[@ryandavid1277]

The best comment here!

[@vibehighest]

sucks that in the world we live in today people are hesitant to share their ideas due to it being stolen etc. Imagine how much further we could progress in science if it were the opposite

[@n-xs8up]

That's why we need billions of human like brain who are not hesitant to share finding with each other. Lets see what AI can bring.

[@jaromor8808]

it was never any different

[@pocojoyo]

You would do the same...

[@maythesciencebewithyou]

Today? It seems you don't know much about Math and science history. In the past, Mathematicians would have competitions against each other, and if they found a formula to easily solve something, they would often keep it to themselves to have the advantage.

[@vibehighest]

@@maythesciencebewithyou lol tell me how much i know about math and science history, please

[@AzfarAbdulHamid]

Having the motivation to solve an unsolved problem at the age of 10 is just mind boggling

[@robertunderwood1011]

I think Champollion Was in his early teens, when he first saw ancient Egyptian hieroglyphics, which were a mystery at the time, and determined to translate them

[@dwacheopus]

It's just an overstimating of their abilities due to the early mental age

[@Tethloach1]

Unsolved problem : Spending billions of dollars on gambling and erotic dancers. Solution: just be a multi-billionaire. Other solution : Don't gamble or go out

[@vincentwu2848]

Especially an unsolved problem as dry as this one.

[@drgetwrekt869]

i dont believe that. he was older

[@Hansulf]

That obsession of some men to put a stone on the foundation of human civilization is what drives us all towards a brighter future! All my admiration towards him!

[@StashiaMass]

That emotional clip of his was quite something - truly shows the blood, sweat, passion and love he put in.

[@BinniamEskender]

Wow, that video was absolutely incredible! Watching Andrew Wiles persevere through all those challenges and finally solve the theorem was so inspiring. It really shows that with enough determination and hard work, you can overcome any obstacle. Truly amazing!

[@mikemondano3624]

Yes, a good video. But the video's contents were even more amazing.

[@hb1338]

If your assertion were true, all the millennium problems would have been solved by now.

[@mikemondano3624]

@@hb1338 You are making the huge assumption that they all have solutions.

[@Dr_LK]

Dear Ms Pom, thank you again for a fantastic exposition of a truly inspiring story. All your videos are amazing. I remember that I was doing my PhD at the time, watched the documentary on British tv, and read the book by Simon Singh.

[@atheistminus5078]

Star Trek TNG season 2 takes place during the year 2365. In the episode "The Royale" Jean-Luc Picard says that Fermat's last theorem remains unsolved, although 20th century mathematician Andrew Wiles came close. He did solve it, same year the show was airing its final season.

[@leemcdonald1342]

Ironically, the Star Trek: Deep Space Nine episode "Facets" did mentioned Fermat's last theorem being solved.

[@Broken_robot1986]

We promised each other that no matter where we went, we would never be separated. He broke his promise.

[@piotr004]

Yea, that was so sad and tragic, especially when his fiancee was so loyal, and loved him so much (such type of love is very rare, and Taniyama could not see her love probably, that's why it's so tragic)...

[@gbreslin6635]

He didn't go anywhere and they will never be separated, or maybe together, sooner or later. ☺

[@wezzla]

Imagine she was the reason for him committing suicide. Coupe of months later: Knock knock, guess who!

[@B3Band]

"I have discovered a proof, but it doesn't fit in the margin" is the 17th century equivalent of "I have a girlfriend, she goes to another school" He made that shit up, but we just believe him because it happened 400 years ago.

[@TheHadMatters]

@@wezzla Do the boomers know you're supposed to love your spouse?

[@pocojoyo]

129 pages ? I did a shorter proof but youtube says its too long a comment. Your loss...

[@DANKKrish]

real!

[@tybofborg]

Monsiour Fermat, I presume?

[@MrDooteronomy]

Well then make it even shorter. Duh.

[@thorr18BEM]

Just put it in the margins.

[@B3Band]

"I have discovered a proof, but it doesn't fit in the margin" is the 17th century equivalent of "I have a girlfriend, she goes to another school" He made that shit up, but we just believe him because it happened 400 years ago.

