Is math based on observations?

  • Thread starter Thread starter EL
  • Start date Start date
Click For Summary
Mathematics is fundamentally based on axioms, which are self-evident truths chosen independently of empirical observations. While the application of mathematics to the real world is informed by observation, the mathematical concepts themselves exist independently of it. The discussion highlights that axioms can be selected based on the desired outcomes in mathematical reasoning, rather than being dictated by the physical world. Logic, as a framework for mathematics, is also constructed from human intuition and reasoning, which are shaped by our experiences. Ultimately, mathematics transcends mere observation, functioning as a system of thought that can describe and analyze reality without being directly derived from it.
  • #31
So, when you say Euclidean mathematics, you just mean mathematics.
 
Mathematics news on Phys.org
  • #32
Matt: Is this is a question that you ask me, or what ?
 
  • #33
The very fact that the totality of our sense experience is such that by means of thinking ... it can be put in order, this fact is one which leaves us in awe, but which we shall never understand. One may say "the eternal mystery of the world is its comprehensibility". Immanual Kant

"The miracle of appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Wigner

"At this point an enigma presents itself which in all
ages has agitated inquiring minds. How can it be that
mathematics, being after all a product of human thought
which is independent of experience, is so admirably
appropriate to the objects of reality? Is human reason,
then, without experience, merely by taking thought, able
to fathom the properties of real things?

In my opinion the answer to this question is breifly
this: As far as the laws of mathematics refer to
reality, they are not certain; and as far as they
are certain, they do not refer to reality."
Address to the Prussian Academy of Science 1921, Dr. Einstein
 
Last edited:

Similar threads

High School Questions about mathematics as a deductive system
  • · Replies 8 ·
Replies
8
Views
2K
MHB -c6. Find the GCF and the LCF of A and B.
  • · Replies 1 ·
Replies
1
Views
1K
High School Is everything in math either an axiom or a theorem?
  • · Replies 72 ·
3
Replies
72
Views
8K
High School Confused about ciphers in the book 'Arithmetic for the Practical Man'
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad How did Euclid go about forming his propositions?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad How Often is First-Order and Modal Logic Used in Math?
  • · Replies 8 ·
Replies
8
Views
2K
High School The Paradox of 1 – 1 + 1 – 1 + 1 – 1 + …
  • · Replies 5 ·
Replies
5
Views
2K
High School Uncomputable Numbers and Rational Approximations
  • · Replies 4 ·
Replies
4
Views
2K
MHB Graph of $y=\sin{x}-2$ on the domain $[0,2\pi]$
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad A Heuristic View of QM: Axioms & Gleason's Theorem
  • · Replies 15 ·
Replies
15
Views
3K