All Quotes

"‘…the transition [to the Hindu number system], far from being immediate, extended over long centuries. The struggle between the Abacists, who defended the old traditions, and the Algorists, who advocated the reform, lasted from the eleventh to the fifteenth century and went through all the usual stages of obscurantism and reaction. In some places, Arabic numerals [more precisely, Hindu numerals] were banned from official documents; in others, the art was prohibited altogether. And, as usual, prohibition did not succeed in abolishing, but merely served to spread bootlegging, ample evidence of which is found in the thirteenth century archives of Italy, where, it appears, merchants were using the Arabic numerals as a sort of secret code.’"

"‘The change did not come about without obstruction from the representatives of custom thought. An edict of A.D. 1259 forbade the bankers of Florence to use the infidel symbols, and the ecclesiastical authorities of the University of Padua in A.D. 1348 ordered that the price list of books should be prepared not in “ciphers”, but in plain letters.’"

"All the algorithms for fractions now used were invented by the Hindus. The Greek treatment of fractions never advanced beyond the level of the Egyptian Rhind papyrus. […] This inability to treat a fraction as a number on its own merits is the explanation of a practice [which] was as useless as it was ambiguous. […] When we remember that the Greeks and Alexandrians continued this extraordinary performance, there is nothing remarkable about the small progress which they achieved in their arithmetic. What is remarkable is that a few of them like Archimedes should have discovered anything at all about series of numbers involving fractional quantities."

"As my father was a public official away from our homeland in the Bugia customs house established for the Pisan merchants who frequently gathered there, he had me in my youth brought to him, looking to find for me a useful and comfortable future; there he wanted me to be in the study of mathematics and to be taught for some days. There from a marvelous instruction in the art of the nine Indian figures, the introduction and knowledge of the art pleased me so much above all else, and I learnt from them, whoever was learned in it, from nearby Egypt, Syria, Greece,Sicily and Provence, and their various methods, to which locations of business I travelled considerably afterwards for much study, and I learnt from the assembled disputations. But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method."

"[negative numbers] ‘…darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple.’"

"The sum of two positive quantities is positive; of two negative is negative; of a positive and a negative is their difference; or, if they are equal, zero. The sum of zero and negative is negative; of positive and zero is positive; of two zeros is zero (31)."

"“And I like it because it pushes me and it gives me that pressure to be at your peak all the time — to be beautiful physically, to be able to say something at the snap of anyone’s finger.”"

"In subtraction, the less is to be taken from the greater, positive from positive; negative from negative. When the greater, however, is subtracted from the less, the difference is reversed. Negative taken from zero becomes positive; and positive [taken from zero] becomes negative. Zero subtracted from negative is negative; from positive, is positive; from zero, is zero. When positive is to be subtracted from negative, and negative from positive, they must be thrown together (32-33)."

"The product of a negative quantity and a positive is negative; of two negatives, is positive; of two positives, is positive. The product of zero and negative, or of zero and positive, is zero; [the product] of two zeros, is zero. (34)."

"Positive, divided by positive, or negative by negative, is positive. Zero, divided by zero, is zero. Positive, divided by negative, is negative. Negative, divided by positive, is negative. Positive, or negative, divided by zero, is a fraction with that for denominator: or zero divided by negative or positive. (35-36)."

"The square of negative or positive is positive; of zero, is zero. The root of a square is such as was that from which it was raised [i.e. either positive or negative]. (37)."

"In a linear equation in one unknown, the difference of the two known terms taken in the reverse order, divided by the difference of the coefficients of the unknown (is the value of the unknown)."

"Of the unknowns, their squares, cubes, fourth powers, fifth powers, sixth powers, etc., addition and subtraction are performed of the like; of the unlike they mean simply their statement severally."

"Multiply half the difference of the tabular differences crossed over and to be crossed over by the residual arc and divide by 900’. By the result so obtained increase or decrease half the sum of the (two) differences, according as this (semi-sum) is less or greater than the difference to be crossed over. We get the true functional differences to be crossed over."

