Roger Penrose - Is Mathematics Invented or Discovered? 

This interview is part of our Mathematics and Philosophy playlist series, created for Mathematics and Statistics Awareness Month. Starting Monday, 4/20/20, we will be publishing two mathematics playlists of all-new, never-before-seen interviews with renowned mathematicians! If you can't wait, the "Is Mathematics Invented or Discovered?" playlist is already available (and freshly updated!) on CTT's channel. Playlist - Is Mathematics Invented or Discovered? - ru-vid.com/group/PLFJr3pJl27pIp1EsDD2rYaTI7GxoXqrLs

We are immensely blessed to be living in an era where such minds are available for our casual consumption and for free.

When he talked about molecules and atoms, in the beginning, I thought, nice! A mathematician who seems comfortable in physics. Then I searched him up and found out he has a Nobel prize in physics. I guess he's more than comfortable.

It’s always a privilege to listen to the great mind of Sir Roger Penrose

I wish… that as a kid, someone had described math to me in this way. That it’s something humanity discovered. It exists independent of us, it’s not all understood or discovered. And in order to predict how reality will play out, you need to understand math. It describes reality, past, present, and into the future.

9:00 if you are wondering where the title question starts.

Today he was awarded with Nobel prize.

This makes you wanna do math. I never in my life had a teacher, that had the same philosophical euphorism that these to convey. It's such an obvious thing you would need to convey, in order for a student to care about learning it and yet nobody does this.

He answered the question with more questions. A wise man

Roger Penrose was awarded the Noble Prize for physics when he was 90 years old; That was an astounding achievement. I am in my early 70s, I can only tell you younger people that to be able to think clearly an and creatively at that age is truly astounding.

Amazing interviewer.Asks pricise questions and let the guest speak without interrupting.rare quality in today's interviewers.

Dr. Kuhn, just to say your overall program and interviews are a gift to our world today. Thank you for creating and capturing all these wonderful discussions.

Access to conversations like this are magnificent to have available online.

Mathematics is just reverse engineering the source code of the Universe.

The amazing part is how someone so intelligent can describe things so incredibly well that everyone can follow along.

As a protagonist in engineering for more than 40 years I still get bamboozled by the depth of maths and it’s relation to physics! (This was by far and away my favourite subject through high school) I recognise that this work is vitally important for human development but there is a point at which we have to make sensible decisions that mean we can develop in a cost effective and acceptably safe way! There is somewhat of a philosophical position to take!

"Pure mathematics is, in its way, the poetry of logical ideas." - A.E

-Is Mathematics Invented or Discovered? Mathematicians: Yes.

Delightful interview to listen to. I had to watch it many times, because at many points my mind went far away thinking about what they'd just said. Very good!

What a glorious conversation! In regards to a simple equation being responsible for producing the mandlebrot set, I wonder what sort of equations are involved in producing the seemingly impossible visual shapes we can witness in a DMT breakthrough.

Remember hearing a great story. I hope I can tell it right. A mathematician walks into his colleagues office to find him reclined in his chair practically motionless with his eyes closed and then slowly steps back out saying “I am sorry I did not know you were working.”

Sir Roger is a mathematical legend. I read his books in high school and college in the 1990s. His achievements are inspirational, and he stands among the greats like: Dirac, Hilbert, Poincare, Lagrange, and Hamilton.

Always had this question but never was able to word it so simple and comprehendible.

I’ve always thought “Mathematics” is universal, we just invented a language for it.

This guy is a great interviewer. Like a common guy who is really curious

Mathematician: "Math is the language of the universe." Physicist: "Math is the language of physics." Engineer: "sin(x) = x."

Thank you for the video. I am grateful for your time and contribution. Kind regards, Akira.

Nice discussion. Thanks for sharing it.

For an egghead, the man is very engaging. He gets his points across with great clarity. When a super genius explains things well enough so that even a cave-dweller like myself can understand, he is an exceptional communicator. Thanks professor, and congratulations on your Nobel prize....

Relationships are discovered, the method of discovery is invented.

I would say, neither of both, but we deciphered and still deciphering it. Mathematics is a language of our universe and as with any unknown language, we try to figure out how does it work. Every time when we find out how something could be mathematically explained, we have deciphered a new area of this language.

