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Fields Medal winner James Maynard in conversation
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- เผยแพร่เมื่อ 4 ก.ค. 2022
- The Fields Medal is widely regarded as the highest honour a young mathematician can attain and is especially hard to win because the medals are only awarded every four years to mathematicians under the age of forty. This year Oxford Mathematician and Number Theorist James Maynard is one of four recipients.
In this short interview, James discusses the award and his work, his love for prime numbers and where he gets his inspiration.
Read more about James's work here:
www.maths.ox.ac.uk/node/60744
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Even though I'm a noob at math, I'm still watching this, congrats Mate.
same here fam
right? because we admire the brigthness of what we can´t achieve I would say
@Lorem Ipsum ly
Genuinely brilliant man, though it's a brilliance which he doesn't wear openly. His humility is inspiring.
It is amazing how the mind works. The sudden insights when the subconscious "gets it done". I have studied foreign language and REGULARLY I will input a difficult to parse passage into my mind, not getting it at all (in spite of understanding every discrete word) and then...I go to sleep. The next day it is as clear as day what the writer's meaning and intent must be. It is astounding and very, very reliable.
Great talk, and huge congratulations to Prof Maynard!
When he mentioned how sometimes a solution just pops out on his walks or when hes not thinking about math, I resonated with that. It's amazing when you can put your problem in the back of your brain / subconscious, and your brain just solves it for you!
Totally! Neuroscientists found that Gamma waves are responsible for these Eureka moments, by measuring brain activity as people learn and create. This is supported by Einstein, as he said that his epiphany of relativity occurred to him while on a walk in the woods. These waves are also activated when we meditate, so maybe going on a walk, or taking a shower is a form of meditation for us?
This phenomena is why Islam claims that all ideas come from God, but perhaps a Platonist would say that sometimes we can briefly perceive the platonic world and the pure forms within.
Either that or our subconscious must spend a heck of a lot of effort chewing over all the data that we feed it while consciously working on these problems.
@@mccleod6235 The latter really resonates with me.
After reading that Einstein discovered relativity while he worked to approve patents, I got the idea that solving these problems is like trying to unlock a door in the dark. Whenever you're exposed to new information it's like trying to insert the key, and once you're exposed to the right information you find the hole, and it just clicks. Einstein was exposed to a lot of novel information.
Although, this is basically how AI works. Just a bunch of organized probabilities.
@Waldel Martell Yeah, that would be terrible, but kind of funny at the same time.
@@mccleod6235 This phenomenon
Congratulations to Prof. James Maynard for making remarkable advances in analytic number theory that have contributed for his winning the Fields Medal this year. I admire the clarity with which he shares his interests and passion for the topic of prime numbers: it goes to show the depth of the mathematical understanding that the Professor possesses in his field of expertise. The questions from the interviewer were clear and informative too.
"What fascinates us about prime numbers is, on the one hand, that they are very irregular and we can't guess what the next prime number might be; and, on the other hand, that their distributions are regular enough to excite our mathematical curiosity." -- Don Zagier (as quoted by Go Yamashita)
Nice sami flag
Congratulations to Maynard for this achievement!!! He deserved this!! I have been following his work since 2019 but I am not trained extensively in mathematics because of which I don't get it completely. But I respect academicians like him. Congratulations!!!
thanks for this interview. for a window to the mind of a top quality mathematician
Congratulations ❤️🌸
أودُ أن أُبارك لك أيها الشاب الطموح العبقري ... أحسنت صنعاً فليبارك الله في الرجال الذين يخدمون العلم ويعمرون الأرض ويساهمون في تطوير الرياضيات ❤️
That was an enjoyable interview with a lovely young man. Congratulations to James Maynard. I wish you much success in your future investigations and in your life in general.
As usual ,great and proper questions asked!Simplicity in understanding of any complicated theory is giving you a way to open more other theories which still require to be simplified.
Genius with clarity of thinking and communicating in a simple language alongside being a humble person
Great interview, always love hearing about things like this!!
Congratulations prof. Maynard and good luck for future achievements!
Congratulations and thanks for the beautiful theorems!
