Stephen Wolfram - Is Mathematics Invented or Discovered

I make my living building this thing called Mathematica which attempts to cover the in the broadest possible sense the kinds of things that mathematics might encompass but so a question that I'd been interested in also from the point of view of basic science is is the mathematics that we sort of practice today the only possible mathematics or is it a mathematics that is sort of a great artifact of our civilization but sort of a historical accident artifact the conclusion that I've Surrey sounding Lee come to is that the mathematics that we have today is in fact really a historical artifact now that's not historically in the tradition of mathematics itself that's not what people have tended to conclude they've tended to think that mathematics is sort of the most general possible formal abstract system if you look at the history of mathematics that's certainly not how it originally started out I mean in ancient Babylon you know there was arithmetic for commerce and other things and there was geometry for land surveying and you know what what I think has really been the history of mathematics is the progressive generalization of arithmetic and geometry plus one key methodological idea that one can make theorems and abstract proofs of those theorems one can ask the question if one just sort of arbitrarily looks at formal systems will they tend to have the character of mathematics as we know it today will they tend to have the feature that most of the things one asks about one can successfully prove theorems about I think in both cases the answer is no not really so for example one thing one can do is to kind of ultimately deconstruct mathematics if one looks at you know there are maybe three million papers that have been published about mathematics okay and these are all based on a certain set of axioms the axioms are what you grow mathematics from the axioms are quite simple our particular mathematics is the particular set of axioms you can write down on these couple of pages but there's a whole universe of possible mathematics is out there what are they like first question might be where does our particular mathematics lie in this universe of possible mathematics is is it possible a thematic so number one is it possible mathematics number ten is a possible mathematics number a quintillion where does it lie the answer is the exactly how you enumerate the space but roughly it's about the 50,000th possible axiom system so right there sort of in the universe of possible axiom systems the universe of possible mathematics says there's logic if the aliens delivered you know a different possible mathematics you know I don't think we would be able to immediately say that's not a reasonable valid mathematics it would be self-consistent even though it would be radically different yes now what's happened in the history of mathematics is that most things people have been interested in have ended up being eventually solvable though sometimes with with effort and centuries of work and so on but one of the things that I suspect is that that's actually not really the way that is the true the true reality to mathematics that really if we were to just sort of ask mathematical questions arbitrarily that the vast majority of them would end up turning out to be unsolvable and in fact that unsolvable ax T is actually very close at hand in mathematics we just don't see it because the particular way that mathematics has progressed historically has tended to avoid it now you might say but mathematics is a good model of the natural world and mathematics has been sort of driven by modeling the natural world I think there was kind of a circular argument because what's happened is that those things which have been successfully addressed in science and studying the natural world are just those things that methods like mathematics have successfully allowed us to address so I think one of the exciting things that that one realizes is that human mathematics has is it's one of the great artifacts of our civilization it's one of the sort of perfect wonderful things that's been produced by a huge amount of human effort but it's an artifact but it's an artifact and there is much more out there in the sort of space of all possible mathematics is and I think in the future we will see an increasing kind of realization and an increasing ability to explore all that all that other universe of mathematics is and it will be profoundly important not only for mathematics but for our science and for our technology

Channel: Closer To Truth

Views: 49,410

Keywords: Stephen Wolfram, Closer To Truth, Mathematics, Reality, Philosophy, Physics, Cosmology

Id: nUCwtLTUPQ4

Length: 4min 17sec (257 seconds)

Published: Mon Feb 22 2016