What a wonderful, flowing and enlightening interaction between these two men, on such a deep subject, without resorting to gobbledygook! Thankyou.

What I find most intriguing about mathematics is that it seems to be a self annihilating language. When we look at quantum mechanics and consider, just to name a couple, the work of Heisenberg and Schrödinger, what we see is that mathematics itself led us to a place where all calculations become void and irrelevant because it is impossible to mathematically predict the behavior of existence itself when we are faced with its particle-wave duality. I find it to be so poetic that mathematics itself had proven to us that the quest to understanding the universe/multiverse at its most fundamental functions will require a language that would be very far removed from the nature of mathematics.

I hope the IRS doesn't discover the math I invented!

I love the old books in the background

Really, some wonderful peopl add to our knowledge and notions and make this world wonderful. How we can know such notions without such a mathematician. Amazing.

I always appreciate good questions as much as good answers.

He's 88, impressive

I don't like numbers, there's like too many of them. - Beavis

Being surprised with the fact that math can be used to describe the world precisely is the equivalent of being surprised English can be used to write poetry that captures human feelings. It's a languague at it's best use. An endeavouring question one can make is in which cases math fails to describe the world accurately and also if we can ever realize it

I am so thankful for being smart enough to appreciate how very very very smart Penrose is.

The principles and the phenomenas are real, we're just figuring them out and giving names and labels to them.

One of the best short discussions about the topic of philosophy of mathematics, and with some insights into the interactions between mathematical structures with the real world. e.g. what Eugene Wigner called "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". He has what I call a beautiful mind.

One thing this shows clearly to me its how crucial the a priori is epistemologically in a sound scientific method. At the same time, it's surely important not to mistake sometimes mathematical correlation for causative mechanism, and to remember that it's possible to obscure discrete causation with calculus' "smoothing out of the continuum".

I simply thank the better sense to put an end to square root on reaching iota,at times I feel tempted to carry it forward similar to logarithm.

After combing through and scanning over all these provocative vid titles, I think I've found the equivalents of gold here on this channel. I'm about to binge all of this.

this was great. so thrilled to think how much more of mathematics might be understood to in fact relate to reality as we experience it, and possibly unite physics and metaphysics.

It is wonderful that mathematics describes the world very precisely or that the world functions in such ordered simple matter, that from adding and substracting you will eventually figure it out

It’s very fascinating, the idea that the physical and non-physical worlds operate independently - yet, work or interact between each other transactionally.

Fantastic presentation, Penrose is a wonderful intellect.

Congratulations to him for winning Nobel Prize 👏🌟

Metaphysics. Loved this. Many thanks.

Nothing has ever been invented, we've only ever discovered the potential that was always there

I love thinking about these topics. It’s gives me a great sense of awe at the natural world.

I really don't know what to say except "Thank you Roger!". Your thoughts are the beacon of our lives. And also thanks to Closer to Truth.

Mathematics was discovered - the method of understanding mathematics was invented.

The mathematical description is the most precise we know. So it is guaranteed to strike us as incredibly precise. In the nature of the case - we possess no greater precision to run it up against.

My intuition tells me that reality has a structure and math is an expression of that.

Mathematics emerges when you try to understand relations in a complex system. It just happens that in our universe everything seems relational so it makes math a good candidate to understand it.

Ahead of watching this, presuming the question isn't misleading, I will guess that the mathematical properties of the natural laws governing this universe is what we discover, and what we invent are systems for expressing them and leveraging what we've discovered both in practical application and also in the pursuit of new discoveries. Now to watch the video and learn how muddled my guess was.

The subject of the video (and of course the discussion) are fascinating, but aside from that, I'm very happy that a video such as this reached over 2mil views.

This is thrilling and fascinating to me, Sir Roger. The confluence of All Mathematics and All Physics is so beautiful and allows us to go deeper into the Reality and Truth of our Universe. And We, most probably, will never find a total solution. But the Theoreticians can dovetail with the Engineers, Scientists, Explorers, Practical People, etc. We can look forward to a testing and interesting future based on your thinking and your Associates and Colleagues. Thank you for your (summary) talk on this.

