A Quote by James R Newman
In the simplest array of digits [Ramanujan] detected wonderful properties: congruences, symmetries and relationships which had escaped the notice of even the outstandingly gifted theoreticians.
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Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package."
Symmetries are the playing field on which the physical world works and which determine the rules of the game. The symmetries of nature determine for us things that remain constant, that can't be changed. Those are the guideposts in physics, the quantities like energy and momentum.
No one really understood music unless he was a scientist, her father had declared, and not just a scientist, either, oh, no, only the real ones, the theoreticians, whose language was mathematics. She had not understood mathematics until he had explained to her that it was the symbolic language of relationships. "And relationships," he had told her, "contained the essential meaning of life."
Mushrooms provide a vast array of potential medicinal compounds. Many mushrooms - such as portobello, oyster, reishi and maitake - are well-known for these properties, but the lion's mane mushroom, in particular, has drawn the attention of researchers for its notable nerve-regenerative properties.
I don't think I've left a trail of weeping women in my wake. I mean, the number of serious relationships I've had has not been into double digits.
The existence of symmetry laws is in full accordance with our daily experience. The simplest of these symmetries, the isotropy and homogeneity of space, are concepts that date back to the early history of human thought.
As my meditative experiences grew, I had wonderful relationships. I met the most wonderful women, who meditated and shared certain understandings that I had.
The seeds from Ramanujan's garden have been blowing on the wind and have been sprouting all over the landscape.
[On the stimulating effects of Ramanujan's mathematical legacy.]
There is great exhilaration in breaking one of these things. ... Ramanujan gives no hints, no proof of his formulas, so everything you do you feel is your own.[About verifying Ramanujan's equations in a newly found manuscript.]
It is not always easy to diagnose. The simplest form of stupidity - the mumbling, nose-picking, stolid incomprehension - can be detected by anyone. But the stupidity which disguises itself as thought, and which talks so glibly and eloquently, indeed never stops talking, in every walk of life is not so easy to identify, because it marches under a formidable name, which few dare attack. It is called Popular Opinion.
Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly-yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.
I think the most important work that is going on has to do with the search for very general and abstract features of what is sometimes called universal grammar: general properties of language that reflect a kind of biological necessity rather than logical necessity; that is, properties of language that are not logically necessary for such a system but which are essential invariant properties of human language and are known without learning. We know these properties but we don't learn them. We simply use our knowledge of these properties as the basis for learning.
NBC News found that FEMA has redrawn maps even for properties that have repeatedly filed claims for flood losses from previous storms. At least some of the properties are on the secret 'repetitive loss list' that FEMA sends to communities to alert them to problem properties.
Advice is offensive, not because it lays us open to unexpected regret, or convicts us of any fault which had escaped our notice, but because it shows us that we are known to others as well as to ourselves; and the officious monitor is persecuted with hatred, not because his accusation is false, but because he assumes that superiority which we are not willing to grant him, and has dared to detect what we desired to conceal.
What a gifted child is, in many ways, is a gifted learner. And what a gifted adult is, is a gifted doer. And those are quite separate domains of achievement.
President Obama is a gifted politician. He is gifted with rhetoric virtuosity. He is gifted with the ability to lie directly to camera without blinking. And he is gifted with some of the most incompetent conservative opposition in the history of the country.
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