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
SUMMARY

The discussion clarifies the distinction between "theory" and "theorem," emphasizing that a theory encompasses a collection of related theorems and definitions, such as the theory of calculus or the theory of groups. The term "theorem" specifically refers to mathematically provable statements. Furthermore, the conversation highlights the existence of laws in mathematics, such as the Law of Excluded Middle and the Law of Large Numbers, which are also referred to as principles. The naming conventions in mathematics are subjective, as illustrated by the differing significance of Schur's Lemma and Mackey's Theorem.

PREREQUISITES
  • Understanding of mathematical terminology, including "theory," "theorem," and "lemma."
  • Familiarity with basic mathematical concepts such as calculus and group theory.
  • Knowledge of logical principles, including the Law of Excluded Middle.
  • Awareness of the subjective nature of mathematical nomenclature.
NEXT STEPS
  • Research the foundational concepts of the theory of calculus.
  • Explore the principles of group theory and its applications.
  • Study the Law of Large Numbers and its implications in probability theory.
  • Investigate the significance of various mathematical lemmas and theorems in advanced mathematics.
USEFUL FOR

Mathematicians, educators, students in advanced mathematics, and anyone interested in the philosophical aspects of mathematical definitions and nomenclature.

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
Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
8K
High School Is everything in math either an axiom or a theorem?
  • · Replies 72 ·
3
Replies
72
Views
8K
High School I've been trying to understand the proof for the binomial theorem
  • · Replies 6 ·
Replies
6
Views
2K
MHB Is Theorem 5.2 in SET THEORY AND LOGIC True or False?
  • · Replies 2 ·
Replies
2
Views
1K
High School Is this a new theorem?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad What is the name of this geometry theorem?
  • · Replies 4 ·
Replies
4
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