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John Michener's avatar

Old physcist turned engineer here. You aren't really going to understand the issues they are considering at the frontier before you understand and master the basics. And it takes a long time to learn the basics. Now I think that some of the fundamentals can be taught better using more modern techniques - the Gibbs/Heavyside formulation of electromagnetism is probably getter handled via a geometric calculus formulation - which also better prepares the student for dealing with spin issues in Quantum Mechanics, but you need to get the student familiar with a lot of areas and techniques before you can start handling the research issues. My experience is that some seminar classes for the best undergraduate students may be approaching such areas in their senior year, typically students start approaching the research areas in or after their 2d year in graduate school. You could certainly give some very interesting classes overviewing what is going on in the research areas, but that is either additional classes or slows down the development of subject mastery.

There were several approaches to modernize the introductory curriculum in physics in the 60's - the Berkeley physics curriculium and the Fenyman lectures come to mind. The Fenyman lectures were and are excellent and some of the Berkeley books were excellent - but in retrospect both were instructional failures - experience showed that only the brightest students could handle them.

I attrited out of math for mathematicians in one semester - I was interested in using math, not doing math. I got a good grade, but I hated it. I still ended taking a LOT of math classes, but I was not interested in proofs for proofs sake. I have read comments from physics professors that they seem to be running a giant filter. I think the attrition rate when I was studying physics as an undergraduate was in excess of 95%.

I would note that being interested in a subject is necessary but not nearly sufficient. Some fields inherently require substantially above normal intelligence and may require other characteristics as well. My Junior mathematical physics text book noted that an understanding and facility with the math was necessary but not sufficient, as an understanding / intuition of the behavior of the physical systems being modeled was also necessary. Now working the problem sets and discussing solution approaches helped develop that understanding and intuition, but you absolutely had to have the necessary ability.

In the past few decades physics students have had mathematical assistance from dedicated algebraic manipulation software - Maple, Mathematica, ... This helps, but you still have to acquire an understanding of the subject matter, the tools, and the techniques to use the software effectively.

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JulesLt71's avatar

Further to this, I’d add the observation in a book I read by a mathematician - either Marcus Du Santoy or Eugenia Cheng - about the difference between those students who went on to become mathematicians vs maths teachers.

That there comes a point, for a mathematician, where you are more excited by the things not proven (the ABC conjecture, the Riemann hypothesis, Generalised Moonshine) than in solving equations.

The conjecture was that a lot of maths (and science) teachers are the people who did very well at the puzzle-solving of school level maths and want to get back there.

They aren’t much interested in their field post-1800.

I suspect the same is true in the sciences

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