I love these meta videos

This guy is great.

I totally agree with him, it's can be nice to hear about his personal work in theoretical physics.

Brian Greene somewhere talks about being in grad school and working with a mathematician: they spent weeks educating each other in their own field which moved each other forward. In addition, Brian noted that sometimes mathematicians were working most on one of two alternatives whereas the physicists needed the other.

The last 30 seconds were pure bliss

This was really fascinating to listen to. Thank you both!

great interview

I found this extra footage even more interesting than the main video. I'm glad I watch it.

I would give everything for having the same understanding of math as he does.

Love this guy - I could listen to him speak for hours

best video on this channel and one of the best on all youtube ever!!!!!!!!!!!

"...it's even more than universal." Wow

I'm happy with thinking of mathematics as the preparation and outline put on the canvas according to the math-master's concept, roughly outlined by the apprentices and technicians, then the mathematical fine details are adjusted according to the physics. It's OK for amateurs to admire the professional work and comment? (to help the apprentices)

One of the biggest still unsolved problems raised by observation is the chiral U(1) anomaly in QCD. This chiral symmetry breaking should generate a Goldstone boson, which isn't observed by any experiments.

Math exists with or without us. We DID discover it. 2+2 will always = 4. If 2 of something is added to 2 of something there is double of that something. What we did is invent the language to describe simply so we could talk about it. I wish I was going to be here in 32 years to witness to Great Breakthrough.

It's good to see someone finally show some love for loop quantum gravity on one of Brady's channels!

I am wondering when the Aliens will visit us, how their mathematical language will look like 😳

Woah dude, more than universal

Fascinating. So here's a thought. Physicists who consider that other universes might exist include the possibility that the laws of physics, and the physical constants might have different values in each. But would a mathematician agree that there could be universes in which different mathematical rules and constants could exist? Could two plus three equal something other than five, or is this rule bound up in the definition of two, three, five and addition? Could there be a universe in which, in a Euclidean region, Pythagoras's Theorem does not hold? Or where Pi has a different value? I think the ultimate answer to this has a strong bearing on whether mathematical rules have an independent (Platonic) existence, or whether they are human derived explanations for what just is.

Lovely :)

Is there a non equivalent set of axioms that is capable of describing and deriving modern physics? I remember using a lot of theorems in theoretical physics , but that doesn't necessarily mean that there can't be equivalent descriptions that are derived differently , at least that prove wouldn't be trivial, since the theorems are implications, not equivalent to the axioms

6:42 I disagree. A universe's rules don't necessarily have to be based on logic. The universe has no obligation to make sense to you and other universes have no obligation to do so either. A universe doesn't have an obligation to feature any rules can sensibly describe using mathematics.

I love you

If you are really interested, I will be delighted to give a talk to your institute at my own expense!

He went to an art school after his bachelor's degree in physics according to wikipedia. Does anyone know on what he was working on?

I think math already explains the physical world that we haven't seen or discovered yet. For example, I think that the concept of imaginary numbers can explain the positive and negative symmetry of electrons and protons, or in smaller particle units, in that they(imaginary numbers) are symmetrical to real numbers. Humans did not reach the concept of negative number until a long time after discovering the concept of positive, but in the universe, the positive and the negative existed together from the beginning. In other words, in the physical world, only 'mutual symmetry' has meaning, not the distinction between positive and negative. It is difficult for humans to imagine the meaning of imaginary numbers that become negative when squared, but I think that just because they are symmetrical to real numbers, we can give physical meaning to imaginary numbers, like protons and electrons. The concept of a virtual particle tachyon, which is thought to have an imaginary mass, or the imaginary part of an impedance in electromagnetism, show that this kind of idea is not just futile. And that's why mathematics and physics are so closely interconnected. Mathematics is a broader sense of physics that describes the physical world that has not yet been discovered. It explains the deductive structure of the universe.

