I really enjoy ideas building on Topology and Algebra, like Schemes in Algebraic Geometry, and others like Moduli spaces; and it always bugs me because these ideas seem really powerful, rich in representation and useful but you don't see them being used outside mathematics. So, my interest is to use such ideas is sciences and engineering; and perhaps the best way to get started is with computation. And it's really nice to see that Professor Harper sort of believes in a similar thing. As in the movies if we are ever in the future, going to extract quantum data from black holes we had better be using Schemes in our computers long before or all of those ideas of simulation like the Matrix they had better be using commuting diagrams as switches long before anything even so significant. I think it is a great time to start taking ideas like these from mathematics and using them in other contexts, and computation seems like a really awesome venture.
52:57 Eventually all the arbitrary programming laguages are going to be just swept away with the oceans and we will have the permanance of constructive intuistionistic type theory as the master theory of computation. Without doubt in my mind. No question. So, from my point of view, there is personal statement, working in antything else is a waste of time. Ok. The right thing is put things in terms of type theory. That's the way.
Hi, I'm Italian and I would like to better understand this point of view but I don't understand English well. What you say is that this math will create programming language that will supplant the current ones?
there are any connection with python? used it type theory? help me please, i have a knowdledge of calculus, classical logic - set theory and basic algebra… i know about concepts of topology and the storic idea of univalent foundation but i don’t understand the big sense of it after the godel’s theorems. Please could you make for me a central map overview to study this field?
@@aldo1560 Hi! This is not my words. I just write down the lecturer's words, because they seem very important to me, but I don't fully grasp them. All I see is just a direction.
I never heard that mechanized theorem proving is essentially impossible in practice until today @ about 36:00. Now, I have heard that answering ALL mathematical questions using mechanized reasoning is impossible in practice AND theoretically. Is there some sense in which the second of these is what he really means?
He was speaking informally, so perhaps the off-hand comment comes with a strawman, but I think it's self-evident from his comment what his stance is. "What I hope we're doing here is completely blowing up the idea, exploding the idea, that 'mechanised reasoning is inherently tedious and pretty much undoable in practice' - I think that's actually not the case."
I'll keep watching your lectures, but I must confess I'm a dyed-in-the-wool platonist. I certainly do agree that fewer assumptions make for a stronger proof; I just hold a nearly polar opposite viewpoint on constructivism.
Hi, I'm Italian and I would like to better understand this point of view but I don't understand English well. What you say is that this math will create programming language that will supplant the current ones?
![รวมเพลงลูกทุ่ง 6 หนุ่มไทบ้าน ฮิตติดกระแส ชุดที่ 1 l มนต์แคน ไมค์ ไผ่ เสถียร ไหมไทย พี [Longplay]](http://i.ytimg.com/vi/GD2v1OjMw5I/mqdefault.jpg)
![[Intro to HoTT - OLD] Martin-Löf Type Theory: Speaking the Language](/img/n.gif)
This guy’s lecture style is so charming-I love it!
Damn this powerpoint presentation is looking HoTT
OH MY GOD IM STARTING TO FEEL IT
Awesome! Thank you for making these lectures available
Iterative deepening 💚
GOOD!!!
I really enjoy ideas building on Topology and Algebra, like Schemes in Algebraic Geometry, and others like Moduli spaces; and it always bugs me because these ideas seem really powerful, rich in representation and useful but you don't see them being used outside mathematics. So, my interest is to use such ideas is sciences and engineering; and perhaps the best way to get started is with computation. And it's really nice to see that Professor Harper sort of believes in a similar thing. As in the movies if we are ever in the future, going to extract quantum data from black holes we had better be using Schemes in our computers long before or all of those ideas of simulation like the Matrix they had better be using commuting diagrams as switches long before anything even so significant. I think it is a great time to start taking ideas like these from mathematics and using them in other contexts, and computation seems like a really awesome venture.
cool! i just came across favonia's channel :)
🙏
What a trove!!! I delayed start studying HoTT for too long. Not anymore. HoTT here we go!
52:57 Eventually all the arbitrary programming laguages are going to be just swept away with the oceans and we will have the permanance of constructive intuistionistic type theory as the master theory of computation. Without doubt in my mind. No question. So, from my point of view, there is personal statement, working in antything else is a waste of time. Ok. The right thing is put things in terms of type theory. That's the way.
Hi, I'm Italian and I would like to better understand this point of view but I don't understand English well. What you say is that this math will create programming language that will supplant the current ones?
there are any connection with python? used it type theory? help me please, i have a knowdledge of calculus, classical logic - set theory and basic algebra… i know about concepts of topology and the storic idea of univalent foundation but i don’t understand the big sense of it after the godel’s theorems. Please could you make for me a central map overview to study this field?
@@aldo1560 Hi! This is not my words. I just write down the lecturer's words, because they seem very important to me, but I don't fully grasp them. All I see is just a direction.
11:05
I love everything except myself
I never heard that mechanized theorem proving is essentially impossible in practice until today @ about 36:00.
Now, I have heard that answering ALL mathematical questions using mechanized reasoning is impossible in practice AND theoretically.
Is there some sense in which the second of these is what he really means?
He was speaking informally, so perhaps the off-hand comment comes with a strawman, but I think it's self-evident from his comment what his stance is.
"What I hope we're doing here is completely blowing up the idea, exploding the idea, that 'mechanised reasoning is inherently tedious and pretty much undoable in practice' - I think that's actually not the case."
@@ManInTheArena-nl4ti
Yes, a strawman.
homophobia type theory? auto-generated CC can be hilarious!
I'll keep watching your lectures, but I must confess I'm a dyed-in-the-wool platonist. I certainly do agree that fewer assumptions make for a stronger proof; I just hold a nearly polar opposite viewpoint on constructivism.
Who was the author of the book?
Hi, I'm Italian and I would like to better understand this point of view but I don't understand English well. What you say is that this math will create programming language that will supplant the current ones?
9:58