"A genuine experience of the unexpected, in maths as much as in magic, demands of its performer at once originality of insight and a lightness of touch. Even a single step too many in a method renders ugly and clumsy the theorem or the trick." (Daniel Tammet, "Thinking in Numbers" , 2012)
"As geometers study shape, the student of calculus examines
change: the mathematics of how an object transforms from one state into
another, as when describing the motion of a ball or bullet through space, is
rendered pictorial in its graphs’ curves."
"Chess is a perfect arena for just such an exerted
exploration of the possible. Its chequered sea is very deep indeed. The
mathematics behind the game’s complexity are staggering. […] For all its
immensity, chess is a finite game. It is therefore at least conceivable that a machine
might one day be programmed with the knowledge, deep down in its nodes, of every
possible sequence of moves for every possible game. No combination, however ingenious,
would ever surprise it; every board position would be as familiar as a face."
"Human beings’ quest for meaning is perpetual; lack of
meaning is offensive to the mind, and whatever the scale of the problem, a
solution is a thing of beauty."
"In a universe teeming with numbers, no physical quantity
exists that coincides with a googol. A googol dwarfs the number of grains of
sand in all the world. Collecting every letter of every word of every book ever
published gets us nowhere near. The total number of elementary particles in all
of known space falls some twenty zeroes short."
"Like works of literature, mathematical ideas help expand our
circle of empathy, liberating us from the tyranny of a single, parochial point
of view. Numbers, properly considered, make us better people." (Daniel Tammet, "Thinking
in Numbers" , 2012)
"Probability is often expressed using large but finite
numbers: ‘one in a thousand’, ‘one in a million’. But perhaps the probability
of life, intelligent life, appearing somewhere in our universe is
infinitesimal. If so, a universe would need infinitely many planets to produce
even a finite number of civilisations (i.e., one)."
"Properly understood, the study of mathematics has no end:
the things we each do not know about it are infinite. We are all of us at sea
with some aspect or another."
"The engineer and the mathematician have a completely different understanding of the number pi. In the eyes of an engineer, pi is simply a value of measurement between three and four, albeit fiddlier than either of these whole numbers. [...] Mathematicians know the number pi differently, more intimately. What is pi to them? It is the length of a circle’s round line (its circumference) divided by the straight length (its diameter) that splits the circle into perfect halves. It is an essential response to the question, ‘What is a circle?’ But this response – when expressed in digits – is infinite: the number has no last digit, and therefore no last-but-one digit, no antepenultimate digit, no third-from-last digit, and so on." (Daniel Tammet, "Thinking in Numbers" , 2012)
"The barrier to an appreciation of mathematical beauty is not insurmountable, however. […] The beauty adored by mathematicians can be pursued through the everyday: through games, and music, and magic." (Daniel Tammet, "Thinking in Numbers" , 2012)
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