Mathematicians are leading the way now because it is such a concrete and tangible science I believe. I am a beginner and started studying math a year ago. Now I am studying chemistry and fumbling with the basics of physics. My only thing is how can I study all of this without having an almost mental break down. Listening to the experts like this is humbling. Thanks for the interview. Awesome stuff.

Though the physical laws might be different in different physical universes, they all are special cases and contained within the much fundamental grander law(s) of Nature defined by physics. And besides, Mathematics may be the language of Nature but Physics (comprising all the physics of all the universes or multiverses) is the Nature itself.

It's mathematics all the way down

I like him

By my understanding, whenever math can't solve a problem by the current framework, they always try to re-define or even define new framework to the current one. Just like how they expand rational number to irrational number when they discover sqrt(2), expand real number to imaginary number when try to solve a polynomial equation. Whenever math find something that can't be solve or not well-defined, they can extend or even define new stuff to solve the problem. Does math 100% true? I don't think so. However, whenever new contradiction find, they can always re-define the mathematical framework to complete the hole.

Out of curiosity: what’s the reason to believe all other universes, if there are such, are based on mathematics?

Math is just the closest WE can come to understand the universe. In many ways it's the most formal and rigorous based on our own sense of logic and reason. No reason as to why something completely different could underlie the universe.

I may be mistaken, but I’d imagine the reason it’s so rare for physics to surprise a mathematician is that by its nature as a natural science, it relies on observation above all else. The issue here is that physicists don’t have the resources to just investigate whatever they want, but funding is only available to things which we have reason to believe could turn up results - since mathematics currently dictates this (as in, the viability of finding some specific result in a known physical and mathematical theory), it should be exceedingly rare for physics to surprise mathematicians, at least if the only tool physicists can use and justify funding through is existing and accepted mathematics.

Math is not just the fact that 1+1=2. It's also the language WE invented to say that 1+1=2. That's why imo maths are an invention, a tool we created to discover and talk about logic, about numbers, etc.

regarding the comment that mathematics were "discovered" , couldn't someone argue that since the exact same mathematics would apply in a universe where (for instance) gravity did not follow the theory of relativity or a different set of Maxwell eq. would apply , then mathematics is a theoretical construction that although can be used to describe physical laws , it has no "actual" bond to "nature" and is a pure mind invention ?

All the sciences are locked mathematics is the key to unlock the sciences by language of the universe and the nature and the reality of truth from quantum mechanics to the general relativity

6:22 - "...whatever that different universe is it's still one based on mathematics". Well, can you imagine a universe that could not be based on mathematics? I can't. At least not in the broader sense of mathematics as the academic field of study of our current times (as opposed to the standard mathematics we use on our everyday). It seems like all possible universes our brain is capable of imagining are, obligatorily, described by SOME KIND of mathematics, so it's no wonder that we predict that other universes will all be described by mathematics. In my point of view, mathematics is the result of our brain trying to make sense out of the world around it. It is the result of the training of a neural network that took a long long time to find parameters that were beneficial to survival, those parameters being our axioms, fundamentally what we call 'logic'.

I think he looks like James Woods.

I find the old question "is math discovered or invented" is not very well defined... and should be "is logic discovered or invented"....

If you don't give tolerance it's not physics. 2+2 is 3 for small 2's and 2+2 is 5 for large 2's and that's why you need to give your tolerance. Also about mathematics being unreal: There is no such thing as a real number in nature. Everytinh in nature is quantified on it's basic level and thus you only need integers to describe it. But real numbers are a useful concept to model the macro level of the universe. But one must remember that every real number is just an approximation what tyhe true value is.

