It's amazing how you can have 2 contrasting ways to do mathematics. One way is almost like showmanship, when you don't have a result yet but you travel and showcase your observations, trying to convince people to work on them, and the other when you retreat to your attic and quietly work on a problem for years.
It's interesting to point out that what we all agree to call a "scientific confirmation" is also, for a big part, a social confirmation : as Ken Ribet pointed out, who is your friend and who isn't matters. This kind of problems has been partly reduced (larger group...etc), but this "social bias" still (and will probably always) exist -in particular in economics sciences-. A scientific will always remain a social individual, part of a social group/class. I'm curious to know if a social confirmation that led to an unscientific conclusion also happened in mathematics, I would guess it probably did.
@@Ruthlessfish Lets not forget that there is the step of rigorous proof verification that mathematics uses to prove hypotheses. Social confirmation is not enough. Ideally it would only play a role in selection of works that are worth verifying and topics to work on, not in the verification itself. I think the danger of wrong conclusions through social confirmation is much greater in other fields where it's harder to verify results.
= THE GREAT! - THE GREATEST!!! Theorem of the 21st century! = !!!!!!!!!!!!!!!!!!!!! "- an equation of the form X**m + Y**n = Z**k , where m != n != k - any integer(unequal "!=") numbers greater than 2 , - INSOLVable! in integers". !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! /- open publication priority of 22/07/2022 / /-Proven by me! minimum-less than 7-10 pp. !!!!!!!!!!!!!!!!!
Dr. Ribet, could you please elaborate on whom the mathematician Demianenko you mentioned at 20:38 was? I tried to look him up, but to no avail; however my stepfather's surname matches the pronunciation and his lineage hails from the Ukraine. I would love to have a mathematician in the extended family! Thank you so much for you contribution to cracking Fermat's Last Theorem, and for doing these videos with the wonderful Brady Haran!
Using polynomial division to solve Fermat's last theorem a^n = b^n + c^n odd number = even number + odd number substitute a with a first degree polynomial that generates odd numbers: 2m+1, 2m+3, 2m+5,... substitute b with a first degree polynomial that generates even numbers: 2m (2m+1)^n = (2m)^n + c^n or (2m+3)^n = (2m)^n +c^n or .... when n=2 c^2 = (2m+1)^2 - (2m)^2 =4m+1 c =9 , m=2 c^2 =(2m+3)^2 -(2m)^2=12m +9 m=18, c=15 polynomial m is a first degree polynomial that generates odd numbers when n=3, m is a 2 degree polynomial c^3 = (2m+1)^3-(2m)^3= 12m^2+6m+1 It is not possible for polynomial 12m^2+6m+1 to be divided by a first degree polynomial without leaving a remainder. Any m polynomial generated when n> 2 will leaving a remainder when divided by a first degree polynomial generating positive numbers therefore no whole number solutions for a,b,c
What a great podcast. I myself am a soon to be graduate of the Brown applied math department (one semester to go!). Maybe I'll get to chat some day with Dr. Ribet at an alumni function.
Great video! could you please explain what's going on in the animation? perhaps an explanation on what type of maths or programming went into making it? Its a beautiful work
@@susanb2140 thank you! This is the kind of answer I was looking for. It's obviously a kaleidoscope effect but I was more interested with the actual curves.
Muy bien narrado todo lo de Fermat's last theorem; este es uno de mis canales favoritos, ¡Felicidades! Ojalá publiques más videos sobre números primos.
does n = 2 work because there are two variables being used in the equation? (x and y). would n = 3 work if there were three variables such as "a^3 + b^3 + c^3 = z^3" and likewise any other value for N where there are N variables being added? and if it's true, does that also mean that in the same way that only n = 2 works for 2 variables, does n = 3 only work for 3 variables and no other number of variables? does n = 7 only work when there are 7 variables?
When I heard this, I had the idea, that Fermat perhaps had some sort of proof, that you need at least n numbers for sum(n_1^n ... n_n^n)=n_0^n to be doable with natural numbers...
This is something Euler has conjectured: Take an equation of the form a^n+b^n+c^n+...=z^n. The conjecture is: if the equation has a solution in positive integers, then the left side has at least n terms. The conjecture is true for n=3 (this is a special case of Fermat's theorem, proven by Euler himself), but counter-examples have been found for both n=4 and n=5 - there are solutions in positive integers for a^4+b^4+c^4=d^4 and a^5+b^5+c^5+d^5=e^5. It is not known if the conjecture holds for n>5.
