Is Math Invented or Discovered Edward Frenkel

what I have learned is a mathematician is that the easy answers I usually know the right ones so if we talk about mathematics and again if we talk about real mathematics the kind of stuff that people like me do on a daily basis and unfortunately we keep most of it locked away from others so I'm trying to open the doors and I'm trying to help others to see to enter these museums of knowledge and beauty which is what mathematics is about when someone gets exposed to this stuff and not the boring and lifeless things which people are terrified of when they got to a forced to study at school then you would realize that a lot of it actually number one have no obvious connection to physical reality the kind of consensual physical reality that you know things around us a lot of it does of course you know I have ten fingers so I can count so yes the numbers I realize manifested in physical reality but there are things in mathematics which are much more much more sophisticated much more much farther farther removed I would say from physical reality there are numerical systems which are not realized anywhere there are infinite dimensional spaces which are not realized anywhere we don't see them so where are they well there are some who say that we humans invent this stuff like elaborate pieces of fiction in a kind of a game like a game of chess but I don't believe that to be the case there are several reasons for that and well first of all if that were so we would be completely free to investigate the rules of the game would be completely free to change the rules of the game we would beaker and and different people who play different games but there's only one mathematics as far as I can tell we all study at school Pythagoras theorem Pythagoras came up with this theorem 2,500 years ago and in fact there is evidence that in other cultures in China and Babylon mathematicians had discovered the same theorem even earlier but let's just say Pythagoras 2,500 years ago I don't know much about Pythagoras I don't know what he what he ate where he lived how he felt but I know that what Pythagoras theorem meant to hear is exactly the same that it means to me and later on others could discover the same thing but it would be exactly the same thing so that's why this kind of knowledge it shows us that this kind of knowledge is timeless is eternal is unchanging so that's very special because for example our physical theories change all the time we had Newtonian mechanics which we thought was so powerful so beautiful and it's described so many almost everything we knew at the time and it was very tempting to say that this is a final theory of physics but of course now we know that that's not the case Einstein's relativity theory sort of turned in Newtonian mechanics and its head and there is no reason to believe that Einstein's special relativity say is a final word the theories will be updated but Pythagoras theorem will not get updated it means the same thing to everyone in the world today and will mean the same thing a thousand years ago so that's one argument that you can make there are more elaborate arguments the great logician could curdle whoo you know one of the Giants of mathematics of the 20th century I would maybe say one of you know really one or two most important people in mathematics of the 20th century he actually gave a mathematical argument why it would be impossible for my file for us to say you know for math likes to be invented there are certain very important properties of mathematical knowledge that he had discovered and which we now understand even better today which show that that is impossible that is an impossibility it's almost like it's almost like you are you are trying to build something if you build something I suppose you want to build a ship okay so of course you make a ship and you don't know exactly how it will move which way it will go how exactly it will float and so on so that's okay that's normal you can still say you all you built it you created it but imagine you're building ship and then suddenly it turns out to be an airplane so how can you claim you created it you know so that's what more or less that's a seraph analogy where we are with mathematics it's so much different from the kind of things that we can create or invent so that points to an alternative which is that mathematics lives in a world of its own in a kind of Platonic reality and of course Plato was one of the first philosophers to theorize that there are certain things which exist outside of space and time and outside of what we usually call physical reality and so mathematics if so then we actually discover mathematics so Pythagoras discovered the Tigers theorem we did not invent it so we discover them by this result these ideas these theorems equations by tapping into this magical world of mathematics that's why I think it's so important from for all of us to realize that it exists and it's kind of the irony the paradox is that most people think mathematics is the most boring subject but in fact I think it's a portal it's a portal into hidden reality because if mathematics exists outside of space and time and outside of logic what else is out there

Channel: Jeanric Meller

Views: 38,845

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Id: IGTJx3Ljh58

Length: 5min 38sec (338 seconds)

Published: Sat Aug 20 2016