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What is mathematics? I like to think of mathematics as the language in which nature speaks... What is mathematics to you?
so could the definition of mathematics be based on personal perspective of it? i see math as a description of our world around us, in the geometric sense, as basic geometry comes super easy to me...i suppose i can see why people call it a language-a universal one, but to me, language is a man made structure of communication rather...Originally posted by selfAdjoint
Sasha, in grad school I discovered that different mathematicians have different talents. It appears that the algebraic talent, doing things with abstract counters in your head, is more widely distributed than the geometric one, manipulating pictures in your head.
By which I don't mean that either algebra or geometry is those simple qualities, but that those talents are what you need to succeed in algebric or geometrical fields.
Well I see mathematics as a human enterprise, more or less inseparable from its sociology, like political science. A platonist would say the math is "out there" somewhere, but I think it exists in people's heads.Originally posted by sascha
By language I mean its very principle: being a structure of several signs, interrelated according to a basic idea (axiom, choice, desire, principle, etc.) -- as opposed to the very principle of thinking, which is to integrate and find the common basis of diversities. These two principles are not man-made; only this or that language, and this or that thought, are man-made.
Sure, a talent for this or that is not distributed evenly. But here we are seeking, if I understand this thread correctly, the systematic reason and structure of math, not some contingent aspects. Or not?
I like to think of it as the study of abstraction, but the notions are essentially the same.Originally posted by selfAdjoint
Mathematics is the study of patterns. This is a recursive study because the relationship of two patterns itself makes a pattern.
i looked at the definition of the word language on dictionary.com and mathematics seems to be a language.mathematics is a language -- in contrast to others a thoroughly formalized one
what this language describes is another question.... sometimes people find out correlations with the external world only very much later than the formulation
what do you mean by contiuous?There I say "Geometry has been engulfed by algebraic analysis", which corresponds to what you tell me about the projective geometry you are familiar with. This is just my point: the universality of the subject matter (as possible in a purely qualitative approach, thinking in geometrical way of thinking, in continuous terms) has been lost by subjecting it to the gesture of algebraization, thinking in discontinuous terms. This is the fashion nowadays, and mathematicians have not yet grasped what they have lost.