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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?

math is the discovery of the laws that are set in place.

Mathematics is a language tool we have invented that allows us to observe and measure the construct of the universe in a way which we can understand.

Please more people join the debate in the comments!

I'd say both. It's symbiotic.

Where can I get this with english subtitles?

is this the guy that made wolfram alpha?

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.

So it is not a Universal fact that square of the hypotenuse is equal to the sum of the squares of the other two sides?

It is just an artifact, and wouldn't be true if humans didn't invent it? Is this what Wolfram is saying?

So if maths is particular to our history, come up with some goddamned examples that are not!

What I took from this video was that there is a difference between the concept of math and the math that we use as a society. Yes math (when you refer to what we have as a society) is indeed an artifact, HOWEVER Math itself is independent of our perception and existence… therefore can only be discovered and not invented… only the NOTATION and logic behind which is used to describe what little of it we can use and prove through application. Although there are arguments for things beyond this as well I believe that is another topic and it may transcend all possible human comprehension i.e. infinity, 1=2 etc.

This is a move in that direction and I am trying diligently to pursue more information on this subject and it is very difficult. Would appreciate anyone who could shed more light on this topic.

Mathematics is not only consistent with itself, but also with nature. Are other axiomatic systems also consistent with nature? How can they be consistent with nature if they are at the same time contradictory to our mathematics which makes reliable predictions about nature? If they are different from our system, they must necessarily predict different outcomes, but these would have to be wrong. It doesn't make sense to me. Any ideas?

he still failed to convince me that the 'artifact', the mathematics human 'invented' or in his view one possible mathematics isn't just truly a discovery of part of the entirety of mathematics. in a word philosophically(or logically, which as part of maths may be hardly adequate for this topic any more), there's no way to affirm those single pieces of mathematics don't form a unified integral mathematics. and he was also far from convincing me that mathematics is not objective and has its objective existence.

I agree that between mathematics, our physical world and our mind, there's something very deep about it. it may be that in the end of the day, when this ultimate problem is solved (if by any chance it is possible), maths turns out to be something non-objective and be immersed with the ultimate real 'physical law' and become one, but i guess this is way beyond what he said here and so far we have discovered.

ahh my brain

He says our mathematics is an artifact, therefore our mathematics was invented. What about the rest of mathematics that he was talking about? Sounds to me like it's waiting to be discovered.

axiomatic mathematics is a recent development and part of a failed attempt to prove consistency and completeness. it is certainly an intersesting field but it is not mathematics nor is it at all obvious that it is capable of capturing mathematics. consider the serious difficulties that exist in set theory or infinities. mathematics and truth transcend our ability to describe them and the formal systems we use for that purpose. thus to conflate mathematics and axiomatic systems

is a mistake.

its a language

so . .its invented