Mathematics in the sense of logic, may be the language of nature. But the way we express logic, our simbology and in general what is commonly known as "mathematics", that is completely man-made and a human invention, not a discovery... ...Is what I think.

discover

Is maths invented or discovered? Well in my opinion even those viewpoints are sort of 'superpositions' you can collapse into one answer or the other of your choice. It's a bit like me saying day follows night from the perspective of a night shift worker & you saying night follows day from the perspective of a dayshift worker. Both perspectives are justifiable but from one perspective or another the other one is wrong so there's no 'truth' or 'falsehoods' either as such - there's just ways of seeing & it's impossible for any one to claim superiority.

obviously the answer is the `complex` or `imaginary` universe, the universe that the universe exists in. it doesn't just exist

Mathmatics doesnt reflect reality, mathmatics is reality. We're an equation of the universe.

Mathematics underpins reality, Dr Dijkgraaf claims or simply asserts. I wonder how he can do that in the face of Gödel's incompleteness theorems and Tarski's undefinability theorem (alongside the work of many other "Greats" such as Church, Turing, Hilbert and others) which make, imho, Mathematics and "Truth" (particularly Truths surrounding reality or our models of it) clearly associated with, or at least more dependent on the Axioms we choose. Axioms are those things we decide are self evidently true such as a + 1 = 1 + 2 . The operators + and = and the symbols 1 and 2 must be defined and their useage explained. Most of us learn these things when we first go to school.

Geometry is part of mathematics and as far as my memory is concerned, we have surpassed Euclidean geometry. If mathematics is so rigorous, then why is Euclidean geometry not sufficient?

When we meet aliens, we will know the extent of discovery vs invention wrt mathematics. The greater the overlap in mathematical knowledge, the greater the weight is on discovery.

three

Ahhhh... 5:45 - - Unitarian.

I really dislike his metaphor at 2:00 likening physics to art. In art, anything goes. If you can conceptualise it (or even just create it in some sense), you can call it art. Then there are the less rigorous scientific disciplines like the humanities, where you are allowed to use very high levels of abstractions, leaving a lot of room for interpretation, argument and mistakes. Physics is the natural science that has to conform to reality the closest, he even said it himself that some of the measurements in quantum theory are some of the most precise we've ever made, through experiments confirming the underlying theories. This level of rigorousness and precision is the complete opposite of art.

Physics without Mathematics is ......

Perhaps knowing too much will cause the possibility of dangerous experiments with the fabric of space and matter itself, wiping out such a universe with intelligent life in it. Perhaps we will get on that brink and we are the first ones to trigger it...

voor Nederland!!!

Problem with Robbert is that he is pre-internet. Back in the day when you did a study like his and you didn't get a definition you were screwed.

Nederlanders always have the most innovative ideas.

Problem is that both string theory and the theory of quantum information are struggling to survive.

Archimedes knew calculus

Isn't Maths an approximation as well..?

You all weak minds that get astonished for little. You make me laugh.

Yet another person that thinks that Mathematics is the basis of reality. It's a nice thought but not a certain truth. The only thing that we can be certain about is that Mathematics is the language for us to understand reality.

Whatever physicst are better anyways

I highly disagree with him when it comes to whether Mathematics is invented or discovered. I think it is very highly informative of his position within Physics to take that belief because Physics is very much discovered in the everyday. Mathematics does have austere beauty but not all types of Mathematics is beautiful. You can think of several examples within physical fields such as fluid dynamics for example or even within calculus itself where the integral to some function is horribly complicated, or might not exist at all. There are some parts of Maths which are elegant in their simplicity, but there are other parts which are objectively horrifying. Also, when he talks about that Maths is a language that is underpinning reality. Well of course it is! That's why we made it like that. Take Group Theory for example, does he think that the reasons the particular axioms for Group Theory were chosen was through some communication with a higher power? Axioms are subjectively chosen by humans because they appear to be the most intuitive, and produce results which are the most satisfying. Even the axioms of Probability theory itself are based on our subjective notions. The greatest argument that Mathematics is invented is in the subjective foundations that they lie upon!

That fundamental unifying theory is called mind. There doesn't seem to be hope of finding anything more accurate and encompassing.