What are your Thoughts on the Philosophy of Mathematics?

V0ODO0CH1LD
How do you think of numbers when you're doing math? I particularly feel like sometimes we get to close to acting like computers. We just scan through a list of symbols and compute another list of symbols that makes sense in a certain context. We hardly ever think of things concretely and how they would apply to real life scenarios. When solving equations we just go through a series of steps and come up with an answer, never thinking of what each of those steps actually imply. I know math is meant to be abstract and all, but what are your views on the subject? Should we even be bothered by this abstraction?

voko
When doing some computations, it is much easier to just compute and not think. That's why we have the numbers and all sorts of a theorems that we could apply to carry out our computations efficiently. Not to mention digital computers which can only compute and never think.

But sometimes it helps when you think about the significance of numbers involved, which is to say you think about their physical meaning. This can help you check that the computation is reasonable, and sometimes it could help you simplify you computation very significantly.

There is no simple answer.

Staff Emeritus
Gold Member
Numbers and computations are a small part of math.

acen_gr
Mathematics is just abstract.

As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality. - Albert Einstein

scout6686
I try to turn what I'm doing into something I can visualize. I often see math expressions and see relationships and proportional groups and such. For me it is idiosyncratic because I like visual more than algebraic.

One of the most interesting math papers/pdf I have ever read is one by Poincare on "intuition and mathematics". He mentions that new math innovations come from creativity and intuitional leaps. He mentions a lot of mathematicians and perceives their mathematical style and perspective. I *really* enjoyed it.

Staff Emeritus