Andrew Wiles - What does it feel like to do maths?
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- čas přidán 17. 05. 2024
- Sir Andrew Wiles is a mathematical legend. In 1993, after years of working in secret, he announced a proof of Fermat's last theorem, which had been taunting mathematicians for centuries.
At the Heidelberg Laureate Forum in September 2016, Andrew Wiles told us what it feels like to do mathematics.
Read more on Plus, the free online mathematics magazine, at plus.maths.org/content/introd... - Věda a technologie
I was a top student in math when I had teacher who taught me to understand. Then I became the worst student in the class when a new teacher only taught us to memorise it.
The irony is that the memorise teacher was more highly respected by the school because she got the students to do better in the exams with short term memorisation. She never taught us how to think, only how to remember steps and repeat.
The problem with maths is that it is taught by people who are not mathematicians.
Ramen Grott True.
As someone who enjoys math, but is studying engineering at the moment who's math teacher is like this, I absolutely hate this way of teaching math
It actually makes me want to quit engineering and become a math teacher, who would actually teach math properly
Very true, but there are also situations where mathematicians not suited to be teachers. It relates to the more general problem where experts are not very good teachers. They can understand it but not able to properly explain. But then you could say they are not that good as being expert in a certain area means being able to explain it to others. It got me thinking now
A wonderfully encouraging interview with one of my favorite living mathematicians. Thanks so much for posting.
Measured, reflective , a quiet determination...beautiful qualities in a great mathematician, Andrew Wiles.
Such a lovely man! Not to mention one of the best scholars in any subject ever to live.
We need to take the fear and the silly competitions out of mathematics and turn it into an enjoyable activity. Yes, some people are born with a greater mathematical aptitude, but I’m convinced that anyone could do mathematics (even highly advanced mathematics) given the right environment and teaching method. There is incredible beauty in mathematics; a beauty that is often blocked by fear.
False
I think you don't know any ordinary people.
@@Frisbieinstein You can also choose the right words for them, and convey the beauty that opens up the practice of mathematics, another thing is that internally this person may still be against doing this.
Can't remember how many times I watched this video. It is very encouraging especially when you get to learn new subjects.
Fantastic analogy with music there.
1:05-3:03 is quite an important message... it's not often to hear admittance from a professional that new math will always be difficult, and that a differentiator between them and a student is the ability to deal with the uncomfortable struggle
Why couldn’t I have had a math teacher who thought about math this way back when I was in school? I always found mathematical ideas fascinating, but with the exception of only one teacher that I can remember, all my other teachers seem determined to make the subject as boring as humanly possible. I suspect I’m not the only one who feels that way.
If he did have an understanding of mathematics he would probably not be teaching high school math. Not saying all teachers are bad , but most teach in a way that forces the student to memorize
I spent two years of secondary school at a 'public' (state run) high school, then went on to a 'private' (fee-paying) school for four years. There I had a mathematics teacher who really fired my interest and made me a devotee all things mathematical for the rest of my life. I'm now writing my own book. Not a school text book, but a treatment of a variety of mathematical topics, using a style of presentation based on my private school teacher's approach. I'm hoping that this may (just maybe) help youngsters at high school gain an interest in the subject.
What I do remember is that at the earlier high school, one of the maths teachers, when teaching us about prime numbers, was asked the question, "is there a largest prime number?". The teacher seemed to think there was and said he'd try to look it up for us (but never did, of course). A couple of years later at the private school, when I'd become fired up in maths, I worked out my own proof that there is an infinity of primes. Later I discovered that it was the same as Euclid's proof!
a wonderful teacher and lover of mathematics, or any subject in general, will definitely not become a school teacher except in rare cases
He's so right about how mathematicians think of themselves. I found this in the most exhilarating way. Once casually visited the systems analysis lab corridor in Aalto University, Finland. There was this completely serene, beautiful environment, with sun shining from windows; someone playing piano live - in a quiet, tranquil way. People were so happy!
I love his enthusiasm, and I love maths
I would like to think that he was not humbling himself down when he said that all of us (he meant mathematicians) are experiencing the same struggle of the third grader but at a much bigger scale. That is sweet, and the man proved to be sweet as usual. But my critical faculties refuse to submit. I know some people who would not produce useful output in mathematics even if they persisted in this struggle for decades. I mean anything useful, let alone solving a centuries-old stubborn problem.
Great questions!
So proud that I could listen to one of his lectures
Most important video of our age, in regards how our schools have ruined our perception of mathematics! They showed us the instruments in class, but never let us played with them and especially never gave us the beauty of music to experience with!
Hey sir, I just watched your video and I must say that it was really informative and well-made. I was wondering if I could help you edit your videos and also highly engaging thumbnails which will help your video to reach to a wider audience.
