Showing posts with label Terence Tao. Show all posts
Showing posts with label Terence Tao. Show all posts

"If we all thought the same way and had similar philosophy, mathematics would be a much poorer environment." - Terence Tao

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"If we all thought the same way and had similar philosophy, mathematics would be a much poorer environment." - Terence Tao
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"Mathematicians often work on pure problems that do not have any applications for 20 years, and then a physicist or computer scientist or engineer has a real-life problem that requires the solution of a mathematical problem and finds that someone already solved it 20 years ago. When Einstein developed his theory of relativity, he needed a theory of curved space. Einstein found that a mathematician devised exactly the theory he needed more than 30 years earlier." - Terence Tao

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"Mathematicians often work on pure problems that do not have any applications for 20 years, and then a physicist or computer scientist or engineer has a real-life problem that requires the solution of a mathematical problem and finds that someone already solved it 20 years ago. When Einstein developed his theory of relativity, he needed a theory of curved space. Einstein found that a mathematician devised exactly the theory he needed more than 30 years earlier." - Terence Tao
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"Of course, accuracy is much less of an objective standard than truth, as it is difficult to attain consensus on exactly what one means by “close” or “typical”, or to decide on exactly what threshold of accuracy is acceptable for a given situation." - Terence Tao

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"Of course, accuracy is much less of an objective standard than truth, as it is difficult to attain consensus on exactly what one means by “close” or “typical”, or to decide on exactly what threshold of accuracy is acceptable for a given situation." - Terence Tao
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"Batch low-intensity tasks together to take advantage of economies of scale and to reduce distraction." - Terence Tao

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"Batch low-intensity tasks together to take advantage of economies of scale and to reduce distraction." - Terence Tao
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"Enthusiasm can be infectious; one reason why you should attend talks and conferences is to find out what other exciting things are happening in your field (or in nearby fields), and to be reminded of the higher goals in your area (or in mathematics in general). A good talk can recharge your own interest in mathematics, and inspire your creativity." - Terence Tao

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"Enthusiasm can be infectious; one reason why you should attend talks and conferences is to find out what other exciting things are happening in your field (or in nearby fields), and to be reminded of the higher goals in your area (or in mathematics in general). A good talk can recharge your own interest in mathematics, and inspire your creativity." - Terence Tao
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"In school, we only give you problems that you can solve, and it gives you a very misleading idea of mathematics." - Terence Tao

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"In school, we only give you problems that you can solve, and it gives you a very misleading idea of mathematics." - Terence Tao
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"Think ahead to understand the way forward; ask yourself dumb questions to understand the way before." - Terence Tao

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"Think ahead to understand the way forward; ask yourself dumb questions to understand the way before." - Terence Tao
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"At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate." - Terence Tao

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"At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate." - Terence Tao
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"Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely." - Terence Tao

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"Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely." - Terence Tao
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"Unsolicited surprise requests from strangers are essentially guaranteed to be met with a negative response." - Terence Tao

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"Unsolicited surprise requests from strangers are essentially guaranteed to be met with a negative response." - Terence Tao
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"I don’t have any magical ability. I look at a problem, and it looks something like one I’ve done before. I think maybe the idea that worked before will work here. . . . After awhile, I figure out what’s going on.” - Terence Tao

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"I don’t have any magical ability. I look at a problem, and it looks something like one I’ve done before. I think maybe the idea that worked before will work here. . . . After awhile, I figure out what’s going on.” - Terence Tao
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"Maybe when I'm in my 60s, I'll look back at what I've done, but now I would rather work on the problems." - Terence Tao

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"Maybe when I'm in my 60s, I'll look back at what I've done, but now I would rather work on the problems." - Terence Tao

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"Education is a complex, multifaceted, and painstaking process, and being gifted does not make this less so." - Terence Tao

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"Education is a complex, multifaceted, and painstaking process, and being gifted does not make this less so." - Terence Tao
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"Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing." - Terence Tao

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"Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing." - Terence Tao
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"Ultimately, it seems that what Deolalikar has really proven is not that P != NP, but rather that pp != ppp (for which we have a simple half-page proof)…" - Terence Tao

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"Ultimately, it seems that what Deolalikar has really proven is not that P != NP, but rather that pp != ppp (for which we have a simple half-page proof)…" - Terence Tao
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"To give a (somewhat artificial) analogy: as I see it now, the paper is like a lengthy blueprint for a revolutionary new car, that somehow combines a high-tech engine with an advanced fuel injection system to get 200 miles to the gallon. The FO(LFP) objections are like a discovery of serious wiring faults in the engine, but the inventor then claims that one can easily fix this by replacing the engine with another, slightly less sophisticated engine. The XORSAT and solution space objections are like a discovery that, according to the blueprints, the car would run just as well if the gasoline fuel was replaced with ordinary tap water. As far as I can tell, the response to this seems to be equivalent to “That objection is invalid – everyone knows that cars can’t run on water.” The pp/ppp objection is like a discovery that the fuel is in fact being sent to a completely different component of the car than the engine." - Terence Tao

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"To give a (somewhat artificial) analogy: as I see it now, the paper is like a lengthy blueprint for a revolutionary new car, that somehow combines a high-tech engine with an advanced fuel injection system to get 200 miles to the gallon.
The FO(LFP) objections are like a discovery of serious wiring faults in the engine, but the inventor then claims that one can easily fix this by replacing the engine with another, slightly less sophisticated engine.
The XORSAT and solution space objections are like a discovery that, according to the blueprints, the car would run just as well if the gasoline fuel was replaced with ordinary tap water. As far as I can tell, the response to this seems to be equivalent to “That objection is invalid – everyone knows that cars can’t run on water.”
The pp/ppp objection is like a discovery that the fuel is in fact being sent to a completely different component of the car than the engine." - Terence Tao

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"Algebra is the mathematics of the "equals" sign, of identity, and of the "main term"; analysis is the mathematics of the "less than" sign, of magnitude, and of the "error term". Algebra prizes structure, symmetry, and exact formulae; analysis prizes smoothness, stability, and estimates. It is because of these complementary foci that either subfield of mathematics looks strange when viewed through the lens of the other." - Terence Tao

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"Algebra is the mathematics of the "equals" sign, of identity, and of the "main term"; analysis is the mathematics of the "less than" sign, of magnitude, and of the "error term".
Algebra prizes structure, symmetry, and exact formulae; analysis prizes smoothness, stability, and estimates.
It is because of these complementary foci that either subfield of mathematics looks strange when viewed through the lens of the other." - Terence Tao
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"The music of the primes is a chord." - Terry Tao

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"The music of the primes is a chord." - +Terry Tao
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"Volume grows spatially slower than scaling." - Terence Tao

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"Volume grows spatially slower than scaling." - +Terence Tao
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