In my view, it is the objectivity of mathematical knowledge that is the source of its limitless possibilities. This quality distinguishes mathematics from any other type of human endeavor. I believe that understanding what is behind this quality will shed light on the deepest mysteries of physical reality, consciousness, and interrelations between them. In other words, the closer we are to the Pla...

2015-09-13 21:13

In my view, it is the objectivity of mathematical knowledge that is the source of its limitless possibilities. This quality distinguishes mathematics from any other type of human endeavor. I believe that understanding what is behind this quality will shed light on the deepest mysteries of physical reality, consciousness, and interrelations between them. In other words, the closer we are to the Platonic world of math, the more power we will have to understand the world around us and our place in it. Luckily, nothing can stop us from delving deeper into this Platonic reality and integrating it into our lives. What’s truly remarkable is mathematics’ inherent democracy: while some parts of the physical and mental worlds may be perceived or interpreted differently by different people or may not even be accessible to some of us, mathematical concepts and equations are perceived in the same way and belong to all of us equally . No one can have a monopoly on mathematical knowledge; no one can claim a mathematical formula or idea as his or her invention; no one can patent a formula! Albert Einstein, for example, would not be able to patent his formula E = mc 2 . That’s because, if correct, a mathematical formula expresses an eternal truth about the universe. Hence no one can claim ownership of it; it is ours to share. 14 Rich or poor, black or white, young or old –no one can take these formulas away from us. Nothing in this world is so profound and elegant, and yet so available to all.

Mathematics and science in general are often presented as cold and sterile. In truth, the process of creating new mathematics is a passionate pursuit, a deeply personal experience, just like creating art and music. It requires love and dedication, a struggle with the unknown and with oneself, which elicits strong emotions. And the formulas you discover really do get under your skin, just like the ...

2015-09-13 20:28

Mathematics and science in general are often presented as cold and sterile. In truth, the process of creating new mathematics is a passionate pursuit, a deeply personal experience, just like creating art and music. It requires love and dedication, a struggle with the unknown and with oneself, which elicits strong emotions. And the formulas you discover really do get under your skin, just like the tattooing in the film.

Think about it this way: mathematics and physics are like two different planets; say, Earth and Mars. On Earth, we discover a relation between different continents. Under this relation, every person in Europe gets matched with one in North America; their heights, weights, and ages are the same. But they have opposite genders (this is like switching a Lie group and its Langlands dual Lie group). Th...

2015-09-13 16:41

Think about it this way: mathematics and physics are like two different planets; say, Earth and Mars. On Earth, we discover a relation between different continents. Under this relation, every person in Europe gets matched with one in North America; their heights, weights, and ages are the same. But they have opposite genders (this is like switching a Lie group and its Langlands dual Lie group). Then one day we receive a visitor from Mars who tells us that on Mars they have also discovered a relation between their continents. Turns out every Martian on one of their continents can be matched with a Martian on another continent, so that their heights, weights, and ages are the same, but... they have opposite genders (who knew Martians had two genders, just like us?). We can’t believe what we are hearing: it appears that the relation we have on Earth and the relation they have on Mars are somehow connected. But why?

This is really a question about the nature of mathematical insight. The ability to see patterns and connections that no one had seen before does not come easily. It is usually the product of months, if not years, of hard work. Little by little, the inkling of a new phenomenon or a theory emerges, and at first you don’t believe it yourself. But then you say: “what if it’s true?” You try to test...

2015-09-13 11:16

This is really a question about the nature of mathematical insight. The ability to see patterns and connections that no one had seen before does not come easily. It is usually the product of months, if not years, of hard work. Little by little, the inkling of a new phenomenon or a theory emerges, and at first you don’t believe it yourself. But then you say: “what if it’s true?” You try to test the idea by doing sample calculations. Sometimes these calculations are hard, and you have to navigate through mountains of heavy formulas. The probability of making a mistake is very high, and if it does not work at first, you try to redo it, over and over again. 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.

Itâ€™s useful to think about mathematics as a whole as a giant jigsaw puzzle, in which no one knows what the final image is going to look like. Solving this puzzle is a collective enterprise of thousands of people. They work in groups: here are the algebraists laboring over their part of the puzzle, here are the number theorists, here are the geometers, and so on. Each group has been able to create...

2015-09-13 10:05

It’s useful to think about mathematics as a whole as a giant jigsaw puzzle, in which no one knows what the final image is going to look like. Solving this puzzle is a collective enterprise of thousands of people. They work in groups: here are the algebraists laboring over their part of the puzzle, here are the number theorists, here are the geometers, and so on. Each group has been able to create a small “island” of the big picture, but through most of the history of mathematics, it has been hard to see how these little islands will ever join up. As a result, most people work on expanding those islands of the puzzle. Every once in a while, however, someone will come who will see how to connect the islands. When this happens, important traits of the big picture emerge, and this gives a new meaning to the individual fields.

Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in the search for truth. Georg Cantor, creator of the theory of infinity, wrote: “The essence of mathematics lies in its freedom.” Mathematics teaches us to rigorously analyze reality, study the facts, follow them wherever they lead. It liberates us from dogmas and prejudice, nurtures the capac...

2015-09-12 23:15

Mathematics is a way to break the barriers of the conventional, an expression of unbounded imagination in the search for truth. Georg Cantor, creator of the theory of infinity, wrote: “The essence of mathematics lies in its freedom.” Mathematics teaches us to rigorously analyze reality, study the facts, follow them wherever they lead. It liberates us from dogmas and prejudice, nurtures the capacity for innovation. It thus provides tools that transcend the subject itself.

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2017-06-20 20:06

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2015-09-13 21:13

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2015-09-13 20:28

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2015-09-13 16:41

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2015-09-13 11:16

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2015-09-13 10:05

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2015-09-12 23:15