The question of whether mathematics is invented or discovered arrives very much from the minds of those concerned with physics and generally the application of mathematics. There is a sense in this Q&A that Andrew Wiles is trying to reel everyone in to considerations regarding pure mathematics.
When he says that all his colleagues unanimously agree mathematics is discovered it feels as though the crowd is thinking about “a mathematical universe” when that is not what he intends even in the slightest.
I love this man
Mathematics is the most important subject.
Why ?
@@ROForeverManwell, It allows us to control our environment with precision, combined with physics has an excellent predictive power something that cannot be said about other subjects, not to say they are not important.
@@hemant5318 But what good does it make that you have 4k tv when you are depressed ? Wouldnt philosophy that teaches you about what is important in life is more important ?
If you think philosophy will help you from getting depressed, you’re completely delusional. Depression is almost always (barring some congenital causes, or causes due to malignancies, but these are rare) caused by nutritional deficiencies (including vitamin D from sun exposure), nutritional imbalances disturbing your metabolism (like an excessive intake of omega 6 ftty acids compared to omega 3 fatty acids), microbiome-related conditions such as SIBO (Small Intestinal Bacterial Overgrowth) intoxicating your small bowel with biogenic amines, D-lactate, lipopolysaccharides and many more, or these dysbiotic intestinal condition upregulating inflammatory cytokines able to cause systemic inflammation such as neuroinflammation, nervous system dysregulation due to a problematic circadian rhythm due to excessive screen time when your bodu shouldn’t be exposed to (blue) light, chronic anxiety due to trauma or lack of exposure, or environmental toxins such as mycotoxins due to living in water-damaged buildings, or heavy metals from water supply in rural areas with contaminated water, and also social isolation; whether or not you consider yourself an introvert, humans require a sense of identity and community, and plenty of enjoyable interaction with their peers.
And math is nothing more than the collection of logical inferences we can draw from it’s premises, mostly in the hope of reducing the computational burden that arise from calculations which apply to real life problems. So in a way, many braches of math collectively provide frameworks as solid as we humans can possibly come up with given the way our brain and thus reasoning works, in order to control our environment. That is not to say that there aren’t any branches of math which are utterly useless by any measure other than how they can be aesthetically pleasing to the person who reaserches it.
@@Ruktiet Who lied to you ?
Two of the questioners seem almost hostile to mathematics, as though they want to accuse Dr. Wiles of something vaguely deceitful, or of cheating and secrets covered up. Reporters and politicians sometimes try to twist science and learning into a knot and make it appear bad and alien. But those who work in these areas can be sure that no politician can damage the reality of science and mathematics, whatever they may manage to do to individuals.
Ralph Dratman I am a layman from my pov I do understand your points. From my pov the problem with questions are more related to the questioner like spiking another languages, if you don't speak it it's hard to see the beauty:)
To prove Fermat clearly, short,absolutely, easily
I use the condition xyz are integer
1^2+2^2+3^2+4^2+....+n^2=Sn=n(n+1)(2n+1)/6=2n^3+3n^2+n/6
2n^3=6Sn - 3n^2 -n
n^3=3Sn-3/2n^2-n/2.
Fermat had said x^3+y^3=/z^3
I supose
x^3+y^3=z^3
3Sx-3/2x^2-x/2+3Sy-3/2y^2-y/2 -3Sz+3/2z^2+z/2=0
x^2+y^2-z^2=2Sx+2Sy-2Sz-x/3-y/3+z/3.
Sx+S(x-1)+Sy+S(y-1)-Sz-S(z-1)=x/3+y/3-z/3.
Or
2S(x-1)+2S(y-1)- 2S(z-1)+x^2+y^2-z^2=x/3+y/3-z/3
So
1^2+2^2+3^2+..+(x-1)^2+1^2+2^2+3^2+..+(y-1)^2- [ 1^2+2^2+3^2+..+(z-1)^2]= - x^2/2- y^2/2 +z^2/2+x/6+y/6-z/6
Because
x(x-1)(2x-1)/6+y(y-1)(2y-1)/6- z(z-1)(2z-1)/6=/ - x^2/2- y^2/2 +z^2/2+x/6+y/6-z/6
Contrary to the assumption
conclusive
x^3+y^3=/z^3.
General, using
1^a+2^a+3^a+...n^a=Sn
Prove
x^n+y^n=/z^n
Bruh I see you in all educational videos
I find that today, mathematics is strangely more devoid of envy, superficiality, and corruption than nearly any other subject or field of study in the real world; apart from a few outliers. The vast majority of people don't do mathematics for profit, or for notoriety, they do it for truth. People who do mathematics for exclusively superficial gain will very rarely be able to progress to a professional level.
Yes
Inspiration
Quick maths!