From Lyon which is approximatively at a distance of 600 miles from Oxford (as the distance between some prime numbers):CongratulationsTo you Mister James Meynard
Congrats! And a delightful interview! I was thinking in terms of sound - numerical values in rhythm patterns, melodic figures, etc - as was also in 2005 at Princeton U our distinguished friend Manjul Bhargava (2014 Fields Medalist), while skillfully accompanying on Indian drums tabla my performance of Indian classical music on Japanese instruments shakuhachi and koto...all the while smiling with obvious joy (at the symmetries and asymmetries he - and likely only he - was observing in the improvised music material as it emerged. Mathemagical musicality. Indian math itself with its roots in long-short relativity in linguistic, poetic & musical discoveries & systematization.
Wow I had no idea he was so accomplished. Much respect.
Always been a fan since the 90s , especially his work of the field of winery octavius math
It's that euphoric eureka moment, that's why I love working with mathematics.
Oh my God! He is so simple.God bless him.
Congratulations! It was fascinating to hear him talk.
I am glad to hear about this. An Indian boy here, who just graduated high-school. I was obsessed with prime numbers ever since I came to know the mysteries behind them and the awesome unproven conjectures. I delved into the world of primes and mathematics (initially with the thought of solving a conjecture) and I came across the works of James Maynard, Zhang, Tao, etc. I binged watched almost every popular video on primes available on TH-cam. I even filled notebooks in an attempt to solve the twin prime conjectures and gone as far as writing a research paper and learning to code on wolfram to visualize my ideas. I even tried to e-mail many mathematicians including Sir James. Though I never got a proper reply, I'm still thankful to everyone who helped me see mathematics and the world differently. Amidst preparing for the heavy competitive exams in India, I still find time to continue my research on primes :D I would like to share a quote I thought of while working on prime numbers :
"Randomness, iterated over an infinite time-span, can produce patterns strong enough for anyone to believe that the universe is deterministic."
Check out IISc's new BS degree course in Mathematics and Computation. They are accepting applications now.
CMI/IMSc (both in Chennai) and ISI Calcutta are great options too.
Your last quote is exactly what i learnt while playing with primes
I am neither a trained mathematician nor someone who had studied mathematics as an optional subject even at predegree level. But somehow I have been captivated by the stunning beauty of the empress of all knowledge, on which foundation every other discipline rests. I would suggest you to go deep into the analytical number theory from a historical perspective where you will find something exiting and invigorating to pursue.
Continue your efforts. You know the great Srinivasa Ramanujan did not succeed so easily in convincing the mathematicians of his times about his natural capabilities as a raw mathematician.
Prime numbers are really mysterious.
Dear Harsh, thanks for that comment. I do agree wholeheartedly with the quote you shared. It seems to me aswell that it is indeed how maths and nature seem to work, simple patterns repeated over a seemingly infinite time-span giving rise to not just deterministic but seemingly intricate and complex patterns. Indeed our universe is deterministic, and course another Indian here!
Well done, I'm just glad my hard work teaching has paid off.
Congratulation James, such an interesting topic you're working in.
Congrats to Prof. Maynard!
Congratulations 👏 James ! Great great achievement!
Number theory is the field that every human understand but don't understand ! Congrats james Maynard ! He contribute to our understanding of numbers !
Just found out he is 35 😱 he look 26 at most
35-26=9
So your guess is off by only 9 years.
(Just trying to make your comment more relevant to this video)
@@bayeshur yhh but x≤26 => he could be 9, 35 - 9 = 26
... and the craziest thing is that none of them are prime numbers.
If only he were single...
He completed his phD at 26, when most of us still doodling with our graduate work.
07:06 What James says about mulling things over was good to hear. I'm learning that's as important as grinding away at the desk.
Congratulations to Research Prof. James Maynard!
Congrats, Prof. James.
What a nice chap. Congratulations, James.
Love that there's an Algebra book on his shelf. Congrats!
Hope for society should be kept high. Would be very interesting exactly what work sent him to this route. A good list of publications or the set of work that granted him the award would be greatly appreciated. People win prices but many of them don't know what they did to obtain it. Yes, I will instantly research what he did since I'm a mathematician but for others who are interested in a overview would greatly get a benefit having the references.
Thank you, Oxford Mathematics for posting these relevant interviews and videos on these subjects.
