Stephen Wolfram - Is Mathematics Invented or Discovered

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?

[Cyrusislikeawsome]

This is literally one of the most interesting questions in the world for me. It's a huge factor in how I got into physics.

[danielt.]

4:09 "My mathematicses ..."

- Gollum

[NorceCodine]

The paradox is that we cannot invent any other new distinct mathematics. Any conceptually new mathematics will only be accepted as legitimate if it doesn't contradict the cardinal tenets of our old existing mathematics, and at that point it becomes immediately (logically) equivalent to our old mathematics. Kind of like an ideal in ring theory - anything from the ring upon coming in contact with any element of the ideal, becomes part of that ideal. Therefore a completely different distinct mathematics can only come from a different species. The frightening possibility is that if our mathematics is not the "right" one, however logically flawless and vast it will become, then our failure as a species in the universe is already predetermined. Our mathematics might never unlock a (the) key in correctly understanding (an aspect of) the universe necessary to move on to the next level.

[AdilKhan-gdsc]

An example of other “mathematics” would have been lovely...

[IsaacDarcheMusic]

absolutely correct and brilliant analysis

[cpt.stranglewank]

every time he says "Mathematics", take a drink

[dr.mikeybee]

Plato's Meno suggests that Learning is remembering. Perhaps recognizing is a better word.

[fviete]

not sure I quite get this. Stephen has a picture behind him of Pascal's triangle mod 2 and we can see the way the nested sierpinski triangles form in this picture, jumping straight out of the natural structure of numbers. It doesn't matter what your axioms are, no matter who calculates that, they will always see those triangles. We didn't *invent* the fact those triangles appear, they just appear. Sierpinski triangle type forms appear on the shells of Conus and Cymbiola, are gastropods inventing their own axioms now?

[Sarita]

Thanks so much for the excellence of yo programs.

[DrDress]

"Mathematicses" You gotta love that word.

[RickDelmonico]

Math is a kind of shorthand, what is important is relationships. These relationships have qualities that vary with scale and resolution.

[timb]

Saying it's an artifact does not definitively answer the question of whether or not that artifact has an existence independent of our discovery of it. Sure...we created it...but we don't have a clue HOW we created it (or how we create anything for that matter).

[duffypratt]

If math is an artifact, then the idea of a possibility space is also an artifact, and one that grew out of the artifacts of math and logic. You can’t then use that possibility space to posit the existence of other, alternative maths. You either stay within your system, which keeps you blind to what’s outside, or you jump outside and lose all rigour.

[hasanshirazi]

It appears that mathematics is existing at the fundamental level of the workings of the universe but what mathematics we have developed is a crude approximation of that. So yes it seems that what we have is something we invented to approximate what is really going on. And that what is real mathematics of the workings of the universe might be very different to our invented one.

[codediporpal]

So it's an invented artifact, but he concludes by talking about "exploring the space of possible which means it's discovered. OK then.

How come nobody notices he just contradicted himself?

[uiuctalkshow]

To learn more Wolfram thoughts on about college, AI, and the Computational Universe. Watch our interview with him.

[TimCrinion]

If maths is invented and not discovered, then it *seems* like all mathematical things can be described. But some mathematical things cannot be described, since the set of all numbers is uncountable but the set of all describable numbers is countable (since the set of all English sentences is countable). Contradiction?

[danellwein]

do you have anything more recent on Stephen Wolfram ... also ... have you interviewed the mathematician Jonathan Gorard .. thanks in advance .. also .. it will be interesting to see if the 'discovery' of computation will allow us to go down to the level of machine code of our universe ...

[elir]

Note to self, wolfram is saying that our mathematics is a single mathematics out of a larger possibility space of mathematics.

[kayrealist]

Interesting theory. My measly human brain till this day believed that the mathematics today was the universal language of the cosmos.