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>> Algebraic and topological structures seem to manifest themselves readily within nature. I should think infinities provide greater concern. So basically what
by smnplk 9y ago
>> Algebraic and topological structures seem to manifest themselves readily within nature. I should think infinities provide greater concern.
So basically what you are saying is that, we can't be so certain that we humans invented math. Math is there, structures were there to be discovered ? Why is there such a thing as monster group ? We named those things, but if we didn't exists, it would still be there in the abstract world ? This is what is bugging me lately, I can't decide if math was invented or not. Some parts may be invented, but some parts may be discovered.
- jansho 9y agoI recommend Ian Stewart's Letters to a Young Mathematician. He addresses your question (Platonism vs formalism) pretty succinctly, in my opinion as a noob. Accordingly "the working philosophy of most mathematicians is a mostly unexamined Platonist-Formalist hybrid ... Math is a product of human minds but not bendable to human will. Exploring it is like exploring a new tract of country ... but the mathematical countryside does not come into existence until you explore it."
- _0ffh 9y agoI like to think that all theses things are already there as implied (by the chosen axioms) but unrealized potential, and then are made explicit by the act of exploring that potential (from a chosen point of view/using a chosen formalism).