A dear, sweet, mathematician. God’s gift to mankind,
I was born curious. And have been punished a lifetime for it.
Fermat's last theorem is a fact.
Fermat's did not claim that there are no whole solutions to equation.
Fermat's claim that are no solutions to the equation in whole numbers.
Hello Professor Jay Daigle, I am looking forward to meeting you online 4/26/2024 about my presentation of Collatz Sequence.
Taha M. Muhammad/ USA Kurd Iraq
Owner of Collatz, Euler, and Fermat's both last Theories
U see Mr.Wiles u have an encounter not with encounter but with your brain I placed that in everybody
Good
定理が発表されるまでに測度論的確率論の入門とルベーグ積分の基礎の学習をしようと考えてます。そこまで勉強したら少しゆっくり読書したいです。
Use translate
Ilovemaths
To answer that man's retort, no, it is not a necessary illusion to believe that mathematics is discovered. Mathematics is discovered, the discovery is not an illusion, and we know this because but we are aware of the fact that that the mathematical facts we study are grounded in abstract objects. These abstract objects and their properties and relationships are understood to exist a priori -- that is, they exist whether we are aware of them or not: for example, 2+2 is 4 whether we recognized it or not. By recognizing it, and by proving it, we haven't invented the relationship 2+2=4 -- we've merely discovered it. We discovered a relationship between two a priori objects. By this token, you can understand that mathematicians don't invent mathematical facts: they find them.
Richard Feynman said, "most of the time you feel stupid" because you can't get the answer.
I hope you honor see my notes, would you please communicate with me because I solved both Fermat's Last Theorems! Please it will be nice of you to take care of my solutions of Fermat. Euler, and Collatz Sequence.
There's a prize, you work for the money that's advertised, so then you can move on to the next one and also have enough to eat and afford rent. No? 1 million doesn't buy a home.
専攻は経済学から数学に変更しようと考えてます。
Only the greats say things like this. I heard Richard Feynman say something very similar. I suspect it's just not true. Things always look doable for everybody to those who are able to do those things. It looks like a sort of winners bias.
Wow! This is a story of self mastery - not of genius.
both :D
genius = self-mastery
USE THE CODE TO SOLVE FERMAT Always be correct (x^1/a+y^1/a)^na=(z^1/a+x^1//a+y^1/a - z^1/a)^na. Call d=x^1/a+y^1/a - z^1/a =>(x^1/a+y^1/a)^na=(z^1/a+d)^na. They are composed of two groups One group contains x^n,y^n and z^n and the other contains all irrational numbers. z^n=x^n+y^n. Impossible!
Can you think of something so much it makes you almost sick?
yes. research can do that to you. hopefully you make a few successes to keep going, but its mostly a very painful and stressful experience. not for the faint of heart.
Cantor, Godel, Boltzman to name a few.
@@robertpalmer8371 I would say *mathematics* doesn't quite fit that particular description, at least for me. It can make you sick but I wouldn't say that it's in a painful way, if that makes any sense.
@@reimannx33 Cantor's pain was because he was ridiculed and strongly opposed by Kronecker, who was mostly well-respected in his time. It was not from the mathematics itself. Godel's pain was because towards the end of his life he developed serious paranoia and actually starved himself to death out of fear of being poisoned. Boltzmann's pain was because nobody believed in his view of the world, even though he was able to produce very applicable equations from it. For the vast majority of professional mathematicians today, this sort of opposition doesn't really exist. In particular Wiles doesn't face this sort of opposition. It definitely is very challenging to do what Wiles' did, and the stress is quite powerful at some times if you believe that a serious issue in your life-work manuscript of 7 years is unfixable. The "sickness" of thinking hard about mathematics though usually is more like a "sickness" like running, in the sense that you feel good about feeling sick since it means you're really concentrated and able to focus on the problem.
The comments must be fun
Godel expresses wff's in odd numbers
every number is prime relative to its own base n = n(n/n)=n(1_n) (primes do not include division by other numbers)
Goldbach's Conjecture "every even number is the sum of two primes" n + n = 2n
Godel's expression does not include even numbers in his defintion of wff's - they are therefore "undecidable"
(o + e) = o is always odd so is undecidable because of the existence of even numbers (e+e) = e
(o and e are sets of numbers).
Proof of Fermat"s Theorem for Village Idiots
c = a + b
c^n = [a^n + b^n] + f(a,b,n) (Binomial Expansion)
c^n = a^n + b^n iff f(a,b,n) = 0
f(a,b,n) 0
c^n a^n + b^n QED
works also for n = 2. Someone go tell the physicists (Especially Einstein and Pauli)
and also for multinomials (tell the cosmetologists..)