[@israelfreire2669]

I cannot put into words how insane this is for me. These people live and BREATHE their passion, it’s so insane to get to hear their stories. Imagine living YEARS devoting your knowledge, your time, everything into a single proof. I cannot even fathom what it is, nowadays seems like most of us just throw away 90% of our brain in absolutely any superficial stuff that disappears from our minds within seconds. Hell, I don’t even remember the video I was watching before this one!

[@willfranklyn2]

Ain’t no way Fermat actually solved that 350 years ago. He probably thought he did but dang this dude did a lot of work.

[@tedwalford7615]

Exactly. Clearly a bulletproof proof took much more than he imagined.

[@postblitz]

The problem there is Fermat was a genius and has a lot of hard bank in math to prove it - which could mean he may have had it but never published it, as it often happens. A lot of his personal work was lost and found much later. The problem is always that you want to be first on anything which means to publish you want everything rigorous and complete. That means most mathematicians will keep their scribbles, however brilliant, stacked in miles of secretive papers.

[@television9233]

A professor once told me that Fermat's proofs are closely similar to an almost solid proof to the last theorem, I say almost because that proof turns out to have tiny flaws that once unraveled show that it is wrong in the end. What likely happened is that Fermat's was using this "proof", did not realize the existence of the small mistake, and truly thought he had a proof that was too tiny for the margins.

[@michaelwirth6843]

It can seem that way but we still have no idea how the Egyptians made the pyramids which means we shouldn't under estimate old technology. The Beatles made Sgt Pepper on a 4 channel tape machine.

[@taknothing4896]

Probably true considering the enormously complex and quite roundabout nature of Weil's solution, but it still leaves a bit of doubt hanging out there.

[@JustInCase_007]

When he said “I’m sorry” I felt that.

[@NewCalculus]

Stupid people often feel things. They don't think.

[@zap9021]

@@NewCalculusyou should keep yourself safe

[@paryanindoeur]

I remember reading about this when it happened. It made world news.

[@mikemondano3624]

I remember when the house on the corner was green.

[@jceepf]

Nice video. A woman was involved in the early attempts: Sophie Germain who had to disguised herself as Monsieur Leblanc to avoid discrimination. She was communicating to Euler and eventually had to admit that she was a woman when Euler planned to me M. Leblanc in Paris.... She had feared that Euler would be angry that she posed as a woman. He was not at all.

[@ratvomit874]

Not Euler, it was Gauss she was corresponding with. But yes, truly great minds want everyone to flourish regardless of gender. In fact, Gauss actually campaigned for Sophie to be given a prize for her work

[@clinger007ringer-xu2ir]

Probably the tea lady....

[@drgetwrekt869]

we need more Eulers and less trumbs

[@calicoesblue4703]

@@drgetwrekt869Facts💯💯💯👍😎

[@mikemondano3624]

It was largely in the humanities that discrimination against women flourished. Math and science could not understand what Emmy Noether's wearing a dress had to do with anything and one said as much explicitly, as one of many examples.

[@soothsayer5743]

This is what impresses me. Passion and dedication. Well done sir!

[@JustSad66]

I read Simon Singh's book on this. Never thought i would manage to finish such a book, never mind read it twice!!

[@vrex]

This video basically described how it felt for me to do my math homework in high-school.

[@DrBreyn]

This shows my favorite aspect of science and math: The power of solving problems over a course of many generations, working together for one thing, even if you may not see the result in your lifetime. Different cultures, different nationalities, different contexts, and even different time eras, but working together and actually making progress that will never be lost!

[@lenudan]

There are those with otherworldly intellect... and there are those with an otherworldly relentless work ethic... in the overlap of the two.. you will find Andrew Wiles.

[@yasirpanezai5690]

He is a fraud

[@keyboard_toucher]

He is neither otherworldly nor a fraud. He is just a man who chased a lifelong passion and never stopped learning.

[@lenudan]

@@yasirpanezai5690 Envy is often rooted in low self-esteem - sometimes from very early unmet childhood needs where the person feels inherently not good enough. An envious person may frequently ‘compare and despair’ and find themselves wanting. And so they seek to bring down the object or person who they perceive is making them feel that way.

