What does research in mathematics look like?

[RonPaul]

For the first problem, have you tried plugging it into the quadratic formula?

[marcnairn]

As a theoretical physics PhD student, it is quite recomforting to see that not all mathematicians are absolutely unhinged proof writing machines and they also spend time having to grasp the concepts from time to time

[gwilym]

"This weird object, which I'm going to call U"

Ouch

[blackhawk]

I’m an econ major and I always find math research so fascinating. The complexity of math and how you guys go on about to solve a problem is mind boggling to me. Respect to you math geniuses

[EmeViDji]

Hi! Just want you to know that I really enjoy your videos. I am currently an undergrad math student with the objective to progress to a masters in pure math and being able to see what further mathematics looks like is really enjoyable to me. Keep up with the great work!

[TheRealOmbreMoon]

Listening to you talk about how you approach your Math PhD really puts me at ease for when I got for mine. I'm glad I'm not the only one who felt the first problem made sense, but also made me wanna run away screaming!

[littlenarwhal]

The second problem is really interesting, please keep us updated on your progress on it!

[thomasbates]

Thank you for posting this and all the other math content you have so far! I've always wanted to see content like this!

[josueramirez]

After hearing how the first problem has already been on a professor’s mind for about eight years, I thought a lot about tenacity and how there are some puzzles that do take a long time to solve

[DynestiGTI]

16:19 "when you work on a problem every single day for like 2 years, it becomes incorporated in you" 😂 man that's too relatable

[zacharysmith]

I dearly miss higher mathematics, this was beautiful. Please keep sharing your progress throughout your phd!

[__a_]

I touched on something very similar to your problem 3 in my master's thesis; definitely one of the more enjoyable and 'novel' parts of my paper!

[juanjuan]

I relate to you in quite a few aways, even though I am almost a decade younger than you. Last year was my first year of Uni and all I did was trying to get really good grades. This led me to have a virtually non-existent social life, I gained a lot of weight, and just everything felt bad in all aspects besides my good grades. I reckon that it even more important to make time for networking, exercise/health and in general having a varying life which does not revolve around uni. So this year, I decided to study less, hit the gym, and socialise a lot more. I am still trying to get good grades, but it feels so good that there is some variety in my life. Anyways, I am super inspired by your channel, I like you are open about your situation and the stresses of being a grad student. I wish the best for you my friend!

[tanmayvadhera]

As an engineering student, this sounds like wizardry.

[spoopedoop]

For the second problem, if you modify it to any bounded, smooth, convex body in R2, I believe the boundaries are homotopic. If you could create an ordering on such curves, then you construct the surface by piecing the slices together with to homotopy parameter giving you the z value, since the problem is essentially generalizing conic sections to convex sections.

[david]

As soon as you said convolution, as an EE, I flinched a little 😂😂😂

[natepolidoro]

Awesome insight. This is what I want my life to be.

[lancemartin]

For the first problem, I would recommend looking at some results from both Functional & Harmonic Analysis. You may be able to use some ingenuity with Fourier Transforms, and use some results about compact & bounded Integral Operators, at least to make some progress. Analysis/PDE was always my favorite subject

[paulmoran]

It looks like NA PhDs are really quite different from my own PhD experience. I didn’t have any classes during my PhD’s as the essentials are covered in your undergraduate degree in Western Europe. I live in the US now, and I was initially really surprised that PhD’s had classes, and that those classes covered material that I considered undergraduate level material (in chemistry at least). Now i see the stark difference in the undergraduate degree philosophy between Europe and the US, and I understand why classes need to be taken.

Ultimately we all end up with the same skills by the end of our PhD’s irregardless of whether it is in the US or Europe, but I am so glad that I did my education in Europe as, for me, it is more focused.

Now, having just turned 50, I am going to University for fun to do degrees in maths and physics…but again I took the European route as the equivalent US undergraduate degrees would not have covered the same amount of material as the European degrees, and would not have been as focused on the core subjects.

no one is better than the other….just different philosophies.

[jennifertate]

I really want you to pull that staple out so badly, after you had that first bit of fun playing with it. 🤣🤣🤣 Enjoy your vids. You're smart and hilarious.