Today there is an old math problem from 1988, which was considered to be presented in the IMO. Professor Michael Penn presents the problem and its solution, which requires skills and knowledge from several fields of mathematics. The combination of those parts is astonishing. You might try to solve it on your own or just enjoy the video.
Professor Tim Maudlin argues that there is a difference between a physical theory and a mathematical formalism. From his point of view quantum theory is not a physical theory but only a formalism which can be used to make predictions. These can be confirmed to high precision in experiments. But the explanatory power is missing in a way. Why does a theory need an interpretation? Bell's theorem is connected to this problem.
Professor James Gates detected an algebraic, geometric and graph theory related connection with formulas from quantum field theory. This looks like an error correction code known from computer science. The only other known occurence of error correction codes in nature is within DNA in the field of genetics. The footage is from quantum to cosmos festival, waterloo at october 18, 2009.
WP: Sylvester James Gates
WP: Adinkra symbols (physics)
WP: DNA
Professor Peter Woit discusses another approach to explain the universe from a mathematical point of view. This >3h video is not intended to be understood by beginners. There is a lot of advanced content. However, it's always interesting to enter unknown scientific territory.
Neil Turok descibes a new model to explain the universe. He has chosen a minimalistic approach which sounds promising. He has got the hope to be able to explain several open questions in modern physics. The model addresses the big bang, vacuum energy, dark matter, the standard model of particle physics and more.
Ever been late to a lecture? Don't worry - you can compensate for this by solving open math problems as George Dantzig did in the year 1939.
Start with a rap song about dark matter:
Now you're in the mood to enjoy scientific arguments regarding dark matter. Is dark matter only an idea? Or is it a real thing? First observations by Fritz Zwicky and later observations by Vera Rubin established the idea that there is something out in the universe which we cannot see but causes gravitational impact. Nice quote at 7m48s: So in the beginning you have the big bang. Lawrence Krauss has got an opinion about which stories should beginn with those words. Maybe we'll come back to this another day. Meanwhile dive into the evidence which leads to the postulate of dark matter. Bonus: at the end (41m32s) there is a crackpot compass presented.
Neil deGrasse Tyson is the host of a cultural highlight for anybody interested in science. He is a great story teller and connects education with entertainment, and he does so with an enthusiasm rarely found elsewhere.
How can a crackpot be recognized? Angela Collier presents an example as follow-up to the first course in this YouTube video. There is one question left over: do you share the judgement? Is is legitimate to speculate in science? Where exactly is the red line to distinguish scientific avant-garde ideas from blank nonsense? Is string theory a story made up by a community of crackpots? Or is it bleeding edge science in terra incognita?
Patrick Winston explains how to structure and set up a talk. This lecture is from MIT IAP 2018.
There is another YouTube video describing the origins of quantum electrodynamics at the Shelter Island conferences after World War II. The coincidences of agreement of the theoretical and experimental values are under scrutiny.
Quantum mechanics evolved to describe the electromagnetic field itself. The first field theory is called quantum electrodynamics. It is considered to be a high precision theory and its success is claimed to have started right from the beginning. However, there is a story behind the story. Theoretical results and experimental results came along in good agreement while both being false. This happend more than one time, as Dr. Alexander Unzicker summarizes in this YouTube Video:
There are several links found in the video description. It is some background research material published by Oliver Consa:
Sabine Hossenfelder presents some background information about economic constraints in modern academia. The paradigm economy first, science second has been evolving for several decades. Whoever wants to do research in modern science, mathematics, physics or similar, should watch, think about and understand this video. The culture of producing justification rather than knowledge in exchange for low payment has led to a self-enhancing mainstream paper production machinery. If this sounds familiar within a different context: the quick motion version of this is actually hyped as AI. Be prepared and keep a sick bucket in range.
In the past decades something went wrong with the academic research system. It is hard to tell when exactly this happened, but the trend to economic optimization of academic structures is a main driver in this story. A first impression is given by the following YouTube Video with focus on the US situation.