[@yasirpanezai5690]

@@lenudan agreed but still the guy is a fraud and the maths question is unsolvable

[@AndresFirte]

@@yasirpanezai5690 oh, look, the math equivalent of a flat earther. It’s always hilarious to see math cranks in the wild. Please tell me which other theories you believe in: what’s your thoughts on the moon landing, the shape of the earth, the 2020 virus, and the existence of imaginary numbers?

[@lgnfve]

I understand his emotions. When I use to have a "perfect" thought, a eureka moment, it was huge joy but came with physical pain from the effort. Hard to explain.

[@SanjaySingh-oh7hv]

Thank you, thank you, thank you for an excellent video. I've been interested for a long time in the Poincare Conjecture and both the drama and the personalities that accompanied its solution by Grigori (Grisha) Perelman in 2006 and onward. I didn't think that I'd have the chance to learn about another mathematicians of comparable heart, drive, and determination as Perelman, until this video about Andrew Wiles. Both Perelman and Wiles built upon the work of other great mathematicians to resolve hurdles and advance pure mathematics, which in the decades and centuries to come, will enable the creation of new technologies that we cannot yet know at this point in time.

[@liefdeltora3088]

Absolutely fantastic video, not strictly historical, not strictly mathematical, a wonderful blend of the two that anyone can appreciate. Rare to find math videos that balance this well

[@jayceinfinitealgharhythmns9814]

I brought The New York Times Book of Mathematics and this article on this time stamp is in it on page 145. So of course I had to read it and thanks for doing the KZbin video for it. It made reading it more enjoyable. It’s here at 0:02

[@tougherguy]

You gave an exceptionally clear summary of the proof approach, better than I have seen/absorbed from other popular sources. Well done!

[@arkdark5554]

"Fermat's Enigma" is really beautifully written book. Joy to read.

[@henrypile2385]

I read the book and watched the documentation by Simon Singh on the subject and was amazed by Andrew Wiles‘ dedication over years and years - incredible and admirable!

[@dfs-comedy]

Fermat's Last Theorem: "I'm the World's Hardest Math Problem!" Riemann Hypothesis: "Hold my nontrivial beers..." (This is a joke. I am not denigrating Andrew Wiles' incredible achievement at all.)

[@magicmulder]

Yes and no. FLT was so intriguing because it looked so simple. Wiles proved the Taniyama-Shimura conjecture which arguably was at least as groundbreaking and important as RH is.

[@dfs-comedy]

@@magicmulder Yeah. I think the hardest "simple-looking" one left is Goldbach's Conjecture

[@barakeel]

@@dfs-comedy The Collatz conjecture is arguably even simpler. It does not talk about primes.

[@JamesJoyce12]

Three Body Problem - suck it - the both of you.

[@copypaste_pro]

I’m with you… the hardest problems remain unsolved

[@Stephen_Lafferty]

Simon Singh's brilliant Horizon/Nova documentary film on Andrew Wiles's triumph is a contender for the best post-War documentary. To make accessible such a high-level achievement is "the stuff of which dreams are made on" for every documentary maker.

[@michaelmartin5995]

It is my thought that what Fermat decided was a proof of the notion that there are no solutions when x > 2, was later determined by him to be incorrect and invalid. He chose not to publish anything about it until he could go back to the drawing board to work through it again.

[@WestOfEarth]

It does seem difficult to imagine Fermat had conceptualized Wiles complete proof in that famous moment when he wrote 'unable to write it in the margins'. So I would tend to agree with you.

[@Matlockization]

You just explained this video better than the narrator did, as I was wondering what the answer was.

[@snakesocks]

Correct. The prevailing theory is that Fermat probably thought his proof worked when in fact, it didn't. It certainly wouldn't have approached Wiles' strategy, which is too modern.

[@luminiferous1960]

You mean when n > 2 in the equation as written in this video: x^n + y^n = z^n

[@michaelmartin5995]

@@luminiferous1960 Yes Einstein, a comment made in the context of the subject matter in the video.

[@jbgood7694]

Andrew Wiles did the equivalent of jumping from the tallest mountain in the world to the next tallest mountain.

