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I read this article which is on how Feynman thought of the difference between physics and mathematics.

Feynman's point is that physics is to understand nature while mathematics is to make their own world. But I'm quite confused with the word 'understanding'.

This answer points out that physics is not to identify the truth. I can connect with this statement. Physics is inductive research as such we don't have any given principle. We just make some artificial principles from observations for our convenience. And we will never know if the principles are the truth behind nature. Nature would not tell us the correct set of principles.

Therefore, we will never understand the nature. At best, we will only pretend to understand nature. What we actually understand is our own artificial theories, not nature. Physicist chooses its own set of axioms and researches the theorems which are allowed by axioms. In this sense, is physics any different from mathematics?

And coming back to the 'understanding', what do we mean when we say 'I understand the nature'? Is that understanding any different from the mathematician understanding his theorem?

Qmechanic
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hbadger19042
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    Maybe we should interpret "understand" simply as refering to something like "being able to predict/apply"? Because what physicists do is to figure out the mechanisms and phenomena of this world. Not the fundamental whys (although they try), but the hows. So that those mechanisms can be utilized by engineers, designers, constructors etc. to create, invent and make. And for this, our understanding is very good in many fields, which is exemplified simply by your smartphone working and your car moving. – Steeven Jul 14 '20 at 09:35
  • Physicists have the strange capacity of working with inconsistent theories, and still being able to predict stuff. Something that mathematicians rarely do –  Jul 14 '20 at 19:08

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For me, physics meaning of "understanding" is related to link several different perceptions, or even different explanations in a bigger frame.

For example, from the changes of location of the sunrise, duration of the day, and different seasons to the understanding of the inclination of the earth axis with the plane of orbit around the sun.

It is different of many empirical formulas or tables used in engineering, that are made to be followed at specific situations, and doesn't have the intention of understanding the situation.

For mathematics, I think it is more linked to the physical world than sometimes we imagine. I like the quote: mathematics is the part of physics where the experiments are cheap.

Claudio Saspinski
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