字幕列表 影片播放 列印英文字幕 >> BRADY: Why do so many people hate mathematics? >> Professor Frenkel: Very good question. I think there are several reasons. The problem is multi-dimensional, no pun intended. Imagine that you had to take an art class in which you were taught only how to paint a fence or a wall but were never shown the paintings of the great masters. Would that make you an art lover? Years later you will talk to your friends and say "Oh my gosh! I hated art at school, I was so bad at it." What you would really be saying is "I was bad at painting the fence." And likewise with mathematics people often say "Oh, I was so bad at math, I hate math." but what they are really saying is "I was bad at painting the fence." So how do we make people realise that mathematics is this incredible archipelago of knowledge? If you want your kids to understand and appreciate the beauty and power of mathematics we have to connect it to our daily lives. Let me give you an example. Say you go on Amazon to buy a book and you are immediately presented with various recommendations. How does Amazon come up with these recommendations? Well, there are sophisticated algorithms at play which analyse your past choices, which correlates you with other users who are deemed to have similar preferences. Then all this data is processed and you're presented with these choices. Now, I'm not saying that this is necessarily a good thing but I think at the very least we have to be aware of this. We have to be aware of these algorithms invading our lives, and those algorithms are based on mathematics. >> Brady: You and I live in houses and we appreciate the houses we live in, it doesn't mean we need to know how to lay bricks. >> Professor Frenkel: That's right. >> Brady: So why, just because we - just because mathematics is underlying some of the technologies in our lives, why does that mean we have to understand it or even appreciate it? >> Professor Frenkel: That's a very good point and likewise people say "well, we fly airplanes without necessarily understanding the, you know, the physics of flight." But there is a difference, and first of all mathematics is part of our culture just like literature and art and to have a fulfilling life we have to be aware of this. But also, because mathematics is becoming so important in our lives there is a lot of opportunity for misuse of mathematics and for manipulating us by using highly sophisticated mathematics. There are many examples of that, global economic crisis was to a large extent caused misuse of mathematic models. Which one could argue often were used by, you know, executives of financial firms who did not fully understand them. What if we lived in a world in which a, say a Wall Street executive, would not say "Oh, I don't get this stuff but as long as it works, it's fine." What if in fact that person would say "OK, tell me more about it, I would like to understand how this model works."? There's this great quote by a great German mathematician Georg Cantor, said "The essence of mathematics lies in its freedom." But, I would augment this with the following; where there is no mathematics there is no freedom. So mathematics is essential to our freedom, to the function of our democracy. That's why it's not just about finding out how some things work, which you don't need to know about because, you know, 'who cares? As long as they work.' I think that our ignorance can be misused by the powers that be, and for us to be, you know, the citizens in this brave new world, we have to be more aware of mathematics. We have to know and appreciate its power to do good, but also to do ill. >> Brady: The art world tells us we should appreciate art more. An English professor will say we need our language skills improved. Computer scientists will say we need to understand code. The mathematicians are telling us we should appreciate maths, well some of the math. [laugh] We've only got these finite brains and only so many hours on the planet, why do you bring mathematics above the others? I know you're a bit biased. >> Professor Frenkel: Well first of all I'm a mathematician, right? But also, I would say that art for example, let's take art. So the situation was, people don't go to art museums of course. We know that, not everyone goes to that, not everyone pays attention. But at least people know that there are, there exists museums. If you say the word art, they don't think about painting the fence but they think about van Gogh and Picasso and Leonardo da Vinci. So they know that at least, if they ... whenever ... if they have an interest they know where to go, where to find those paintings. Or they can go online and find those paintings, right? In the case of mathematics they are not even aware of the masterpieces of great mathematicians the way that they are aware of the existence of masterpieces of the great artists. Art of course is important because it speaks about our emotions and it speaks about the world and about ourselves. But in a way, one can survive without art, but one cannot survive without mathematics. Everything is based on mathematics; it is the language of nature. >> Brady: Well, let's apportion some blame, let's blame someone then. It sounds to me like you're blaming high school teachers? You were saying, you know, back in our school days they're making us paint fences instead of showing us Picasso. >> Professor Frenkel: Well, if I really were to assign blame I would assign the blame to myself and my colleagues. Professional mathematicians. We don't do nearly enough, exposing these ideas to the public in an accessible way. Often times we're not willing to come up with good metaphors and analogies and this is how science should be communicated. You have to communicate science in a way that would, you know, in a way that's creative. That links to something people already know. And I feel as though other scientists are doing a much better job; physicists, biologists. We keep talking about the solar system about the universe, about galaxies, about atoms and molecules, elementary particles and DNA. Those concepts are no more complicated than things we do in modern mathematics. Why is it that, you know, DNA and stars and elementary particles are part of our cultural discourse but mathematical ideas are not? Well, in part because we are not doing nearly enough. We professional mathematicians are not doing nearly enough. I don't blame the teachers because, you know, they are in the precarious, really unenviable position often times because they are, you know, overworked and under paid and also teachers themselves are products of the same flawed system. My solution is that, first of all, more mathematicians should go out and let other people in on the secret. Because it's really almost like a secret and we're almost like this elite which is sort of keeping this secret, and I don't want that to continue. I want everyone in on the secret. I want everyone to realise there is this beautiful world out there, which is so important for our daily lives, which possess the, you know, unparalleled power and beauty. We have to convey this idea; we have to find ways to convey those ideas. And then, you know, we have to also work through our education system. We also have to help teachers to learn the necessary content and to learn how mathematics connects with the real world, so that they make the study of mathematics for students more enjoyable, more fun, more interesting. >> Brady: Why has that not happened? It sounds so obvious. What you've said is not like a huge conceptual leap. Why has this not already happened? >> Professor Frenkel: What has it not already happened? Well sometimes I wonder myself, why has it not already happened? It's almost a conspiracy, I mean honestly, it's almost like there's a system of mirrors that has been created which distorts, you know, reality. Which does not allow most people to see what is out there. And let's face it, how many more things are left to discover? We can't be the first to discover another continent like Columbus; we can't be the first to step on the moon. But what if I told you there is this beautiful world out there and you don't even have to travel anywhere to find it? It's right at your fingertips. Wouldn't you want to go and find out more about it? And if you do this in the right way you will have children, you will have students, you know, running to class! Not away from the class but running to the class, like "I want to know more. I want to find out more. I want to talk to my peers, to my classmates about this stuff." This is the coolest stuff in the world, that's what it is. >> Brady: Coolest stuff in the world? And yet, everyone hates it? >> Professor Frenkel: And yet everyone hates it. Isn't it ironic? >> Brady: If you'd like to hear more from Professor Frankel about his love of mathematics, this is his book 'Love and Math'. You can't have this one, this one's mine, but you can get your own copy, and one of the ways you can do that is through the sponsor of this particular video, Audible.com. Biggest range of audio books you can image, and one of them is this one. As you probably know by now you can go to Audible.com/Numberphile and if you sign up you can download a free book and it could be this one, it'll be the book of your choice. So if you're going to check them out go to Audible.com/Numberphile and then when it comes time to pick your free one, Love and Math. I'm sure he'd appreciate it.

A2 初級 人們為什麼討厭數學？ (Why do people hate mathematics?) 274 19 vincent 發佈於 2021 年 01 月 14 日 更多分享 分享 收藏 回報 影片單字