[coldtea]

>I am a mathematician. Nature is of no consideration whatsoever in some fields of maths.

It's not about actual nature (the universe etc) being into consideration.

It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process.

So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).

[mbeex]

The controversy between assuming a point of view of "creating" vs "discovering" things is as old as mathematics.

> rather than a simple constructive process.

This requires some more distinction. 'constructive' can mean very different things. Some non-intuitionists would consider their counterparts definition of 'constructive' as possibly OK, but simple - and held other cases still for construction. Anecdotally, Ramanujan received his results as an inspiration from his household deity. Thinking about it probably brings up 5 different opinions among two people.

[mkl]

Yes, that's what my comment says (but maybe you read it before I edited it to be clearer):

>> Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "discovered", for example.

[coldtea]

Yes, that.

Though I wouldn't necessarily consider it "muddying the waters", but taking another criterium as important in the distinction of physics-like or not.

Namely, not whether it concerns the study of the material universe, but whether it involves experimentation/discovery of in place structures, and other such physics-like processes (which they think it does).

[nobodyandproud]

This is muddying the waters though, though I think you’re in good company.

I’m not sure if mathematics belongs in the sciences or art; it really has hallmarks of both.

It a modeling language that can be used to describe the universe. You don’t have science today, without the math.

Yet some of the proofs and mental exercises in pure math are almost divine; inspired in a way that resonates like a beautiful work of music.

[coldtea]

>This is muddying the waters though

In a way, yes, as it extends the casual/conventional understanding of the term. I'm just saying it's not done to intentionally muddy the waters, but to introduce an alternative understanding.

So, yeah, we agree!