Dear Dr. Amrani: In my opinion, physics without mathematics is empty: instead of testable predictions, it is reduced to fairy tales. This is the problem with many (most? all?) popular physics books: they present a view of physics that is not shared by actual physicists. The root cause is that they try to relate counterintuitive concepts to a lay audience without using the precise language that mathematics offers. (They also tend to hype the more "spectacular" aspects of relativity or quantum theory.)

It is not the fault of physics (or physicists) that Nature has more than a few counterintuitive surprises. That there is no absolute time. That at the fundamental level, elementary systems are described by noncommuting quantities, not numbers. But precisely because these secrets of Nature are so far removed from (and alien to) our everyday experience, the rigor offered by mathematics is absolutely needed.

Yes, it makes it hard (and outdated textbooks or unprepared lecturers don't help either.) Physics is arguably a lot harder today than it was a century ago. But then... also don't forget that physics is what gave birth to numerous mathematical ideas, starting with the very notion of calculus. That's because physics needed the exactness of mathematical language to describe, say, the relationship between position and velocity, even though the mathematics of the time was not yet ready to provide it.

Having said that... I agree with you on one point: sometimes, physicists treat purely mathematical constructs with no testable predictions as reality. Some even have the hubris to suggest that pure thought is sufficient to comprehend nature, and experiments may not even be needed anymore! That is just wrong. The foundation of physics is observation; we must not forget that.

In my personal personal opinion:

Mathematics is the language that can help to simplify our thinking and ideas.

Physics is a beautiful symphony that is based on the uses of mathematics that can show us...how everything works around us.

Dear Dr. Amrani: In my opinion, physics without mathematics is empty: instead of testable predictions, it is reduced to fairy tales. This is the problem with many (most? all?) popular physics books: they present a view of physics that is not shared by actual physicists. The root cause is that they try to relate counterintuitive concepts to a lay audience without using the precise language that mathematics offers. (They also tend to hype the more "spectacular" aspects of relativity or quantum theory.)

It is not the fault of physics (or physicists) that Nature has more than a few counterintuitive surprises. That there is no absolute time. That at the fundamental level, elementary systems are described by noncommuting quantities, not numbers. But precisely because these secrets of Nature are so far removed from (and alien to) our everyday experience, the rigor offered by mathematics is absolutely needed.

Yes, it makes it hard (and outdated textbooks or unprepared lecturers don't help either.) Physics is arguably a lot harder today than it was a century ago. But then... also don't forget that physics is what gave birth to numerous mathematical ideas, starting with the very notion of calculus. That's because physics needed the exactness of mathematical language to describe, say, the relationship between position and velocity, even though the mathematics of the time was not yet ready to provide it.

Having said that... I agree with you on one point: sometimes, physicists treat purely mathematical constructs with no testable predictions as reality. Some even have the hubris to suggest that pure thought is sufficient to comprehend nature, and experiments may not even be needed anymore! That is just wrong. The foundation of physics is observation; we must not forget that.

At then end everyrhing is Mathematics , Physics uses Mathematics .

Its impossible to write Physics without Mathematics .

I think that Mathematics is a language for discussing in Physics.

Ideas are expressed in mathematical language in the field of physics.

So if there is any other LANGUAGE more effective to discuss, which will be an alternative way.

But as I know, there is no other such thing except mathematics, so far.

Yes physics need mathematics

I just wish see more simplified formulas explaining physics all field of physics such as nuclear physics or particle physics. 

You may suggest the simplified formula.

But that may belong to mathematics eventually, because mathematics is logic in itself.

I liked physics more than chemistry, but due to my poor mathematics I studied chemistry

To understand Science anyone should know both Mathematics and Physics.

Naïma Amrani

According to me Mathematics is the language of Physics. To understand Physics correctly Mathematics is the basics need. Without proper understanding of Mathematics it is really very difficult for anyone to understand Physics. To understand Science anyone should know both Mathematics and Physics.

Regards,

Mahamad Nabab Alam

Dear Naïma,

you may wish to have simpler formulas but I guess this will just remain a wish because an equation in physics is describing something. If the mathematical description matches the experimental observation you will have to deal with it the way it is. This means you cannot expect that you just simplify your equation until it gets "easy enough" and still obtain the same correct/acurate results.

There are some cases where you can examine special cases of a more general phenomenon and reduce the complexity of the equation but this has to be done very carefully in order to keep the physics right (an example would be Newtonian mechanics as a simple limit of relativistic mechanics). This will give you pretty good results as long as your velocity is much smaller than the speed of light but as soon as you approach c Newton's simple laws will break down.

The truth is that nature simply does not care if we find the mathematical formulation of the natural laws simple or complicated, they just are as they are. However, we have to keep in mind that each theory in physics has to be testable by experiments - so, a purely mathematical formulation of a problem without any testability is also not really sound, but as long as it's testable, it can be as complicated as it will.

Mathematics is the language of every science - we must understand the nature of the problem and we must be able to handle with the proper mathematical model.

As others have said, physics requires the precision of mathematical tools to be meaningful. Without that precision, what would it be? Vague concepts? Intuition? There would be no substance to the subject, without mathematical rigor.

My feeling on this matter is that to the non-technical layman, engineering curricula appear more like physics than what they would expect from engineering, physics looks more like math, and pure math curricula are quite incomprehensible.

Math is key.

I think almost all "fields" require the precision of mathematical tools to be meaningful, not physics only.

Speech of "what mathematics" are reprehensible.

I want to add to the words of Christian...

It really does not matter where you use math. If its application is not limited to statistical data collection, then you have to deal with a variety of models (not only in physics).

The model (if you look at the definition) is an idealized analogue of an object that reproduces with some accuracy a certain limited set of properties of an object in a certain range of conditions.

This is equally true for the mathematical models. The mathematical model can be many times verified, free of math errors and internally consistent, but its compliance with simulated object is determined only by the correctness of the concept and degree of idealization.