Howdy Philippos Afxentiou,

Yes.

A new paradigm that opens science, engineering, and production for numerous practitioners will come from an individual who has not succumbed to training, whether in math or literature (of science). It will not work to enlarge the human reservoir of individuals who might experience insight like someone else experienced it using the petty inputs of education or training. Insight is not an increment achieved by "the right methods of thought or expression." Information is essential, but I worry about education and training as sources of valid information after 300 semester hours of it in residence and four certifications of my ability to learn in several ways.

In the meantime, most persons embracing careers in physics will become members of that vast, productive workforce that has made changes in the material and conceptual environment that have, with wisdom, improved the lives of all who have access to the new ways. With wisdom! I have issues with the emphasis William Thompson, Lord Kelvin, placed on numbers as better than concepts because I affirm discovery over use in my life, but I want my bridges designed by engineers using physical theories that are the best we can formulate to date. Hurray for numbers! Beware of warm fuzzy feelings about design of bridges however exquisitely expressed!

Educators got their way in the 60's in America because of competition in space - teach everyone to be a creative scientist - bosh ... Support a suitable education and productive life for each of us as equals in value but differing in talents and other details. Cling to the awareness that "the whole ocean of truth lies undiscovered before me (us)." It is too early in human understanding to program creativity. If one wants to do physics, one must embrace mathematics.

Happy Trails, Len

Physics is the mathematical description of natural phenomena. So the mathematical framework isn’t the ``main emphasis", it’s what physics is about. Of course it’s not only about that. But it’s just meaningless to claim designing an experiment, that doesn’t take into account the mathematical description. On the other hand, what matters for mathematics are the assumptions; it doesn’t make sense questioning the consrquences, but changing the assumptions.

Hi Leonard Hall,

The current paradigm is that "you learn physics by solving numerical problems involving calculations in specific situations". Its working to some extend but it has been unchallenged. It is simplistic, primitive and not sophisticated. I would say it leans more on the side of assesment than (instructive or student-centered,any) learning. This shows that it is narrow in scope. I hope one day I will substantiate this to publish an article in journal.

Pedagogically and learning theory speaking it is very weak. Physicists don't take advice from mainframe educational research.

They only value physics education research which downplays more results of generic research.

I think we need a new paradigm.

Howdy Philippos Afxentiou,

Well, yes and no. I must wonder whether the current paradigm is driven by the educators or by the students.

My wife took a CNC Lathe Operators course in a tech school. She studied, but many of the other students just took the test over and over, learning from the provided answers until they passed, and didn't crack a book. They did not experience the larger body of knowledge in the texts. When I used a homework quiz to encourage study in a college physics course, my office filled with students to the amazement of other professors. The assessment threat is significant, and it is justified to the extent that you want your bridges well designed. An alternative view was provided by a mathematics professor learned in learning theory (a'la The University of California, Berkley) who pointed out that a student who has decided to learn fractions can accomplish it in a few weeks without threats.

Compare the safety programs in factories or other general workplaces when exploring human behavior. The monthly lectures are tolerated and ignored unless certain persons are watching, and not all supervisors want production delayed by such nonsense. "Think Safety" pffftt, it should be "Habit Safety" so one does it safely when it matters. A fellow was asked during an accident review, "How did it happen?" He responded, "Like this!" and injured a second finger in an auger. Safety procedures undertaken in the wisdom of most workers are laughable, after all they will not be injured.

Your ideas will help some persons, but attempting to teach persons "how to think out of the box" just changes the box, it does alter the diversity of human character. An older friend expressed concern that one of her sons was following the crowd and asked me about it. I suggested that if he did not trust himself he should stay with the group, "because there are no signposts out here." To increment the methods of education in keeping with validated benefits to students is sound. "Hickory stick 'rithmetic" has gone by the wayside with good reason, but forming habits that guide "doing it right" is a good practice in all areas, not only for violin soloists.

Well, I ramble, but for me any effort to create an arena in which all concerned persons fit and endeavor to be the best they can be is quite complicated.