I have been saying this question to people my whole life. I never knew it was an actual thing people like Dr. Penrose studied! I always thought discovered, just our units to describe things are "invented" but also based on discovered properties of reality as well.

What I understood from this video, mathematics has two functions, one it enables us to understand the behave of objects and fields, either they are classical objects or quantum particles, either field or quantum field, the second function, mathematics serves the reality that not need to be proven by any means, reality that stands there for us to discover.

As an EE, it is amazing how electrical parameters are so related in straight forward equations and that many of the constants that bind the equations also work well in other disciplines. The only thing that the math doesn't seem to fit very nicely is that a number of the constants are irrational numbers.

So deeply interesting. Would love to see more.

this for me is one of the most satisfying videos on youtube an I've seen a few... thanks :)

Well done, gentlemen!

Thanks!

A group of mathematicians were trying to measure the height of a long flag pole but it was too high. A group of engineers came along and said they could help. They pulled out the flag pole and laid it on the ground and had no difficulty measuring the pole. The engineers smiled and left. The mathematicians scoffed at the engineers, "Engineers! We wanted the height, they gave us the length!"

I like Penrose, he seems like a very humble man. And the interviewer is likewise. Two good men grappling with the most important questions in life.

I absolutely love these discussions. Thank you, Dr. Penrose, for your life of work and discovery, and your willingness to engage the public about it. That said, I disagree with Dr. Penrose regarding where mathematics stands in relation to reality. Our zone of agreement- the Universe is real, and a great deal about it is mechanistic to a high level of precision, at least by human standards. And it would be so even if we weren't here to observe and acknowledge it. The human ability to model the Universe with math vastly outpaces the growth in our ability to test/ detect whether the model's predictions pan out. But what about the math? First- The extreme precision of mathematical predictions is an artifact of math as a descriptive tool, not an indication that the prediction is correct. Even math that has no descriptive utility, still renders extreme precision. Second- Calculus is not a model or a mechanism, it is a coping strategy. Geometry truly rendered clockwork Universe models, and with Kepler got as far as elliptical orbits. In a break that I would compare to Einsteinian mechanics v Quantum Mechanics later, Newton/ Leibniz' introduction of the concept infinitessimals, and how to use them in a system of thought that allows the rate of change and the area under the curve to be computed, abandoned the project of a mathematical model that is supposed to operate as the Universe operates. It is true that some parameters in the Universe appear to be quantized. Maybe time and space are quantized too? But infinite infinitessimals can fit into any quantum. Whether the Universe runs smoothly, as Einstein and Newton hoped, or in quantum events, as may be the case, there was never any pretense that the concept of infinitessimals should describe the universe. It was simply a way to use math to make predictions and capture appearances. Third- The math, while useful and illuminating at every stage, never quite works. It always leaves something out. Newton did work good enough to get us to Mars, but he was a little off, and didn't explain everything. Einstein did work so good that a hundred years later we are still corroborating things we only just became capable of measuring. But he was a little off, and didn't explain everything. Then with Quantum Mechanics, in a desperate attempt to model the evidence they were seeing, scientists abandoned mechanism and just started modeling God's game of dice. The body of knowledge they are collecting is impressive and mindbending, but I think they know better than to expect their math to get to the bottom of it. Math is always almost enough, but never captures the Universe. Very suspicious. But just as particle/wave duality cries out for the invention of a new entity that the object under test can be full-time, the almost-rightness of mathematics cries out for a rethinking of our models. There is an underlying order, and disorder, to the Universe. Mathematics may or may not ever develop to capture it. But from a human perspective, we will have to wait until we have invented more math to find out.

Thanks a lot

It is a wonderful video. I have to congratulate everyone who has participated in it, not only the great R. Penrose, because the most important merit is having shared it for free. Thank you. This video should be seen in every school in the world.

Isn't that like Michelangelo's answer to the question, how he could make such beautiful statues, which was: "I didn't do anything special. The statue was inside the block all along. All I had to do was to chip off the unnecessary pieces."

