This had me thinking whether or not I have profound and impactful insights to share. Turns out I have none. But I still stick around anyway.

This was what I wanted my PhD to be like, but I ended up researching a topic that my professor didn't know that much about or was interested in, and ended up just casually informing her at times on how it was all progressing. My first real discussion was with a colleague, and the nicest discussion came at my doctoral defence itself. Bit late. Completely different field but really nice to see the exchange, different frames of reference on how each person is looking at the topic and with what goal. And also, it gives people an insight into how science is actually conducted on a day-to-day basis, even in a field like mathematics which one associates with endlessly sitting in a room alone and writing down functions. Very nice video.

I love that Maynard used that term: "conservation of difficulty". Its such a pervasive law that anyone who has ever thought about a deep problem will encounter.

Being able to hold a conversation with Professor Maynard, one of the greatest expert in the world in that field, must be a huge accomplishment by itself.

I understood many of those words!

I would not be able to stand the pressure to have a supervisor that is so high level

More of this please

Read it as Maynard James. Was expecting Tool. Came for Tool. Stayed for the Math.

very unique and helpful content. thanks.

Although I am not an expert in this field, but after carefully watching this video, I have came to the conclusion that I have nothing to contribute to this discourse. As I have established, I am not an expert in this field of study.

This is amazing to think about the access we have now. I think the only way you could improve on this as a window for students or people becoming interested in math is I would love to hear how much maynard is tracking in his mind, obviously he could know exactly what every line is referring to if he was studying it himself, but I wonder since he is context switching and not involved in the detailed calculation it would be great to hear what his mental model is while listening, he must be keeping some generalised /simplified version in his head? Or maybe he is so intimately involved in the area and probably even provided the problem that he can easily track exactly what is going on at each point in his head? Would be curious to here what qualified/ experienced people would say on this.

Nice Meeting ❤

Dear Prof James, Please give a course on analytic number theory on youtube. Whole world will appreciate it. I am studying independently. I request you 🙏

great learning

This guy should buy a tablet, that aside it's wonderful to being let to see this ideas interchange and technical details review Which is the base of scientific method

thanks a lot sir ❤❤❤❤

At some point I was wondering if they were still speaking English....

I never thought I would hear the words "gut feeling" in such an exchange. Perhaps that's why math is called intuitive by many great scholars. My gut feeling on the other hand gently nudges me towards the left over take out food that has likely putrified over a set period. Oh well..

Hello all, I am a Geometer that is interested in the same structures as everyone else: In particular, arithmetic things concerning the naturals. I thought we were going to converge in interest; however, you brought up using the cauchy-swartz inequality: This is perhaps an important result to manipulate on an exam. As a functional analyst, I am professionally obliged to acknowledge that I don’t know where this comes from: (1) the topological structure of affine euclidean space (2) the vector structure of affine euclidean space. One is reffered to the observation that the euclidean 2-sphere: and in this sense of topology, … (i’ve been distracted and forgot!) ….. (Whatever that’s about) it isn’t a 2-dimensional vector space. So the concept of a norm is where we split paths. That’s why I’m a geometer.

@31:00 (For WITTEN HOTSHOT) ‘You glue variables’: I do identify as a geometer, But that would have to be rather precise algebraic knowledge being demonstrated to imply that these kinds of synthesis have anything to do with each other… (1) topological concatenation: Whatever epsilons’ existence one can find propagating downward as one performs ‘surgery’ I don’t know how one could exactly say that this Will correspond to algebraic synthesis between modules: Through action, as it were, if they aren’t the same ring… Obviously whatever tensor product one can define over a ring - this may not be the same product between rings by group action. So I wouldn’t necessarily sit lightly with him using ‘glueing’ like this…. The number theory is NOT geometry. Primes: to me , they are things that one can hold in ones hands.

Ah yes, elementary.

Well, I am lone wolf, but this is a way to do Mathematics, idk maybe in the future it will be interesting for me have a Maynard person near me... By this moment I have enough with e-mails to ask for generous answers. Thanks for upload this, even that I have seen 4 minutes of the video, not really interested in their work. ^^.

AI will reveal that there is nothing to know.