Edward Frenkel Famous Quotes
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If you experience this feeling once, you will want to go back and do it again. This was the first time it happened to me, and like the first kiss, it was very special. I knew then that I could call myself mathematician.
Where there is no mathematics, there is no freedom.
What if at school you had to take an art class in which you were only taught how to pain a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it ... Of course this sounds ridiculous, but this is how math is taught.
It is really this "mathematical mindset" that seems to be most useful to those who are not trained to think as mathematicians.
Writing papers was the punishment we had to endure for the thrill of discovering new mathematics.
Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can't be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what's also amazing is that we own all of them. No one can patent a mathematical formula, it's ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It's too precious to be given away to the "initiated few." It belongs to all of us.
In fact some of the best ideas come when you least expect them,
As someone told me later, writing papers was the punishment we had to endure for the thrill of discovering new mathematics. This was the first time I was so punished.
More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try something else. These are the moments of frustration and despair. You feel that you have wasted an enormous amount of time, with nothing to show for it. This is hard to stomach. But you can never give up. You go back to the drawing board, you analyze more data, you learn from your previous mistakes, you try to come up with a better idea. And every once in a while, suddenly, your idea starts to work. It's as if you had spent a fruitless day surfing, when you finally catch a wave: you try to hold on to it and ride it for as long as possible. At moments like this, you have to free your imagination and let the wave take you as far as it can. Even if the idea sounds totally crazy at first.
The laws of Nature are written in the language of mathematics. Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. In our world, increasingly driven by science and technology, mathematics is becoming, ever more, the source of power, wealth, and progress. Hence those who are fluent in this new language will be on the cutting edge of progress.
How to describe the excitement I felt when I saw this beautiful work and realized its potential? I guess it's like when, after a long journey, suddenly a mountain peak comes in full view. You catch your breath, take in its majestic beauty, and all you can say is "Wow!" It's the moment of revelation. You have not yet reached the summit, you don't even know yet what obstacles lie ahead, but its allure is irresistible, and you already imagine yourself at the top. It's yours to conquer now. But do you have the strength and stamina to do it?
As the story goes, Albert Einstein's wife Elsa remarked, upon hearing that a telescope at the Mount Wilson Observatory was needed to determine the shape of space-time: Oh, my husband does this on the back of an old envelope.
Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.
Michael Harris opens the doors and gently guides you into a magic world. Once inside, you can't help but feel mesmerized, eager to see how deep the rabbit hole goes. And no wonder: a major thinker of our time is talking to you about math and so much more, like you've never heard before.
In fact, it is virtually impossible for students to do their own research without someone guiding their work. Having an advisor is absolutely essential.