Happy Trails, Len

Je pence qu'il y a une grandes différences entre la physique mathématiques et les math, où les maths sont des outils utilisés dans la physique comme les langues, par contre la physique mathématiques est une description mathématiques pour les phénomènes naturels, c'est a dire ces une autre représentation discret des phénomènes par des équations ( ces variables c'est des être naturels comme le temps, distance, énergie massa...), des ça aide à bien maîtriser et comprendre ces phénomènes. Bien sûr pour un physiciens il devrait maîtriser les math pour qu'ils puissent expliquer ces phénomènes et mieux comprendre la nature

Howdy Salim Benaiche,

Your insight is clear and important. Your separation of math from the collection of descriptions of nature called mathematical physics is very good. That insight has enhanced a sense of value in comprehending nature as described by mathematical physics. That sense of value supports Philippos Afxentiou's hope that future physicist training will include nature awareness along with "you learn physics by solving numerical problems involving calculations in specific situations." Wisdom matters in science, too.

Happy Trails, Len

P.S. Fortunately, one-language persons like myself have online translations available. I am happy I did not miss out on your insight. lfh

السلام عليكم ورحمة الله وبركاته: من وجهة نظري المتواضعة ان الفيزياء الرياضية مهما فعلاً في المجال الرياضي ويعود السبب في ذلك هو ان اي حركة تحدث تكون من متأثرة بالمتغيرات الفيزيائية وخصوصاً الزوايا وبما ان علم اليايو ميكانيك يدرس تلك الظاهرة للحصول على الحركات المثالية من خلال ضبط الزوايا حسب الحركات الصحيصة والتي تخدم الانجاز

For theoretical physics, mathematics plays key role.

The question is "Should mathematical physics be the main emphasis in master/Ph. D physics curricula?"

The answer depends on what your goals are. Anyone that intends to study physics will need to learn some math. But the amount of math is what distinguishes "physics" from "mathematical physics". If your goal is to work on the problem of merging quantum mechanics with general relativity, you will need a lot of really fancy math. But it is possible to be happy with the study of physics without participating in the solution of that problem. A lot of people have a Ph.D in physics, not mathematical physics, and still have happy lives.

You can also change your goals later after graduating. Most knowledge accumulated during a career comes after graduation from school, so if your goals change and your schooling was not adequate preparation for your new goals, no big deal.

In general physics is the science that observe a phenomenon, gives it a name and describes its properties. And because we can only observe phenomena – humans are phenomena too – we actually describe the mutual relations between the phenomena. The relations are expressed with the help of measurement units (SI system) so we don’t have to compare multiple phenomena to get an answer. We just use the units as a “measuring interface” between all the distinguishable phenomena.

Now where is the math?

When I was young engineers had books full of formulas. To calculate steam turbines, electric motors, mechanical constructions made of concrete, steel, wood, etc., etc. Nobody said that these formulas are mathematical formulas. Because we only need arithmetic to calculate the mutual relations, not math. Math is something else.

So what is math? The problem is that nobody knows the real answer. The ancient Greek philosophers had the opinion that our universe is a mathematical existence. That means that the primary properties of our universe are dynamical geometrical properties. An idea that shows some similarity with the general concept in modern Quantum Field Theory (there are no particles, there are only fields). Unfortunately, in physics we can only determine the mutual relations between the phenomena, we don’t know “what’s inside”. So the ancient Greek philosophers may be right, but modern physics is still too limited to make statements about the subject that are convincing. And more worse, in mathematics there is also the search for the unifying theory… For example, probability theory has no mathematical foundation, it is an empirical theory.

Studying theoretical physics has not much to do with pure math itself, in physics we use math as "arithmetic" tools. However, in pure mathematical physics the situation is different. Mathematical physics use mathematical models to “simulate” physical reality. In other words, they build up physical reality “from scratch” and the model is constructed with the help of “facts” that originate from physics, mathematics and philosophy. Because before we can construct a model we have to create some kind of a conceptual framework.

An example… There is a nice video about mathematical physics, the Causal Dynamical Triangulations approach (https://www.youtube.com/watch?v=PRyo_ee2r0U). They use the Planck units and Einstein’s curved spacetime (therefore the math is directly related with the Ricci scalar curvature in Riemannian geometry because they have to implement the universal scalar field, the Higgs field, in the model). So if this is the way you want to do physics, try to become a mathematician too.

With kind regards, Sydney