By the Way, Cohn Algebra 1, Algebra 2, Algebra 3 are extraordinary books on the topic of Algebra. That author explains the topic in a clear way giving examples, proofs, exercises WITH solutions and thorough discussions on the subject difficulties. Those are outstanding books.
Will check out Cohn’s books, thanks
@@gauravdabas9872 The Algebra books 1,2,3 are out of print. But P.M. Cohn's 'Classic Algebra' is still in print and covers Vol. 1 as well as parts of vols. 2 and 3. Highly reccomended.
@@gauravdabas9872 There are some Russians that writes extremely pedagogic books in Algebra and Analysis too. Worth checking the Russian federation on those matters. Mir Publications has extraordinary exemplars.
I have never met Prof Maynard but I first heard his name when he just barely got scooped by Zhang Yitang (a brilliant mathematician in his own right) on bounded prime gaps. He was only 27 and a postdoc at the time. I knew he had a great career ahead of him!
I think his approach was somewhat different, though, right? And that his approach pushed the boundary further down?
I once asked my discrete math professor if there were really only as many numbers as there are primes, and she told me no. I now realize that I went about asking it in the wrong way - it seems there are people regularly researching this. This just emphasizes to me that articulation is difficult, and proving something is even more so - it's like the most sophisticated form of articulation. So to not only answer a question like that, but to substantiate it is kind of amazing. Good Job, Maynard.
I'm glad your math professor was discrete. Most people cannot be trusted to respect your privacy.
I mean, if by "numbers" you are including irrational numbers, then the answer is trivially "no" because the primes are a proper subset of the naturals, which already have a lower cardinality than the irrationals. If you are only referring to natural numbers, then the answer is trivially yes, as there is a 1-1 bijection between the primes and the naturals (or more precisely, there is a bijection between the naturals and a proper subset of the primes, and there is a bijection between the primes and a proper subset of the naturals). This has all been known for almost 150 years.
@@jonathanstatman82 I agree with you. Also, right, I wasn't including irrational numbers in my question. At the time, we were talking about encryption algorithms and prime numbers in a discrete math class. I think the closest we came to irrational numbers was proving that the result of a function was irrational, like the square root of two. I was a sophomore at the time, and didn't learn about different sizes of infinity and things like that until way later.
@@neiljohnson7914 If I had a penny for every time I heard this joke upon mentioning the word discrete... lol. What more interesting, though, is what everyone who makes this joke has in common.
@@ProbablePaul I do understand the difference between "discrete" and "discreet". Just making a joke.
He's very well spoken and good at explaining what he's doing in general terms.
Congratulations prof. James Maynard.
Gosh what a wonderful interview. :)
Thank you.
Your way of explaining is very good I understand very well.....
Congratulations James Maynard
In the equation n1and n2 €N and n2
Congratulations James.
Congratulations Prof Maynar on this huge achievement. Here is the way more discoveries as you investigate the atomic pieces of integers.
MAYNARD
Heartily Congratulations 🎉
The awkward long pauses and the lackluster tone of the interviewer seem to suggest this is a boring interview. It is quite the opposite. Professor Maynard used laymen's language to give a beautiful idea to people not in his field of his outstanding achievements. It is a great interview!
James Maynard won the fields medal? Hell ya right on brother been watching you for a while
Congratulations to most handsome mathematician! 🎉,
Yesterday my math teacher shared an article about him on FB and today I got a TH-cam recommendation video the same
Congratulations James
Great interview, I really liked it.
Interesting to see a vintage (ca. 1960) Teach Yourself Book on his shelf
Congratulations!
So serious :) Congrats, James!
Congratulations to you dear!
He's a superbrain and yet admirably modest.
Congratulations prof. Maynard.
Congrats James
Well done, James!
Remember seeing him on numberphile. Wow
He certainly deserves that reward.
Big cong to James!
At the age of 35 his contribution in mathematics is much much more than his age. Some people's are intelligent and some are too intelligent. This man is the later one.
Congratulations sir 🙏
What a motivation!
This is off topic but what is the name of the music playing at the beginning of this video? Who composed it? It sounds so good. Sounds like some type of ambient music.
Congratulations.
Congratulazioni!!!
Congratulations！
The interviewer asking "What have you done that's so advanced our understanding of the primes?" feels incredibly pointed, almost as if he's being grilled.
Great Video! Love it!
Congrats!
Congratulations! Amazing mind.
