I was good at mathematics in high school , I can make and understand proofs , and if there is something wrong in proof I can recognise it but all of this without knowing what is the real reason , I just see that "this makes sense" .. For example no one explained to me What "assumption" or "definition" means I have seen it several times so I understood it .. the thing is I'm confused is the way I'm dealing with mathematics correct? Does this have something to do with philosophy? And if so should I start learning philosophy of mathematics before learning basic mathematic topic like calculus ?
2026-03-30 10:37:44.1774867064
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Is dealing with mathematics without understanding philosophy behind it good aproach?
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"[S]hould I start learning philosophy of mathematics before learning basic mathematic topic like calculus?" No -- and I say this as a one-time philosophy don! If anything it is the other way around: to understand serious work on the philosophy of mathematics you already need to understand something of the mathematics which is being philosophised about.
However ...
Maybe by "philosophy" you don't so much mean philosophy as conceptual understanding. And yes, it is hugely important in getting into an area of mathematics to understand why various basics concepts of the area are defined as they are. Why, for just one example, is a topology defined as it is? As @PrimeMover remarks, knowing the history behind a mathematical idea can be conceptually illuminating in this way. An explicitly historical approach isn't the only one: but still, decent textbooks should indeed aim to engender conceptual understanding, to make it clear why the definitions of key notions aren't arbitrarily pulled out the air, etc.
Good question.
In my opinion, it greatly enhances the whole mathematical experience to find out the history behind (and hence the reason for) the development of a mathematical idea (so as to find out, for example, what the motivation behind it was).
If nothing else, it enhances the understanding.
Many good text books include some of the historical notes behind the development. As an example of this, the textbooks of George Finlay Simmons are among the best.