Theory vs Theorem: Understand the Difference

In summary, the conversation discusses the difference between the terms "theory" and "theorem" in the context of mathematics. The main distinction is that a theorem is a mathematically provable statement, while a theory is a collection of related theorems and definitions. It is also mentioned that some theorems in physics are referred to as laws or principles, and there is no set naming convention for mathematical concepts.
  • #1
Physics is Phun
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What's the difference?
 
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  • #2
"Theory" usually refers to the physical world and "theorem" refers to the mathematical world.
 
  • #3
A theorem is a mathematically provable statement.

A theory in mathematics is usually thought to be a non-trivial collection of related theorems and definitions like, the theory of calculus, theory of groups, etc.
 
  • #4
this is sort of related, but why are some theorems in physics called laws? why arent there "laws" in math too?
 
  • #5
There are. Law of excluded middle, for instance. Law of large numbers. They are also called principles. There is no immutable naming law, or principle or theorem. One man's lemma is another mans theorem. For instance's Schur's Lemma is a vital theorem, but Mackey's Theorem is just a lemma... (though things starting if...then... ought to be called propositions).
 

FAQ: Theory vs Theorem: Understand the Difference

What is the difference between a theory and a theorem?

A theory is an explanation of a natural phenomenon that is supported by a large body of evidence. It is a well-tested and widely accepted explanation for a specific aspect of the natural world. A theorem, on the other hand, is a statement that has been proven to be true using logic and mathematical rules. It is a generalization or conclusion that has been derived from a set of axioms or assumptions.

How are theories and theorems used in science?

Theories and theorems are used in different ways in science. Theories are used to explain and predict natural phenomena, while theorems are used to prove mathematical concepts and principles. Theories can also be used to generate hypotheses and guide further research, while theorems are used to build upon existing knowledge and develop new theories.

Can a theory become a theorem?

No, a theory cannot become a theorem. Theories and theorems serve different purposes and are based on different methods of validation. A theory is based on empirical evidence and can change as new evidence is discovered, while a theorem is based on logical proof and remains true regardless of new evidence.

How are theories and theorems tested and validated?

Theories are tested through experiments and observations, and their validity is continuously evaluated through peer review and replication. Theorems are tested through logical proofs and their validity is evaluated by other mathematicians. Both theories and theorems can be revised or disproved if new evidence or logical inconsistencies are found.

Are theories and theorems equally important in science?

Yes, both theories and theorems play important roles in the advancement of science. Theories help us understand the natural world and make predictions, while theorems provide a solid foundation for mathematical principles and allow for the development of new theories. Without either, scientific progress would be limited.

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