[@mikemondano3624]

He had a huge number of collaborating sherpas across whom he could almost have walked.

[@KoushaTalebian]

IF we assume Fermat didn't lie about having a proof, there should now be an award for someone discovering a proof that doesn't require any new math invented in the last 350 years.

[@toeknee-chestnut]

My first thought was that Fermat didn't have a proof but it was a marketing ploy to keep himself in the history books. :-)

[@timwhite1783]

I think you know this but he probably didn't have a proof. It's most likely he was either lying (as you said) or he *thought* he had a proof but in reality it breaks down.

[@Traumatree]

@@toeknee-chestnut Or, his reference that the proof couldn't fit in the margin was an indication that it was/would be be very long...

[@television9233]

The most likely option is that Fermat didn't lie... he was just mistaken that his proof was completely absent of any flaws.

[@schrodingerscat1863]

This is not the same proof as Fermat would have had. It is a modern proof building on the work of other modern proofs. It is also conceivable that Fermat's own proof was incomplete and would not have stood up to scrutiny.

[@gregparrott]

Excellent presentation on what works created by others Wiles relied upon to develop his proof. I remember when this was announced, thirty years ago. One item mentioned then was that for at least two reasons, Fermat's proof could not use the same methodology as what Andrew Wiles used. This implies Fermat's proof (if it exists), must be more compact & elegant. #1) Wiles' proof was extremely lengthy, on the order of 100+ pages. That is WAY, WAY beyond something which would not 'fit in the margins'. #2) The 'tools' (the works created by others) Wiles used had not yet been developed in Fermat's time. There remains an open question as to whether a more compact/elegant solution exists.

[@RedSkyHorizon]

I always wondered this too.

[@oberonpanopticon]

I wonder what Fermat’s idea for the solution was. We’ll never know, but it’s interesting to think about

[@francoislechampi2002]

If I understood it well, many proofs were given after Fermat's death. But they all had a flaw. So maybe Fermat's proof was simply false, and it was impossible to proove with the maths knowledge of that time.

[@timonix2]

There have been a few contenders that Fermat himself likely could have come up with. But they all contained mistakes. Likely answer is that Fermat himself made a mistake trying to prove it and he likely did write down and promptly threw away the "solution" once he realized it was wrong.

[@arthurmaniaci4498]

Fermat was closer to solving it than people realize using a technique he originated, the method of descent, he proved the case for n=4 and let other people know. I believe his comment was about the method of descent, but he didn’t realize until later that it didn’t work in any case. That in itself is very worthwhile when you consider he was not a full time professional mathematician.

[@modok_ff]

@@francoislechampi2002 but if his proof was false, how did he come up with it in the first place?

[@francoislechampi2002]

@@modok_ff we don’t know about his proof but we know about all the other attempts by no-so-good mathematicians. If I understood it well , they all assume about some property which has been proven for real numbers but not imaginary numbers. So maybe (just maybe) Fermat did the same mistake. Don’t forget that Fermat was not a professional mathematician. He did maths for fun after work and we know him having other false maths proofs.

[@TrustifierTubes]

Every time I have heard the story I have I have wept with joy. What an incredible incredible life. I remember hearing the news of the initial proof at the department of mathematics at University of Ottawa where I was a student, I did not know of the history behind it at all but I remember being completely in awe. It is equivalent, do what I think people around the world felt, when we landed on the moon. Even as I watch this video tears started rolling down my face. It's incredible.

[@nothosaur]

Andrew Wiles gently smiles, Does his thing, and voila! Q. E. D., we agree, And we all shout hurrah! As he confirms what Fermat Jotted down in that margin, Which could've used some enlargin'. Tom Lehrer

[@cboria148]

Excellent narration, you did a great job with this video. Very well explained.

[@KeithTax]

The real question is, did Fermat actually have a "marvelous proof" to the equation, as indicated in the margin?

[@dgnoob18]

He was joking.

[@schroedingersdog7965]

Some time after writing his famous notation, Fermat published a treatise including a section describing equations of the form X^n + Y^n = Z^n. This would have been the perfect place to have published his "proof", yet no such proof was included. Because of this, most mathematicians believe that Fermat realized he'd made a mistake in his "proof".

