- #1

- 135

- 0

Is mathematics discovered or created?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter opticaltempest
- Start date

- #1

- 135

- 0

Is mathematics discovered or created?

- #2

AKG

Science Advisor

Homework Helper

- 2,565

- 4

- #3

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

Someone should move this thread to philosophy where it belongs.

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 965

I'll also answer: "Both!"

Mathematical theorems are

- #5

selfAdjoint

Staff Emeritus

Gold Member

Dearly Missed

- 6,852

- 10

HallsofIvy said:Mathematical theorems are created when we choose the axioms for the mathematical system. Of course, what statements are theorems (are provable in that system) is not immediately obvious ("emergent properties" is a good phrase to use here). We "discover" the theorems when we prove them.

But surely if anything is freely created, it's the proofs. Granted Erdos had the Platonic ideal of the

We seem to "find" the theorems in our heads as potential truths and then prove them by creating chains of logically interrelated statements.

- #6

- 23

- 0

opticaltempest said:Is mathematics discovered or created?

I'm currently in a process which involves both. Experiences in research lead to discovery of results which are real. This is then driving me to create an abstract description out of whatever i can find that initially feels right. The creative process is vital, and for me this involves self teaching a very steep hill. Things are going well, perhaps in spite of the fact i am not allowed to post how my ideas are developing here.

Getting stuff right, tried and tested can come later. What arises without the intial creativity ?

- #7

matt grime

Science Advisor

Homework Helper

- 9,420

- 4

You are allowed to post if you observe some conventions such as if you use a phrase you define what it means if it is not alread known, and do not use extant words to mean different things without explaining what the new meaning is. I doubt that your posting or not posting here has any bearing on anyone's research. This however is not the place for that discussion. There is a forum feedback section that might be more appropriate.

Now, onto philosophy: but does your 'abstract' model actually exist in any platonic sense? Arguably what you have discovered isn't maths. It might be mathematical, it might use mathematics, but that does not make it mathematics but an application of mathematics.

Now, onto philosophy: but does your 'abstract' model actually exist in any platonic sense? Arguably what you have discovered isn't maths. It might be mathematical, it might use mathematics, but that does not make it mathematics but an application of mathematics.

Last edited:

- #8

honestrosewater

Gold Member

- 2,132

- 5

That reminds me of a quote I liked.selfAdjoint said:We seem to "find" the theorems in our heads as potential truths and then prove them by creating chains of logically interrelated statements.

(Also spelledKarl Kerenyi began his 1976 English language translation of Dionysus with this passage:

"The interdependence of thought and speech makes it clear that languages are not so much a means of expressing truth that has already been established as means of discovering truth that was previously unknown. Their diversity is a diversity not of sounds and signs but of ways of looking at the world."

(http://en.wikipedia.org/wiki/Sapir-Whorf_hypothesis) [Broken]

Last edited by a moderator:

Share: