Number rules the universe.
Reason is immortal, all else mortal.
The highest form of pure thought is in mathematics”.
Nature’s great book is written in mathematical symbol.
Wir müssen wissen, wir werden wissen.
We must know, we will know.
Pure mathematics is，in its way，the poetry of logical
Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
< 拙译> 数学，当你正确地看待它时，不仅拥有真，而且拥有非凡的美 —— 一种犹如雕塑般冷峻而素朴的美，一种不引诱任何我们的较软弱天性的美，一种没有绘画和音乐那样富丽花俏的装饰的纯净之至的美，同时又能达到一种唯有最伟大的艺术才能表达的严格的完美。
The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
< 拙译> 正如在诗歌中一样，在数学中同样能找到真正的欢乐的精神，升华的快感，那种超越凡俗接近神祗的美妙感觉——它是最高级的卓越成就的试金石。
Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world-understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.
< 拙译> 数学是除了语言与音乐之外，人类心灵自由创造力的主要表达方式之一，而且它是通过理论的构建理解宇宙万物的普适工具。因此，数学必须始终是我们得传授给下一代的知识和技能的要素和我们要传承给下一代的文化的要素。
What we do may be small , but it has a certain character of permanence ; and to have produced anything of the slightest permanent interest , whether it be a copy of verses or a geometrical theorem , is to have done something utterly beyond the powers of the vast majority of men .
Archimedes will be remembered when
Aeschylus is forgotten, because languages die and mathematical
ideas do not. "Immortality" may be a silly word, but probably a
mathematician has the best chance of whatever it may mean.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
躺在临终病床上，天才的印度数学家拉马努金写下了谜一样离奇难解的函数，他说它们是在他的梦境中出现的，他对这些函数的性态有直觉的预感。一百年后的今天，研究人员说他们证明了拉马努金是对的。“我们解决了他的最后几封神秘的信件中的问题，对于研究这个数学领域的人来说，该问题已经悬而未决九十年了，” 美国艾莫利大学 (Emory University) 的日裔数学家小野（Ken Ono）说。
Researchers Unlock Mysterious Formula Written
By Ramanujan On His Death Bed
While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to him in dreams, with a hunch about how they behaved. Now 100 years later, researchers say they've proved he was right."We've solved the problems from his last mysterious letters. For people who work in this area of math, the problem has been open for 90 years," Emory University mathematician Ken Ono said.
Ramanujan, a self-taught mathematician born in a rural village in South India, spent so much time thinking about math that he flunked out of college in India twice, Ono said. But he sent mathematicians letters describing his work, and one of the most preeminent ones, English mathematician G. H. Hardy, recognized the Indian boy's genius and invited him to Cambridge University in England to study. While there, Ramanujan published more than 30 papers and was inducted into the Royal Society. "For a brief window of time, five years, he lit the world of math on fire," Ono told LiveScience. But the cold weather eventually weakened Ramanujan's health, and when he was dying, he went home to India.
It was on his deathbed in 1920 that he described mysterious functions that mimicked theta functions, or modular forms, in a letter to Hardy. Like trigonometric functions such as sine and cosine, theta functions have a repeating pattern, but the pattern is much more complex and subtle than a simple sine curve. Theta functions are also "super-symmetric," meaning that if a specific type of mathematical function called a Moebius transformation is applied to the functions, they turn into themselves. Because they are so symmetric these theta functions are useful in many types of mathematics and physics, including string theory.
Ramanujan believed that 17 new functions he discovered were "mock modular forms" that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren't super-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.
Ramanujan died before he could prove his hunch. But more than 90 years later, Ono and his team proved that these functions indeed mimicked modular forms, but don't share their defining characteristics, such as super-symmetry. The expansion of mock modular forms helps physicists compute the entropy, or level of disorder, of black holes.
In developing mock modular forms, Ramanujan was decades ahead of his time, Ono said; mathematicians only figured out which branch of math these equations belonged to in 2002. "Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died," Ono said.