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Axiomatic Theories [duplicate]

In Number Theory and other areas of Pure Mathematics, whatever theorems we have are there forever because they are derived logically from a set of axioms. I would like to know which theories in ...
Rajaram Venkataramani's user avatar
88 votes
11 answers

Why must a physical theory be mathematically self-consistent?

I always read in modern physics textbooks and articles about the need for physical theories to be mathematically self-consistent, which implies that the theories must not produce contradictions or ...
Maxis Jaisi's user avatar
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122 votes
4 answers

The Role of Rigor [closed]

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
Gil Kalai's user avatar
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35 votes
18 answers

Can a mathematical proof replace experimentation?

I know that this is very similar to How important is mathematical proof in physics? as well as Is physics rigorous in the mathematical sense? and The Role of Rigor. However, none of the answers to ...
Aspiring Mad scientist's user avatar
7 votes
2 answers

How important is mathematical proof in physics?

How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
Richardbernstein's user avatar
8 votes
4 answers

Final theory in Physics: a mathematical existence proof?

Some time ago, I read something like this about the issue of "a final theory" in Physics: "Concerning the physical laws, we have several positions as scientists There are no ...
riemannium's user avatar
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2 votes
4 answers

What is fundamentally physically impossible?

Mathematical logic defines quite clearly what is true or false in math, and also that some theorems are impossible to prove. This resulted in some clear definitions of axioms set like Peano, ZF or ZFC,...
Dr. Goulu's user avatar
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4 votes
4 answers

How do I convince my students the Newton's first Law is the way it is?

Every time I teach this law, there are always a few students asking me why a net force is zero on a system moving at a constant velocity. This group of students takes physics for the 1st time. It is ...
TBS500's user avatar
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2 votes
4 answers

What is the difference between a physical theory and mathematical theory?

Is there same approach in physical theories like primitive notions,axioms and theorems as in maths ? If it is then is it an only method or approach to study different fields of knowledge?
Remy's user avatar
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6 votes
3 answers

Can we construct Axiomatic system of physical laws?

If we construct axiomatic system of physical laws that are independent one another as in axioms in mathematics, what should they be? Can there be such a finite system of physical laws that can explain ...
Henry's user avatar
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0 votes
1 answer

Has anyone ever created a formal system for quantum mechanics? [duplicate]

I've heard that quantum mechanics is really hard to teach people how to fully understand. Maybe there are some statements that some people seem to be able to prove are true according to a certain ...
Timothy's user avatar
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What generates physical meaning in mathematical quantum theory?

Let mathematical quantum theories be theories of Hilbert-space rays together with probability / amplitude / unitary evolution / Hermitian operator machineries. Observations essentially correspond to ...
Nobody-Knows-I-am-a-Dog's user avatar