Max Tegmark - 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? Or is mathematics discovered—always out there, somewhere, like mysterious islands waiting to be found? Whatever mathematics is will help define reality itself.

Closer To Truth presents the world’s greatest thinkers exploring humanity’s deepest questions. Discover fundamental issues of existence. Engage new and diverse ways of thinking. Appreciate intense debates. Share your own opinions. Seek your own answers.

[anonymousbosch]

I love that at the very end the interviewer has the giant cheesy smile saying “we are now far more confused than when we started” as I now have a lot more questions and wonder if the original question even makes total sense

[BigParadox]

I very much enjoy reading books by Tegmark as a physicist. This question, however, in its deepest sense, is best answered by not talking so much about physics. As someone else here commented, Tegmark answers the question in the best way in his first sentences where he distinguishes between our mathematical language (which we invent) and mathematics as such (which we discover). After that, I think the interview loses track in the hunt for the sought answer and deeper understanding of it.

[jamaalrichardson]

Tegmark essentially answered the entire question in the first sentence. Mathematical language is an invention, a way of describing mathematical principles, confined to our known universe, which are "self-consistent" as Tegmark notes.

[veritasetlibertas]

"For every single physical entity, that we can think of something we can touch or measure with a detector, there is corresponding mathematical entity there in the mathematical structure."

[donaldpiel]

The problem with insanely intelligent people is their ability to put their thoughts into a clear statement. The easiest answer to this question isn't explaining how math is real because of some multiverse theory but rather by giving an easily understood analogy. Say you have 1 marble in your left hand and 1 marble in your right hand. Now when you put both of those marbles in your right hand, you now have 2 marbles in your right hand. This proves math to be real. The word "two" is used to describe how many marbles (or whatever you're counting) you have. One + One = Two. So let's just say instead of the word "two" mathematicians decided the word should be "owt." So in this case One + One = Owt. So you can see that no matter how you describe how many marbles you have. You will always have a set answer that is manufactured by a predetermined set of laws in our universe. The language of math is invented. The laws of math are universal and discovered.

[Racerdew]

I've always enjoyed when Max says: "We physicists..." he loves saying that in all his interviews haha

[rdallas]

Max is a hero. Love his attitude and intelligence.

[andacomfeeuvou]

Numbers have emerged in our history as a simple tool for counting units around us. We could never imagine how many things these numbers would still show us.

[richardventus]

'Nature prefers simplicity....this is a deep mystery' My favourites are E=mC^2, Euler's Identity ad the beauty and complexity of a simple fractal.

[mickeylin]

To me, mathematics has always been a language used to describe the physical world and the intrinsic laws of nature. But all I have is first year college math to back that assertion.

[inccommensurable]

I really like the attitude and passion Max has in his interviews as much as I enjoyed his first book. Nonetheless I have to say that in this interview he really dodged the question several times, whereby the interviewer was clearly concerned about the cardinality of the platonic realm (or level 4 multiverse in Max's terminology).

[johnfite]

A=A is an axiom, and mathematics is a system of restating that in more complex ways in order to describe and leverage what we observe with our senses.

[markuspfeifer]

Thing about math being discovered is: we would first have to agree on an ontology of math to meaningfully discuss this question. Otherwise we can’t tell if math pre-exists or is created by us, because we didn’t even specify what existence means for math. The ontology of math has been highly controversial for centuries though.

[ASLUHLUHC]

So this goes further than Platonism in asserting that not only do all mathematical objects exist, but nothing else does. All structures that exist mathematically also exist physically.

[jdbrown]

We discover mathematical truths and invent our ways of understanding them.

[noumenon]

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” – Albert Einstein

[leahmae]

Don't over complicate mathematics> It is a system for human beings that helps them under their existence. It is nothing more.

[paull]

The fact that the 20 or so so called universal“constants” are not in fact constant, the best our mathematics is is an approximation.

[kiffeeify]

If a mathematician says: "The symmetry of mathematics is beautiful", I immediately have to think of observers bias - Still, I agree :-)

[welshriver]

I prefer the question: are the truth-conditions for mathematical statements dependant on our naming them as such?