(Hint: Wiles had to use modular functions, which are only defined on the positive half of the complex plane.)
there are no negative numbers: -c= a-b, b>a iff b-c=a, a >0, a-a = 0, a=a
if there are no negative numbers, there are no square roots of negative numbers. The ""complex" plane is affine to the real plane (1^2 1, sqr(1^2) = 1 2qr(1) (Russsell's Paradox; a number can't both multiply and not multiply itself).
more on this on the physicsdiscussionforum (dot org)
shame the person coughing blanks out what he says at times.
Look to GOD for guidence
Every time they say encouraging shit like "Everyone is good at math. People being bad at math is just an illusion" I get pissed off and offended.
It's just as obnoxious as saying, "Just work harder, and you can improve your height."
BULL. SHIT.
Well, the statement "Everyone is good at math" is pretty much bullshit. I would rather say everyone sucks at math until he/she starts practicing. The bigger problem is the way people feel and think about math. If your education ha led someone to the conclusion that he sucks at math he will pretty much avoid it and as a result suck at it.
They are justified in hating math.
Many math nerds who try to convince them otherwise probably avoid and HATE sports for the same reason.
Yes, you're right. That's unfortunately how psychologie works. Seems like we all have to try things we hate so we have a chance to change our opinion about it.
Nightingale Orphi Are you generalizing that All math nerd hate sports? lol
Nightingale Orphi Andrew Wiles is saying that once you get rid of the things hold you back, you can advance, like a sport,
Fermat's Great! Theorem -... 1637 - 2016 !!!
I proved on 09/14/2016 the ONLY POSSIBLE proof of the Great Fermat's Theorem (Fermata!).
I can pronounce the formula for the proof of Fermath's great theorem:
1 - Fermath's great theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!!
2 - proven! THE ONLY POSSIBLE proof of Fermat's theorem
3 - Fermath's great theorem is proved universally-proven for all numbers
4 - Fermath's great theorem is proven in the requirements of himself! Fermata 1637 y.
5 - Fermath's great theorem proved in 2 pages of a notebook
6 - Fermath's great theorem is proved in the apparatus of Diophantus arithmetic
7 - the proof of the great Fermath theorem, as well as the formulation, is easy for a student of the 5th grade of the school to understand !!!
8 - Me! opened the GREAT! A GREAT Mystery! Fermath's theorem! (not "simple" - "mechanical" proof)
!!!!- NO ONE! and NEVER! (except ME! .. of course!) and FOR NOTHING! NOT! will find a valid proof of the FGT!!!!!!!!!!!!!!!!!!!!!!!!!
خيه عليك
AI is doing ur math tutor and it's removing call center and 300m jobs and so we have new areas of work not me❤❤🎉🎉
Professor Wiles, who wisely departed from the toxic realm that claimed the best two mathematicians of the British Empire (Turing and Ramanujan), practices MATHEMATICS, not that french-originated abomination "maths"
I am Taha M. Muhammad
Solved
Collatz Sequence in 3 Ways
Euler Perfect Box
Fermat’s Last and General Solutions
On January 23, 2024 I put all above at CZcams & Twitter
Congradulations! Are you a professor?
Jesus Christ!!!!
gimpy dosser
You're just jealous.
Nah he is a great man. Also there are gimpy dossers that go to the gym regularly and stay gimpy dossers in their very core.
There is no such word as maths. The shortening of the word mathematics is math.
Prove it!
There is no such English as British English. Not a thing!
Though I omit the "s" in speech, I do see how it is strange that one may say they do mathematics but shorten it to math without the plural. Would "maths" not be the more correct shortening? Well, that seems like an issue of culture and as such it should not be limited by one's opinion.
Cai gi ma the gioi bi thi Vn lam.đây là phương trình luôn luôn đúng;(x^1/a+y^1/a)^an=[z^1/a+(x^1/a+y^1/a) - z^1/a]^an. Dat
d=(x^1/a+y^1/a - z^1/a ) =>(x^1/a+y^1/a)^an=(z^1/a+d)^an=>x^n+anx^(n - 1//a).y^1/a+....+any^1/a. x^(n - 1/a)+y^n=z^n+an.z^(n - 1/a)d+....+an.d^(na - 1).z^1/a+d^an=0
Xong roi
Neu chua hieu thi coi them =>
na.z^n= {[z¹/a / (x¹/a+y¹/a - z¹/a)]}.{
nax^(na - 1)/a.y¹/a+….+nax¹/a.y^(na - 1)/a - [+….+naz¹/a.d^(na -
1)+d^na] }
Sai khi (So nguyen bang vo ty) khi (a) la so nguyen va z^1/a la vo ty.
Nếu z^n=x^n+ý^n khi don gian van dung nhung sai vay z^n=/x^n+y^n
Om mani padme hum.
It's hard to understand what you have describe here. But I guess it's have something with the Fermat-Wiles theorem