[@stevezelaznik5872]

Some of Fermat’s theorems were disproven so it’s always possible his Last Theorem just had a flaw somewhere in it too

[@television9233]

A professor once told me that Fermat's proofs are closely similar to an almost solid proof to the last theorem, I say almost because that proof turns out to have tiny flaws that once unraveled show that it is wrong in the end. What likely happened is that Fermat's was using this "proof", did not realize the existence of the small mistake, and truly thought he had a proof that was too tiny for the margins.

[@calicoesblue4703]

Lmao, No Fermat definitely did not have a proof for his Fermat theorem. There was not one shred of evidence for that. For a solution like that it would leave a huge paper trail.🤷

[@larryboone5865]

So what numbers can be inserted and show the formula solved?

[@randyduncan3190]

Exactly.

[@byronwilliams7977]

This was an excellent talk.

[@GlorifiedTruth]

"...all I had to do was prove the Tamiyama-Shimura conjecture." Sounds easy enough to me.

[@thejils1669]

Did it in my sleep!

[@ggrthemostgodless8713]

Very informative, very short, no fluff, and very concise... I love you woman.

[@Liberty4Ever]

A few of the greatest accomplishments were serendipity, but most have been the result of obsession bordering on madness.

[@SomeoneCommenting]

Presuming that Fermat wasn't trolling when he said that, it means that he was able to find a solution *using only the math known in the world up to that moment* . It would mean that his proof is something really simple, as he claims, and who knows if it is so simple that it escaped all these mathematicians who always try to look for proofs in the hardest and most complicated ways. Imagine the surprise in all these mathematicians if one day someone figures it out, and it only takes like two pages to prove it.

[@AndresFirte]

If he wasn’t trolling, then he was just wrong. He probably found a flawed proof. And mathematicians don’t try to look for the hardest things, it’s quite the opposite: the reason why Fermat’s last theorem became so famous for 350 years was precisely because most people would expect the solution to be quite simple. There’s been literally thousands of amateurs who have submitted proofs of FLT. People that don’t have fancy phds. But they have all been wrong, their proofs have always been found to have mistakes. So it’s way, way, way more likely that Fermat simply made a mistake, and no simple proof is possible. It would have been found by now.

[@schrodingerscat1863]

His proof may well have been incomplete or flawed in some way and would not have stood up to peer review.

[@jonnoel8606]

@4:00 !!! Wow, look at the stacks of paper on and around his desk! I'm almost more amazed he could sort through all this.

[@StefanReich]

Haha. Yeah, me too

[@4fgaming925]

@@StefanReich this is me as I dont clean my desk after studying for like 9-10 days lol

[@yellstr]

129 page proof, using methods not known 357 years ago… are we sure that is what Fermat called a "truly marvelous proof"?

[@television9233]

Why do you ask "are we sure" on something that was never stated nor is true in the first place. Fermat's proof either had a flaw (most likely) or he was joking/lying (possible but unlikely)

[@EAOO]

Fermat didnt have a truly marvelous proof lol

[@dougstewart5656]

@@television9233 another logical possibility is that Fermat did have another, correct, shorter, more elegant proof

[@mikemondano3624]

@@dougstewart5656 Yes, a "logical" possibility. But most logical possibilities do not exist.

[@lordhenry2965]

​@@dougstewart5656 Very unlikely

[@ThorkilKowalski]

Beautiful! Thanks for making this.

[@enkilugal3282]

I'm in awe of these people that can understand (and solve!) problems such as this. I'm curious to know how solving the Fermat theorem translates to real world applications.

[@schrodingerscat1863]

It doesn't on it's own but there is a lot of other math that is built on Fermat that was at risk if Fermat was found to be wrong.

[@henkn2]

If everyone was trying to solve this kind of problems there was no time left for warfare

[@schrodingerscat1863]

@@henkn2 There are only about a dozen people on earth capable of solving this type of problem. Everyone else would be wasting their time.

[@enkilugal3282]

@@henkn2 Best comment I've seen.

