Love and Math的笔记(17)

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  • 任平生

    任平生 (能吃能睡,没心没肺)

    朗兰兹懂很多语言:英语、法语、德语、俄语和土耳其语。 作者觉得朗兰兹非凡的语言能力与他能在不同数学领域间建立联系是有关系的。 盖尔范德自比为数学界的莫扎特:很多作曲家都因个别突出的作品而被人们记住。但莫扎特不是这样,莫扎特的所有作品造就了他这个天才。

    2014-01-02 21:58   1人喜欢

  • [已注销]

    [已注销]

    问题1: 弗拉基米尔卡扎科夫(Vladimir Kazakov)是怎么用矩阵模型来证明德国数学家约翰哈勒尔(John Harer)和唐查吉尔(Don Zagier)的“组合论问题”(combinatorial problem)的? 量子场论的拉格朗日(Lagrangian)函数,并用拉格朗日函数解决了这个问题。 具体方法呢? 问题2: 怎么理解福克斯说的作者论文的意义 “n次多项式有不等根的判别式,而我的研究成果可以用来描述判别式的纤维拓扑结构,等等“

    2017-06-20 20:06

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    [已注销]

    对于自然数n的每一个约数(每一个辫子中线的数量),存在群Bn'的贝蒂数,该贝蒂数与该约数的“欧拉函数”Eluer function相等。 作者发现辫群与数论之间存在一些隐藏联系。 在知识的前沿领域探寻新的规律,是一件令人神魂颠倒、兴奋不已的事情,而坐在桌旁厘清思路,把这些新发现写成论文,其乐趣与研究本身却有天壤之别。 《泛函分析及应用》《Functional Analysis and Applications》 Gelfand-Fuchs cohomology

    2017-06-20 19:30

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    [已注销]

    欧拉函数以一个自然数为任意自然数d赋值,记作∮(d),表示数值在1和d之间且与d互质的整数的个数,即与d没有公约数(当然,1除外)的整数的个数。假设d=6,那么,1与6互质;与2不互质(2是6的约数);与3、4、6也不互质。简言之,在1与6之间,与6互质的自然数有两个,分别是1和5.因此6的欧拉函数等于2,记作∮(6)=2。 欧拉函数在实践中的应用: 1,可用于在线交易,作为信用卡号码加密的RSA加密演算法。

    2017-06-20 19:17

  • 气死我了💢

    气死我了💢 (没有签名档)

    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

  • 气死我了💢

    气死我了💢 (没有签名档)

    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

  • 气死我了💢

    气死我了💢 (没有签名档)

    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

  • 气死我了💢

    气死我了💢 (没有签名档)

    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

  • 气死我了💢

    气死我了💢 (没有签名档)

    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...

    2015-09-13 10:05

  • 气死我了💢

    气死我了💢 (没有签名档)

    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

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Love and Math

>Love and Math