Can Pure Math Experience a Paradigm Shift Without Experimental Validation?

[Organic]

Hi,

A Paradigm Shift happens in physics mostly when fundamental concepts of some system are deeply changed by a new theory and/or new experimental results that supporting and/or triggering a new theory for enough long time.

Pure Mathematics has no experimental side like physics, therefore a Paradigm shift depends
on deep changes of our understanding fundamental concepts like: definition, logic, axiom, number, set, operation, limit, function, infinity and so on.

My question is this, because there are no experiments that determine the validity of some theory, what kind of tests can some new theory has to “pass” until a paradigm shift really happens in Pure Math?

Another question on the same subject:

What do you think is the “nature” of a paradigm shift in a pure theoretical system?

Thank you,

Organic

 

[Stevo]

Revolutionary views on the philosophy of mathematics inevitably involve a novel perspective on the ontology of maths, the formalism of maths, and the epistemology of maths. These are the three major issues of mathematics.

 

[marcus]

Hi,

A Paradigm Shift happens in physics mostly when fundamental concepts of some system are deeply changed by a new theory and/or new experimental results that supporting and/or triggering a new theory for enough long time.
...

Here is a great page about Thomas Kuhn ("The Structure of Scientific Revolutions", 1962) and his ideas

http://www.emory.edu/EDUCATION/mfp/Kuhnsnap.html

 

[Organic]

Dear marcus,

I really want to know what do you think about a paradigm shift in pure mathematics?

 

[Organic]

Hi Stevo,

Revolutionary views on the philosophy of mathematics inevitably involve a novel perspective on the ontology of maths, the formalism of maths, and the epistemology of maths. These are the three major issues of mathematics.

Can you give an example of this novel perspective?

 

[Hurkyl]

My question is this, because there are no experiments that determine the validity of some theory, what kind of tests can some new theory has to ?pass? until a paradigm shift really happens in Pure Math?

Usefulness.

 

[Rader]

"creative thinking"

Creative thoughts lead to a "Paradigm Shift" The mathematics come later. Is not mathematics proofs of what is already known.

 

[Organic]

Hi Hurkyl,

Usefulness.

And what if a paradigm shift in some language (and Math is first of all a form of language) includes in it the meaning of "Usefulness"?

 

[Organic]

Rader,

Creative thoughts lead to a "Paradigm Shift" The mathematics come later.

Do you mean that a paradigm shift starting (in some sence) out of what is called mathematical system?

 

[Stevo]

Hi Stevo,

Can you give an example of this novel perspective?

Bourbaki are one of the most infamous.

 

[matt grime]

And the modern trend away from Bourbaki, too, mainly coming from the pedagogical influence in the last 30 years. (The let 2=n school.)

 

[Rader]

Rader,

Do you mean that a paradigm shift starting (in some sence) out of what is called mathematical system?

If all knowledge was in essence, mathematics, the answer would be yes. Although mathematical proofs exits, of things we are not sure exist, are they anything more than creativity? If all knowledge was in essece "Reality" mathematics would be a subset of it. Creativity seems to be a sign of genius, at least, that is what I have learned from history. Thats why I posted what I did. Creativity would be a tapping of that database, to change the paradigm, mathematics would be one of its finer tools.

That is the way I see it to be, mine being a world view of a non-mathematician.

 

[Stephen Mooney]

The paradigm shift in physics has already occurred, see http://paradigm.blogharbor.com

Mathematics was not capable of representing the true quantitative nature of the process of the Universe.

This new physics paradigm, through symmetry across the sub-atomic/atomic and biology domains, integrates science.

Stephen Mooney