[@notrhythm]

now if only we had a simple equation for pi

[@christophmeirich5928]

I got goosebumps while listening and this tension. Amazing. Chapeau. Xn + yn = zn ... It looks so easy. Greetings from germany Christoph 😊

[@jijilr]

Thanks for explaining. I could not get such holistic, simplified explanation elsewhere

[@mikemondano3624]

It's the opposite of holism. It is exactly the sum of its parts.

[@damonthomas2975]

Seeing him tear up and almost cry when talking about finally solving the problem is extraordinary. I feel like it's the same emotions a woman has when giving birth. In a way he did give birth...to the final theorem.

[@VonNothias-f7h]

*Start early with diversified investments in stocks, bonds, and real estate. Maximize contributions to tax-advantaged accounts like 401(k)s and IRAs. Regularly review and adjust your strategy to ensure security.*

[@RAKelBerquist1320]

People dont understand that the prices of things are never going back down. This inflation is deeper than we think. Those buying groceries are well aware that the real inflation is much over 10%. The increments dont match our income, yet certain investors still earn over $365,000 in stocks and assets. Wish I could accomplish that.

[@cheryllauris545]

Very possible! especially at this moment. Profits can be made in many different ways, but such intricate transactions should only be handled by seasoned market professionals.

[@DelphineBarkley-r3g]

Some persons think inves'tin is all about buying stocks; I think going into the stock market without a good experience is a big risk,

[@DelphineBarkley-r3g]

that's why I'm lucky to have seen someone like mr Brian Humphery Services.

[@NatalieScott6124]

Finding yourself a good broker is as same as finding a good thing, which you go less stress, you get just enough with so much little effort at things

[@abhishekchhikara4100]

what was fermet thinking of putting a proof like just 1 page or 2 page long ? as this margin isn't enough ?

[@trubblman]

The real story is that it shows that no matter smart one is one still needs to rely on the work of others

[@davidh2550]

What an amazing story. Thank you for narrating this so beautifully

[@angryman5517]

I read somewhere that after Wiles completed his proof, only a handful of people in the world could understand it, let alone verify and cross examine it.

[@dovydenaspdx]

No doubt this is very true. I also have a theory of gravity which will allow warp travel, and I've proved it with a 200 page esoteric paper no one can understand. I might be a total faker, but as far as Wiles goes, what exactly is the result? Not even warp travel, not even new vector parameters for parabolic curves. Nothing. So it's nothing, understood by no one. At least I shot for the moon. Eh, that's life.

[@tbunreall]

they literally said that in the video

[@warpdrive9229]

You didn't watch the video.

[@ednorman9881]

Brilliant! A fascinating subject to focus on and share with us. Thank you

[@AlexTrusk91]

If Fermat didn't lie, he couldn't have used the same tools. But I deem it probable that Fermat hat a flawed or ratehr unfinished prrof that he thought was complete and valid, without any peer review.

[@mikemondano3624]

You don't need peer review to be correct. The false or fraudulent claims in 70% of published papers all had peer review. (That number is much higher now. Tens of thousands of fraudulent papers were submitted last year and many published. AI is much used.)

[@blacksmith67]

I remember the excitement, disappointment and jubilation as it unfolded. One of the few times that news for nerds made it into general media coverage.

[@gamingwithdingo]

I can listen to this woman all day❤

[@ValidatingUsername]

Certainly covers the content well that she’s covering 😊

[@lanzer22]

So glad she's on her way to 1M subs. I remember when she was at 60k and I was thinking the same thing.

[@stefanoviviani6064]

Yet, I like to believe Fermat's words were not a stunt and that there's a simple, beautiful solution to the inequality

[@CellRus]

These people are incredibly smart, and their analytic skills are just applicable to literally every thing in our world. We need more people in STEM.

[@hindugoat2302]

STEM is particularly easy for AI to handle... people wont have jobs in those fields soon. We need people in jobs that AI cant do, like electrician, plumber, nurse...

[@abd_cheese7353]

Stem is not at all easy for AI to handle ​@@hindugoat2302

[@CellRus]

@@hindugoat2302 ​​⁠So can AI dissect embryos for biologists? You seem to equate STEM with just people sitting around thinking and do nothing. Plumber requires less skills than dissecting an embryos so with your logic, Ai would replace that job much faster than STEM.