X^n + Y^n = Z^n where Z is an interger solution, when Y is infinitely greater than X or X is infinitely greater than Y, for all n and every X,Y pair with a difference of infinity 😋😎😂
You're watching the wrong guy. Fermat's Last Theorem was proved by Andrew Wiles, not by Ken Ribet. As much as Mr. Ribet has tried to put his brand on this, he did not solve the problem. ... kiddies, the word for the day is HORNSWOGGLE ...
I think perhaps you do not appreciate how many cuts are made in a (good) podcast edit... the video would be crazy unwatchable without a HUGE amount of extra work. Also - a camera adds a very different dynmaic to an interview. I have some experience in this area.
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It's amazing how you can have 2 contrasting ways to do mathematics. One way is almost like showmanship, when you don't have a result yet but you travel and showcase your observations, trying to convince people to work on them, and the other when you retreat to your attic and quietly work on a problem for years.
It's interesting to point out that what we all agree to call a "scientific confirmation" is also, for a big part, a social confirmation : as Ken Ribet pointed out, who is your friend and who isn't matters. This kind of problems has been partly reduced (larger group...etc), but this "social bias" still (and will probably always) exist -in particular in economics sciences-. A scientific will always remain a social individual, part of a social group/class.
I'm curious to know if a social confirmation that led to an unscientific conclusion also happened in mathematics, I would guess it probably did.
@@Ruthlessfish Lets not forget that there is the step of rigorous proof verification that mathematics uses to prove hypotheses. Social confirmation is not enough. Ideally it would only play a role in selection of works that are worth verifying and topics to work on, not in the verification itself.
I think the danger of wrong conclusions through social confirmation is much greater in other fields where it's harder to verify results.
I love that distinction! Wiles is the attic-dweiller-problem-solver. Einstein is the mathematial showman, imho!
Isn't the abc conjecture proof subject to social bias issues?
= THE GREAT! - THE GREATEST!!! Theorem of the 21st century! = !!!!!!!!!!!!!!!!!!!!!
"- an equation of the form X**m + Y**n = Z**k , where m != n != k - any integer(unequal "!=") numbers greater than 2 , - INSOLVable! in integers".
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
/- open publication priority of 22/07/2022 /
/-Proven by me! minimum-less than 7-10 pp. !!!!!!!!!!!!!!!!!
You plebs should address him by his proper title! He is Master Math Frog of Berkeley to you! (ribet ribet)
He is not master. Do not extoll his virtues man.
Thanks for the entertaining podcast. I was lucky to see Dr Ribet present an overview of Wiles' proof at a joint meeting of the ams and maa.
yessss thank you Brady for creating the numberphile podcast.
What a lovely podcast, very nice to hear Dr Ribet's life story, and once again great work Brady!
Can’t believe I’m taking a class with prof Ribet next semester!
How did it went?
Dr. Ribet, could you please elaborate on whom the mathematician Demianenko you mentioned at 20:38 was? I tried to look him up, but to no avail; however my stepfather's surname matches the pronunciation and his lineage hails from the Ukraine. I would love to have a mathematician in the extended family! Thank you so much for you contribution to cracking Fermat's Last Theorem, and for doing these videos with the wonderful Brady Haran!
Vadim Andreevich Demyanenko.
Using polynomial division to solve Fermat's last theorem
a^n = b^n + c^n
odd number = even number + odd number
substitute a with a first degree polynomial that generates odd numbers: 2m+1, 2m+3, 2m+5,...
substitute b with a first degree polynomial that generates even numbers: 2m
(2m+1)^n = (2m)^n + c^n or (2m+3)^n = (2m)^n +c^n or ....
when n=2
c^2 = (2m+1)^2 - (2m)^2 =4m+1
c =9 , m=2
c^2 =(2m+3)^2 -(2m)^2=12m +9
m=18, c=15
polynomial m is a first degree polynomial that generates odd numbers
when n=3, m is a 2 degree polynomial
c^3 = (2m+1)^3-(2m)^3= 12m^2+6m+1
It is not possible for polynomial 12m^2+6m+1 to be divided by a first degree polynomial without leaving a remainder.
Any m polynomial generated when n> 2 will leaving a remainder when divided by a first degree polynomial generating positive numbers therefore no whole number solutions for a,b,c
The little tune that plays every so often sort of reminds me of Flandre's theme from Touhou.
I like your profile picture. Still only have reached floor 24 after almost 1000 attempts.
Brady, quality of life^2 since you created numberphile!
Brady, this is worthy of the main channel! Great podcast! I enjoyed it alot and more people should too!
Agreed👍
P. S.:
There is no such word as
“alot”. It’s two words but I see that
A LOT! Surprised to see it here though🧐👍😇
What a great podcast. I myself am a soon to be graduate of the Brown applied math department (one semester to go!). Maybe I'll get to chat some day with Dr. Ribet at an alumni function.
