Stephen Wolfram - Is Mathematics Invented or Discovered?

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Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music?

[@theraven6836]

I’m still confused, but at a much higher level.

[@danielgiegerz1251]

Von Neumans article, "Danger Signals" is a nice explanation of how abstraction, that useful in math, is rooted in empirical thinking. Abstract ideas, are based on abstract models, which in turn come from the empirical organization of information. That is to say, those who believe in circles, owe it to the moon.

[@irisbunky]

My new favorite phrase: "possible mathematicses"

[@camilogallardo4338]

you can tell a video is old when you see fermat still remained unsolved then

[@longcastle4863]

A superb discussion on this topic. One of the best I've heard, and for me it contained some ideas I never considered before -- like, for example, that one of the reasons we see mathematics as soon good at describing the natural world, is because we tend to use it on just those kinds of questions it is ideally suited to answering. Very thought provoking.

[@ZiiiP2142]

A dubious sounding channel that actually has amazing content.

[@patrickhickman3832]

I find unsolvibility in most mathematics

[@rclrd1]

Physics is mathematical not because we know so much about the physical world, but because we know so little. It is only its mathematical aspects that we can discover.

[@gmshadowtraders]

My gosh, what a heavyweight this guy Stephen Wolfram is. Robert Lawrence let him speak for 5 minutes straight without interrupting.

[@GregBechtel88]

See, I think there's some equivocation going on here. Kuhn asks Wolfram whether the other systems of mathematics are self-contradictory and therefore unused and Wolfram answers no, they are self consistent and valid and their disuse is a just a consequence of the contingency of history. Kuhn should have asked, "but what is self-consistency, or validity without reference to our supposedly contingent mathematics?" That question would bring Wolfram back to Kuhn's original. The set of possible mathematics cannot in itself be fundamental if we can say things of them like they are possible, they are a set, they are valid and etc. Our math is the historically contingent instantiation of one self-consistent system out of the set of all possible self consistent systems, but self-consistency, validity, all those attributes which the set of all possible mathematical systems share and by which they count as such systems must be more fundamental and it's these fundamentals that may be necessary and eternal.

[@kafiruddinmulhiddeen2386]

This was totally clear to me. Very insightful, yet simple.

[@QMPhilosophe]

Excellent conversation!

[@louw49]

Brilliant thinker. Wish I had such a mind as my teacher when I was a young student of mathematics.

[@pacg1]

It was a great pleasure to use that incredible set of tools developed by Wolfram Research ("Mathematica") in my undergraduate years as a student of Comp. Science, there in the nineties. I was writing some pieces of code in several programming styles for diverse areas, as Bayesian Calculus, Neural Networks, and things related. Even using those early CLI-based versions which I started with, previous to the first GUI ones, it was a very good intellectual and learning experience. Thanks to Mr. Stephen Wolfram for doing it possible (and obviously, my teachers! :) God bless him.

[@jwbflyer]

Excellent. One of my favorite interviews. Sold thoughts from Stephen Wolfram

[@CloserToTruthTV]

Thanks for the note. We lightened the video in KZbin for now, and will look into reposting a better version soon.

[@theodorewinston3891]

Holy crap! that was that a clear and concise description of the "landscape"/"space" of this discussion and a putting-into-context of many of the key arguments that have been brought up in it, like Hilbert's "unreasonable effectiveness of mathematics". I definitely think it's worthwhile to have a formalised meta-discussion of mathematics (in case the usefulness of a "philosophy of mathematics" was ever doubted), to sort out trivial or naive responses to the question from more sophisticated ones. Way to go Prof. Dr. Wolfram! Exciting to think of future research into "possible other maths" and how they might impact society and as a consequence human consciousness.

[@amert1265]

That was mindblowingly amazing, thank u for explaining it so well!!!!

[@imranq9241]

The idea of computational irreducibility is an interesting one.. sort of like conservation of energy . Getting to equivalent statements from different axioms is equally difficult.

[@MMrandomdude12]

It's interesting how he uses the idea of "the space of all mathematics's", in so doing using the notion of an abstract space, which comes from human mathematics. Presumably there are completely equivalent ways to describe this idea in all the other possible mathematics's. Does this not hint at the idea that there is some kind of universality across all the mathematics's? For example, what reason would there be for an alien race, with a totally different mathematics to our own, to not be able to consider the idea of other mathematics's (or the "space of all mathematics's"), in whatever way that their version of mathematics dictates?