He may be the most legendary living scientist at the moment. Maybe if Watson or Crick are alive (not sure if they are) they are as well.

Ever since Ant Man came back from the Quantum Realm our understandings of things have really progressed at an amazing pace.

I actually thought about this question a few months back

Looking at reality through mathematics, is the reason there is a separation between the two, looking at reality through mathematics, geometry and the relationship between the two will render a solution that is indistinguishable from reality.

Math itself is inarguably, definitionally a human creation But what it attempts to describe already exists and it can be a great tool for discovery. But it is a language we made up to make sense of the world around us

“I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it.” - Mark Twain. The context of the quote is the fear of death, but it applies here. Two and two was always four, we just happened to stumble upon it.

We certainly didn't invent it, but we invented its language. When you look at anything, even if you aren't aware of mathematics, you can tell the difference between one of something and a hundred of something, even if you don't know what they're called or how to describe it. Mathematics is the language we invented to describe measurements of things around us, the labels and lengths we use are only a way to navigate through what is built into the universe.

Physical laws and concepts exist, you discover said physical concepts and use language to convey or understand them, this language is numbers, formulas, symbols, equations.This whole process is mathematics. That was in my head and i wanted to get it out

Years ago I'd read all the popsci books (kip Thorne, hawking etc etc) and felt like a kid in a candy store discovering all of these things and understanding them as they were put to me... But I couldn't really find anything else like that, everything else I picked up seemed to rehash what if already read and understood... So I bought the road to reality by penrose, I read a quarter of it and had to put it down, its so far above my head, that I didn't feel like a kid in a candy store anymore, I felt like an ant trying to understand space travel... It was horrible. So... Thanks Roger, that hurt a bit.

I love Penrose so much. I feel intuitively and logically that his answers are correct about mathematics being a discovery. Our labels of math and language are the invention, the reality always existed.

As one Mathematician said to me in conversation tht I may expand upon, "Math is just imperfect Man's desperate way to interpret the infinite Beauty of Almighty God's Creation." And since God is infinite - no beginning, no end - Humankind will nvr kno fully the means, concepts, principles or substance of the Cosmos made by His hand, or holy spirit & power, artistry & depth, all based on His love for others 2 share in His joy of being. But it's sure fun to try nvrtheless! AWESOMENESS!

Depends on if you ask a historian or a financial adviser.

You need to ask also about invention of computer program or software

i was told once to read the elements by euclid. They were some very important geometrical ideas that influenced mathematics. I dont think its a required read I'd say its sufficent to learn its principles as they apply to your field

Mind blowing as usual, but greatly helped by Prof Penrose’s precision and clarity. Maybe there are also platonic worlds of logic, music and morality, equally fascinating.

Mathmatics equations accuracy on micro and macrocosmos observed reality, is incredibly precise. Some minor aparent discrepancys, may be due to observer's factor.

Mathematics describes what is happening, and somehow reveals to us what that reality is. It's like a communication pathway... a medium of exchange of information...

"Mathematics" is a human contrivance used to describe change and motion. We can't be sure it's accurate over remotely vast distances and time scales. The ancient Greeks pondered this question.

We invent the characters and symbols used to explain mathematics but the formulas, the very essence of it is just something we discover

Anyone who's still a materialist after studying mathematics at a high level is kidding themselves. The existence of numena, immaterial objects, is pretty much self evident when you think about math a bit. After that, it's a hop, skip, and a jump to religion, but lots of people aren't ready for that conversation.

Dank library 📚

What I think is fascinating is how often maths departments have musicians trying to break free! 🤔

I noticed Robert Lawrence Kuhn's repeated invocation of the idea that mathematics must be 'out there'. It seems 'out there' is his criterion for 'what really exists'. But the point about mathematics, is that it transcends space and time - it's not 'out there', it's true by virtue of inherent reason. The intellect's grasp of the transcendental nature of intelligible reality is fundamental to traditional platonist philosophy, but has been squeezed out of Western thought due to the influence of nominalism and, later, naturalism. Thank heavens there are some leading scientists such as Sir Roger who are fighting the good fight.

Eye have a beautiful answer for this question.

What is the criterion for the accuracy of the description of reality by mathematics?