Theory vs Theorem: Understand the Difference

  • Context: High School 
  • Thread starter Thread starter Physics is Phun
  • Start date Start date
  • Tags Tags
    Theorem Theory
Click For Summary

Discussion Overview

The discussion revolves around the distinctions between "theory" and "theorem," particularly in the contexts of mathematics and physics. Participants explore definitions, implications, and naming conventions associated with these terms.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that "theory" refers to concepts in the physical world, while "theorem" pertains to the mathematical realm.
  • One participant defines a theorem as a mathematically provable statement and suggests that a theory in mathematics consists of a collection of related theorems and definitions.
  • A question is raised about the terminology in physics, specifically why some theorems are referred to as laws, while similar naming conventions do not appear to exist in mathematics.
  • Another participant counters that there are indeed laws in mathematics, such as the law of excluded middle and the law of large numbers, and notes that naming conventions are not fixed, as what one person considers a lemma might be viewed as a theorem by another.
  • It is suggested that statements beginning with "if...then..." should be classified as propositions.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the definitions and implications of "theory" and "theorem," as well as the naming conventions in mathematics and physics. No consensus is reached.

Contextual Notes

Participants express varying interpretations of the terms and their applications, highlighting the lack of universally accepted definitions and the subjective nature of naming conventions in both fields.

Physics is Phun
Messages
100
Reaction score
0
What's the difference?
 
Mathematics news on Phys.org
"Theory" usually refers to the physical world and "theorem" refers to the mathematical world.
 
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.
 
this is sort of related, but why are some theorems in physics called laws? why arent there "laws" in math too?
 
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).
 

Similar threads

High School Understanding the Pythagorean Theorem
  • · Replies 38 ·
2
Replies
38
Views
5K
High School I've been trying to understand the proof for the binomial theorem
  • · Replies 6 ·
Replies
6
Views
2K
Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
10K
High School Is this a new theorem?
  • · Replies 9 ·
Replies
9
Views
2K
High School New solutions to old, historic problems
  • · Replies 2 ·
Replies
2
Views
3K
High School What geometry theorem is used in this figure?
  • · Replies 38 ·
2
Replies
38
Views
4K
High School A question about a YouTube video on Thales's Theorem
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Clarification of Mihăilescu's Theorem (Catalan's Conjecture)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why certain topics in elementary number theory?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Why certain topics in elementary number theory?
  • · Replies 2 ·
Replies
2
Views
2K