Great video! could you please explain what's going on in the animation? perhaps an explanation on what type of maths or programming went into making it? Its a beautiful work
Franco Miranda
It looks like a simple 12 sides kaleidoscope effect
It is a kaleidoscopic effect. You can replicate it with two mirrors placed at 30 degrees to each other and having a moving shape between them.
I believe the curves (which are repeated by the kaleidoscope effect) are a family of elliptic curves. Quite appropriate!
@@susanb2140 thank you! This is the kind of answer I was looking for. It's obviously a kaleidoscope effect but I was more interested with the actual curves.
Muy bien narrado todo lo de Fermat's last theorem; este es uno de mis canales favoritos, ¡Felicidades!
Ojalá publiques más videos sobre números primos.
WOW THANKS NUMBERPHILE2!!!!
does n = 2 work because there are two variables being used in the equation? (x and y). would n = 3 work if there were three variables such as "a^3 + b^3 + c^3 = z^3" and likewise any other value for N where there are N variables being added? and if it's true, does that also mean that in the same way that only n = 2 works for 2 variables, does n = 3 only work for 3 variables and no other number of variables? does n = 7 only work when there are 7 variables?
Very nice to hear the story from the horse's mouth. (I hope, as I am only 42 second in)
Btw, ribet means complicated in bahasa Indonesia LOL
not inaccurate considering he does arithmetic geometry
That was a wonderful podcast
Excellent news: impasse Ribet in Paris has been renamed passage Ribet!
Great to see that notification
Well this is amazing!
Thanks Brady! Didn't know NP2 has a Podcast, insta sub
Wait what. Fermat's last theorem has been proven/disproven. Forgive my math ignorance. Can you do a video?
There are some on the Numberphile channel. The proof is rather complicated so they don't go into the proof itself much, just the history of it.
It was proven in the 90s
It was proven, then they found a "leak" and after some years they managed to fix it. So it's all gucchi now
Where have you been the last 25 years?
maybe you confused that with riemann hypothesis
I'm curious if Ansel Adams inspired you, given his history with Berkeley.
I’m interested in mathematics, not AMS bureaucracy. And I’m an AMS member.
When I heard this, I had the idea, that Fermat perhaps had some sort of proof, that you need at least n numbers for sum(n_1^n ... n_n^n)=n_0^n to be doable with natural numbers...
This is something Euler has conjectured: Take an equation of the form a^n+b^n+c^n+...=z^n. The conjecture is: if the equation has a solution in positive integers, then the left side has at least n terms. The conjecture is true for n=3 (this is a special case of Fermat's theorem, proven by Euler himself), but counter-examples have been found for both n=4 and n=5 - there are solutions in positive integers for a^4+b^4+c^4=d^4 and a^5+b^5+c^5+d^5=e^5. It is not known if the conjecture holds for n>5.
Wow, I was at The Rockaways just days ago.
Berkeley professor... ... ...
California... ... ...
Oh boy...
Ellis Island is also where the term kyke is said to have originated
I want to see you guys
Look in this link to find right solution for Fermat's Last Theorem
Sounds a bit to me like Edward Snowden cloned Ken’s voice aye? Pleasant talk. Thanks a bunch.
Porizon
cool
Please dont put cuts, keep it RAW!!
Ribet fan club member.
Nope nope nope, too jealous to listen to this.
funny if you recognize a name from mythbusters.. :D
X^n + Y^n = Z^n where Z is an interger solution, when Y is infinitely greater than X or X is infinitely greater than Y, for all n and every X,Y pair with a difference of infinity 😋😎😂
You're watching the wrong guy. Fermat's Last Theorem was proved by Andrew Wiles, not by Ken Ribet. As much as Mr. Ribet has tried to put his brand on this, he did not solve the problem. ... kiddies, the word for the day is HORNSWOGGLE ...
Ken ribet - forever overshadowed by andrew wiles. Now he wastes times running for political pisitions.
first
JayBee reported for gayness. Get electroshock therapyd noob
Please, lose the animation...
If you know someone with a video camera, you could get them to video the interview :)
its a podcast, you dont need to watch the video
I expect most people just open the podcast in a tab and don't even look at the animation - it's just wallpaper?
I think perhaps you do not appreciate how many cuts are made in a (good) podcast edit... the video would be crazy unwatchable without a HUGE amount of extra work.
Also - a camera adds a very different dynmaic to an interview. I have some experience in this area.
@@numberphile2, I meant a still will do just fine. ;)