A Quote by Terence Tao
I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
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You must understand that violence in a movie is only a tool. If it's used badly, it will be horrible. If it's used correctly, it can be very interesting. But, essentially, it's just a tool.
We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols.
The twentieth-century artist who uses symbols is alienated because the system of symbols is a private one. After you have dealt with the symbols you are still private, you are still lonely, because you are not sure anyone will understand it except yourself. The ransom of privacy is that you are alone.
We thought of universities as the cathedrals of the modern world. In the middle ages, the cathedral was the center and symbol of the city. In the modern world, its place could be taken by the university.
Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
There’s an assumption that if someone writes in the first person it’s self-indulgent and self-regarding. I just look at it as a tool to understand the world and my experience in it. It’s not a tool to understand myself.
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas.
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
In 1958, Anne and I returned to Australia, where I got a very attractive research position at the Australian National University in Canberra. But soon I felt very isolated because at that time game theory was virtually unknown in Australia.
Concern for the symbol has completely disappeared from our science . And yet, if one were to give oneself the trouble, one could easily find, in certain parts at least of contemporary mathematics... symbols as clear, as beautiful, and as full of spiritual meaning as that of the circle and mediation. From modern thought to ancient wisdom the path would be short and direct, if one cared to take it.
Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience.
In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Young man, in mathematics you don't understand things. You just get used to them.
I remember, playing in college especially, I cried in almost every game I played. I just felt so much stress and pressure that I was letting everyone down if I didn't score a goal or win the game. I carried that weight with me into every game.
I don't know if anyone's ever done that, where they do a big college game and then do a game in the NFL. It would have to be a Monday game, obviously. If it were a Sunday game I wouldn't be able to do college and pro. Ideally, in a perfect world, I would love the challenge of trying to do both.
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