[@hindugoat2302]

@@CellRus if they can make a robot arm that can perform heart surgery, than yes they can make one that dissects embryos and this stuff just gets better and better over time, unlike a human surgeon who has limitations

[@hindugoat2302]

the high thinking jobs can be done by AI high precision jobs (like surgery) by robotic arm with AI. highly repetitive and predictable jobs like driving can be automated easy. But some jobs are hard to automate, because they are not repetitive, require human interaction or are difficult for robots to interact with. -like plumber

[@schroedingersdog7965]

Now we have to get busy and prove (or disprove!) Goldbach's conjecture: Every even number larger than 2 is the sum of exactly two primes.

[@84com83]

Why is it interesting to know (the consequences of) his conjecture?

[@schroedingersdog7965]

@@84com83 Simply to satisfy mental curiosity. I strongly suspect there's absolutely no practical value in solving this problem.

[@nicholasgloc8555]

I have learnt an incredible amount without understanding..........from this man.

[@EternalSearcher]

a fool like you never learns

[@mikemondano3624]

Sorry you didn't learn anything. Maybe start from the beginning since "learn" means "understand"..

[@nicholasgloc8555]

@@mikemondano3624 It`s clear you`re the one who didn`t understand my comment. i think it`s to deep for you.

[@mikemondano3624]

@@nicholasgloc8555 To deep or not to deep, that is the quest, chum.

[@Cradien]

​@@mikemondano3624there's nothing more sad than a fake intellectual

[@jannetteberends8730]

I remember that. The absolute joy of that man in his press conference.

[@AndrewBlucher]

Wiles showed that the proof was indeed too large to write in the margin.

[@ghyslainabel]

"showed"? I think you mean he "proved" it.

[@rasimbot]

There may be another, simpler proofs

[@Biosynchro]

It depends on the magnitude of the margin. :-P

[@FranktheDachshund]

So what numbers or groups of numbers solve that equation?

[@magicmulder]

None for n >= 3, infinitely many for n=2 (Pythagorean triples like 3,4,5).

[@pauljohnson6019]

Going monk mode celibacy gives you super brain power and genius ability.

[@musicandmathyvids221]

you just summarized one of Seinfeld episodes where George Costanza did exactly that.😂

[@tinafeyalien]

He was married with children while working on the proof.

[@mikemondano3624]

It certainly focuses the mind which is why we have Incels. But the search has not yet uncovered a celibate monk.

[@DjVortex-w]

The funny thing is that the modularity theorem (which is what the Taniyama-Shimura conjecture became after it was proven) is much more useful to math than Fermat's theorem itself.

[@lorenwilson8128]

We aren't sure that this is the hardest math proof until someone solves the Riemann hypothesis.

[@hb1338]

BSD (Birch-Swinnerton-Dyer) is likely to be the hardest of all the millennium problems to solve because it is so very general and abstract - it can't even be stated in a simple fashion.

[@parkamark]

I recall watching the BBC Horizon documentary when that came out in the mid-90s (which is still available on BBC iPlayer to this day) when I was still just a school kid. The fact this problem came back for a second attack at his first attempt of the proof shows just how insane this problem has been, spanning 3 centuries. Just like the Balrog in Lord of the Rings when Gandalf defeats it and it starts to fall into the cavern, but it swipes its whip back for one final hit. Truly a wonder of our times, and as Ken Ribet has said, has paved a path into areas of extremely fruitful mathematics.

[@shinningim]

so what is the solution 🤔

[@StefanReich]

The solution is 200 pages long... ^^ She did her best to give a high-level description (which methods, theorems and conjectures were used)

[@AndresFirte]

The solution is that there’s no numbers that satisfy the equation

[@mattski1979]

That man's severely impressive. Great job. Thank you.

[@maxbaugh9372]

I wonder how long before we get a proof (or disproof) of the Riemann Hypothesis, arguably the "heir" to Fermat's Last Theorem

[@mikemondano3624]

It is arguably completely unrelated and there are far more and better candidates for "heir".

[@knaz7468]

I very distinctly remember when this happened ... people in the math world were angry it was all done in secret.

