What is Mathematical Research?

Описание: If you're interested in personal help, I've posted my tutoring services on Fiverr: https://www.fiverr.com/s/dDYkBlz

I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring.

My channel has received considerable attention recently for reasons that I'm not aware of. This is an update video, so that I have something to show on the channel, and to indicate a potential further direction for the channel. I've been tremendously busy with my research and lecturing recently, which explains the complete absence of anything to the channel. So that there is some content to the video, I answer a question relating to how one goes about mathematical research in the first place. What mathematics looks like behind the scenes.

I apologise in advance for the number of jump cuts and the likely terrible audio. I wanted to minimise the amount of time required to get the video out, in a hope that it will be easier to produce videos in the future.

Other videos along these lines:
What is Mathematical Research? Have all math problems been solved?    • Have all math problems been solved? What i...  

My website: https://www.kylebroder.com
My papers can be found here: https://www.researchgate.net/profile/... and on the arXiv: https://arxiv.org/search/?query=Brode...

Timestamps:
0:00 Opening chit-chat. The channel has been receiving attention.
1:30 How do mathematical discoveries occur?
2:10 Example from my Ph.D. research.
3:08 First steps. Finding out where others have gotten stuck.
3:38 Learning for the purpose of solving a problem.
4:26 Trying to make a small improvement.
6:00 Next step. Can you do better?
6:12 Picking up problems along the way. The Schwarz lemma.
6:50 Proliferating results.
7:18 High level perspective on how the research goes.
8:35 Breakthroughs.
9:15 Closing chit chat. Rambling about vague hope of posting more consistently.


These videos are separate from my research and teaching roles at The University of Queensland.

💪🙏 Support the channel by signing up to a free trial of Skillshare using the affiliate link https://www.skillshare.com/r/profile/... If you would like free access to the manim course without signing up to Skillshare, send me an email and I'll send you a free link to the course :)

I have not had the opportunity to teach mathematics as much lately, given the amount of focus I have given to my research. I enjoy the process of teaching and interacting with students and so have decided to do some online tutoring. If you're interested in personal help, I've posted my tutoring services on Fiverr: https://www.fiverr.com/s/dDYkBlz