Is mathematics discovered or created?

[opticaltempest]

Is mathematics discovered or created?

 

[AKG]

I wonder how many threads have the exact same title. Seeing as there are so many threads on this topic, you should either just search those old posts, or try to say something interesting about it here.

 

[matt grime]

Someone should move this thread to philosophy where it belongs.

 

[HallsofIvy]

I'm moving it to philosophy of science and mathematics.


I'll also answer: "Both!"

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.

 

[selfAdjoint]

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 Book of maximally elegant proofs, but that was an ideal not a present resource for mathematicians.

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

 

[sprinklehopper]

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 ?

 

[matt grime]

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.

 

[honestrosewater]

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

That reminds me of a quote I liked.

Karl 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)

(Also spelled Carl Kerenyi.)