[@michaelhenault1444]

In his book on Fermat's Last Theorem, the author noted that the tools available to Willey weren't available to the French mathematician.😮 The Professor had found a unique way to solve the problem. Read the book by Simon Singh. It's very interesting.

[@DougCube]

3:28 The image is not correct. Taniyama-Shimura conjecture implies FLT but not necessarily the other way around. The implication is only in one direction. And to be precise it was a weakened version of Taniyama-Shimura that allows it, not necessarily the entire conjecture.

[@joschmoyo4532]

Looks pretty straight forward to me.

[@MatthewSuffidy]

That is impressive. One thing though is he does seem to rely on major building blocks done by others though. You kind of wonder if there was a more direct algebra method than making proofs about surfaces.

[@willyh.r.1216]

I would say, Poincare conjecture is way harder than this one.

[@calicoesblue4703]

Yep, I agree. Newsthink needs to do a Video on Gregory Perelman.

[@julien5053]

@@calicoesblue4703 Andrew Wiles is brilliant, but Gregory Perelman is a genius.

[@pookz3067]

The proof is definitely not way harder, as someone who has read and understood both. Both require a fair but a machinery and both have had very clear And easy expositions by now if you understand the machinery.

[@westbrook0853]

⁠@@pookz3067”As someone who has read and understood both…” Yeah sure lol - who are you then?

[@neerajnongmaithem392]

Might be math professor​@@westbrook0853

[@waldro49]

I remember watching this long documentary on PBS, and so my love of math continues, kudos to you Andrew Wiles🎉.

[@asicdathens]

With the mathematical knowledge of Fermat's day it was impossible to solve the last theorem

[@nikoladjuric9904]

Maybe it is,just we need enough people to try it.

[@alexeyporubay2400]

I watched it only for 3 and a half minutes and there is already at least two drama films and one biopic that netflix can make, wow

[@BrianMosleyUK]

Imagine how the world will be transformed if AI becomes capable of solving such theorems in simple and elegant ways.

[@mikemondano3624]

Solving and proof-checking software is already in wide use. The problem with AI is that it has learned to lie.

[@BrianMosleyUK]

@@mikemondano3624 well, from that perspective you'll love Grok - the maximally truth seeking AI under development by Elon Musk's company.

[@mikemondano3624]

​@@BrianMosleyUK Lies may become undetectable until it's too late.

[@schizo5189]

​@@BrianMosleyUK if you think Grok is what you say it is, you're one of the dumbest mfers I've ever seen.

[@hb1338]

Simple and elegant requires the use of imagination, which is one thing that AI will not have in any meaningful or useful form for a very long time.

[@4000angels]

This was an awesome video. Thank you!

[@chamuuemura5314]

It’s ironic how prideful and paranoid of having ideas stolen, yet each idea depends on paths paved by the ideas of predecessors. He didn’t want it solved, he wanted to be the solver. Kind of an unnecessary hero complex. Being more open from the start would’ve saved him a lot of time.

[@ecMathGeek]

History remembers the one who solved it, not the one who got 90% of the way there. Awards are given to the one who solves it, not to the people who produced the steps to do so. No human in existence is going to be okay having their hard work stolen for someone else's achievement.

[@dmitripogosian5084]

Next time tell it to some distance runner that it is not important that he beats world record in 100m, just that somebody does it. See how it will motivate him, and helps him is unnecessary hero complex

[@zat5176]

@@dmitripogosian5084Exactly

[@elisabettajdj335]

It wasnt Ken Ribet who showed this case 2:39, it was Gerhard Frey

[@TIO540S1]

Wiles’ accomplishment was and is amazing and he’s worthy of the praise he’s been given. But I don’t think even he would be comfortable calling it “the world’s hardest math problem.” I think most mathematicians wouldn’t be comfortable naming any problem that way. It would be like saying something was “the world’s most beautiful symphony.” Plus, as Wiles would say, he built on work by Ribet, Taniyama, and others, as all math breakthroughs do. I think it’s likely that, with a gun to their head, so to speak, most would name the Riemann hypothesis as the world’s most important unsolved problem, and certainly as difficult as any.