Is that his bookshelf? The variety of topics is greater than expected.
Congrats 👏
Congratulations
1:30
“Dr. Maynard, would you not be so kind as to refuse to not negatively reject accepting the Fields Medal?”
Dr. Maynard: “… yes… wait, no… fuk.”
I admit that I envy him his brilliance.
Oh, for sure mate. Each one of use would like to be in his place. Also, most of the people don't know how much other professors have to work hard in order to stand out. In particular, those ones who don't posses such brilliance
@@edoardodomenicone4225- I personally would not "like to be in his place", and I don't "envy him" either. I would feel very uncomfortable with the expectations this prize would bring, and I would be afraid to lose my (childlike) curiosity.
To me, finding answers and explanations is much more rewarding than receiving admiration and acknowledgement.
I would also hate the many distractions such a prize/award would cause.
@@edoardodomenicone4225 How do you know we are not just as. Rolling as je..he had to work hard that was the key..don't know why anyone else who does can't achieve what he did..
@@j.vonhogen9650 he got the prize because made some real advances in math, so at least for me, i envy his brilliance, not the prize or fame. We have tons of good researchers that will not have the honor to make the field advance, because it is too hard to do that. The prize is just one way to acknowledge that.
Nice. He's in the Prime of his life.
And by removing that misconception I have found the general rule for the discussion of prime numbers for proof of my work I am sending you 1 equations from my work to find primes for 7 and all the primes smaller than 7. All these numbers are with unit digit 9 and belongs to 6n-1 groupe
210n1+30n2 - 91
YOOOOOOOOOOOOOO
CONGRATS, Dr. Maynard!!
Congratulations to Maynard on the honor of depth; awards won over time amounting to its recognition. Unfamiliar with James work. After watching this I can't help but wonder about small gaps and large gaps that are also a prime away. Is large larger than itself? (1/[twin+])/(1/[twin]*)?
Semantics mathematicians don’t know about
Congrats
Bravo!
What are the conclusions of current research where can we have a look?
Now I I know why the pieces fit.
Rando question - what work has been done (if any, bc it's a dumb question), by transforming primes to a different vector space (might be a non sensical transformation), as the sum of fractions (or other mapping) and analyzing the problem in that space? Or using topology, algebraic geometery, are there any interesting results?
Thanks and awesome to follow this genius work!
(edit - a quick google says " It is, by construction, simply a relabeling of the natural numbers, so it will have the same structure they do.") :/
congrats! well deserved.
Congatulations to prof. James! I like this man very much! :)
Does James have any papers on the complex relationships between addition and multiplication? I've been interested in this, beyond the obvious explanation of their relationship (that is, of multiplication as serial addition). Can anyone offer some breadcrumbs to follow?
An interesting observation is addition is inherently 1 dimensional (shifting things on a line, increasing length of line, etc…)
Multiplication is a “2 dimensional” operation (calculating area)
You may enjoy this video where he explains a bit about the complexity between addition and multiplication: th-cam.com/video/ZwJy_-vPZuQ/w-d-xo.html
@@MagnumCarta, thank you, sir!
Reposting and slight editing of recent mathematical ideas into one post:
Split-complex numbers relate to the diagonality (like how it's expressed on Anakin's lightsaber) of ring/cylindrical singularities and to why the 6 corner/cusp singularities in dark matter must alternate.
The so-called triplex numbers deal with how energy is transferred between particles and bodies and how an increase in energy also increases the apparent mass.
Dual numbers relate to Euler's Identity, where the thin mass is cancelling most of the attractive and repulsive forces. The imaginary number is mass in stable particles of any conformation. In Big Bounce physics, dual numbers relate to how the attractive and repulsive forces work together to turn the matter that we normally think of into dark matter.
The natural logarithm of the imaginary number is pi divided by 2 radians times i. This means that, at whatever point of stable matter other than at a singularity, the attractive or repulsive force being emitted is perpendicular to the "plane" of mass.
In Big Bounce physics, this corresponds to how particles "crystalize" into stacks where a central particle is greatly pressured to break/degenerate by another particle that is in front, another behind, another to the left, another to the right, another on top, and another below. Dark matter is formed quickly afterwards.
i to the i power: the "Big Bang mass", somewhat reminiscent of Swiss cheese, has dark matter flaking off, exerting a spin that mostly cancels out, leaving potential energy, and necessarily in a tangential fashion. This is closely related to what the natural logarithm of the imaginary number represents.
Mediants are important to understanding the Big Crunch side of a Big Bounce event. Matter has locked up, with particles surrounding and pressuring each other. The matter gets broken up into fractions of what it was and then gets added together to form the dark matter known from our Inflationary Epoch. Sectrices are inversely related, as they deal with all stable conformations of matter being broken up, not added like the implosive "shrapnel" of mediants.
Ford circles relate to mediants. Tangential circles, tethered to a line.
Ramanujan Infinite Sum (of the natural numbers): during a Big Crunch, the singularities being sheared off at inflection points are a twelfth of the original stable particle's mass.
Sectrices: the families of curves deal with black holes and dark matter. (The Fibonacci spiral deals with how dark matter is degenerated/broken up and with supernovae. The Golden spiral deals with how the normal matter, that we usually think of, degenerates, forming black holes.) The Archimedean spiral deals with dark matter spinning too fast and breaking into primordial black holes, smaller dark matter, and regular matter. The Dinostratus quadratrix deals with the laminar flow of dark matter being broken up by lingering black holes.
Delanges sectrices (family of curves): dark matter has its "bubbles" force a rapid flaking off - the main driving force of the Big Bang.
Ceva sectrices (family of curves): spun up dark matter breaks into primordial black holes and smaller, galactic-sized dark matter and other, typically thought of matter.
Maclaurin sectrices (family of curves): older, lingering black holes, late to the party, impact and break up dark matter into galaxies.
Dark matter, on the stellar scale, are broken up by supernovae. Our solar system was seeded with the heavier elements from a supernova.
I'm happily surprised to figure out sectrices. Trisectrices are another thing. More complex and I don't know if I have all the curves available to use in analyzing them. But, I can see Fibonacci and Golden spirals relating to the trisectrices.
The Clausen function of order 2: dark matter flakes off, impacting the Big Bang mass directly and shocking the opposite side, somewhat like concussions happen. While a spin on that central mass is exerted, all the spins from all the flaking dark matter largely cancel out. I suspect that primordial black holes are formed by this, as well. Those black holes and older black holes, that came late to the Big Bounce, work together to break up dark matter.
Belows method (similar to Sylvester's Link Fan) relates to dark matter flaking off during a Big Bang event. Repetitious bisection relates to dark matter spinning so violently that it breaks, leaving smaller dark matter, primordial black holes, and other matter. Neusis construction relates to how dark matter is broken up near one of its singularities by an older black hole and to how black holes have their singularites sheared off during a Big Crunch.
General relativity: 8 shapes, as dictated by the equation? 4 general shapes, but with a variation of membranous or a filament? Dark matter mostly flat, with its 6 alternating corner/cusp edge singularities. Neutrons like if a balloon had two ends, for blowing it up. Protons with aligned singularities, and electrons with just a lone cylindrical singularity?
Prime numbers in polar coordinates: note the missing arms and the missing radials. Matter spiraling in, degenerating? Matter radiating out - the laminar flow of dark matter in an Inflationary Epoch? Connection to Big Bounce theory?
"Operation -- Annihilate!", from the first season of the original Star Trek: was that all about dark matter and the cosmic microwave background radiation? Anakin Skywalker connection?
Prime time!
Wow what a cool dude !
Is he Daniel Ricciardo of maths?
I'm very close too bro ;) asif the 199th triangular number is 19900 however I do prefer my prime correlations,
If you make a uk masters degree based on prime numbers I'll sign up 😉
Why did the interviewer say billions of us who will never win anything?
All evens can be expressed as a power of 2, a power of a prime, and yet it's close enough for him...oh the humility 😆
He must have the quietest office room in the entire world. What a joy must it be to work at such a quiet place at Oxford University. Most people don't realize how noise at work reduces their health and life expectancy. Noise pollution at work, at home and at other places is one of the most poorly understood phenomena, yet with so much consequences.
From my very low perch on the number theory tree - undergrad number theory 101- I learned it's vey easy to formulate deep, easily understood questions in number theory - which then can take centuries to answer, if at all so far. Is this telling us something about number theory - or us?
What are his favorite books?