"The old calculations dealing with planets based on the system of Brahma have become erroneous in course of past ages and therefore I, the son of Jishnugupta would like to clarify them."

"Florian Cajori, the noted historian, summed up the matter in an extraordinarily suggestive manner: The perversity of fate has willed it that the equation y2 = nx2 + 1 should now be called Pell’s Problem, while in recognition of Brahmin scholarship it ought to be called the “Hindu Problem.” It is a problem that has exercised the highest faculties of some of our greatest modern analysts. Indian mathematical historians would like to call it the Brahmagupta–Bhaskara problem, keeping in mind that Bhaskar perfected Brahmagupta’s method of solution in the twelfth century; Bhaskara used “Chakravala”, or a cyclic process, to improve Brahmagupta’s method by doing away with the necessity of finding a trial solution."

"This present art, in which we use those twice five Indian figures, is called algorismus."

"In case of multiples from the units place, the value of each place (sthana) is ten times the value of the preceding place."

"The importance of the creation of the zero mark can never be exaggerated. This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol but helpful power, is the characteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power.’"

"The cord stretched in the diagonal of an oblong produces both [areas] which the cords forming the longer and shorter sides of an oblong produce separately."

"The diagonal cord of a rectangle makes both (the squares) that the vertical side and the horizontal side make separately."

"The cord stretched in the diagonal of an oblong produces both [areas] which the cords forming the longer and shorter sides of an oblong produce separately."

"The diagonal cord of a rectangle makes both (the squares) that the vertical side and the horizontal side make separately."

"Some of the things, which belong particularly to the history of mathematics, we will not refrain from attributing to Pythagoras himself. Among them is the Pythagorean theorem, which we want to preserve under all circumstances. (Cantor 1880: 129)"

"In the Shulba Sutra appended to Baudhayana’s Shrauta Sutra, mathematical instructions are given for the construction of Vedic altars. One of its remarkable contributions is the theorem usually ascribed to Pythagoras, first for the special case of a square (the form in which it was discovered), then for the general case of the rectangle: “The diagonal of the rectangle produces the combined surface which the length and the breadth produce separately.”"

"The first writer to attribute this proposition to Pythagoras is Vitruvius, hardly a reliable witness. From then on, this account became more widespread, but always in connection with the famous hecatomb that Pythagoras is said to have offered in celebration of discovering the proposition—an anecdote that severely undermines the credibility of the entire story. This sacrifice is incompatible with the strict prohibition of all bloody sacrifices, which writers of the same period, indeed often the very same ones who elsewhere recount the hecatomb, have handed down to us from the Pythagorean ritual laws. Cicero himself took offense at this anecdote, and in the latest Neopythagorean tradition, the bloody sacrifice is replaced by that of an ox formed from flour. For this reason, the hecatomb is not only incongruous with the Pythagoreans, but also with the Pythagoreans themselves. Proclus, an insightful writer, expresses himself remarkably vaguely: ‘When we listen to those who want to tell old stories, we find that they trace this theorem back to Pythagoras.’ As this shows, he too was unaware of any reliable source."

"‘These operations are all founded on a very distinct conception of what happens in the case of an eclipse, and on the knowledge of this theorem, that, in a right-angled triangle, the square on the hypotenuse is equal to the squares of the other two sides. It is curious to find the theorem of PYTHAGORAS in India, where, for aught we know, it may have been discovered, and from whence that philosopher may have derived some of the solid, as well as the visionary speculations, with which he delighted to instruct or amuse his disciples.’"

"If we listen to those who like to record antiquities, we shall find them attributing this theorem to Pythagoras and saying that he sacrificed an ox on its discovery. For my part, though I marvel at those who first noted the truth of this theorem, I admire more the author of the Elements for the very lucid proof by which he made it fast."

"It is more likely that Pythagoras was influenced by India than by Egypt. Almost all the theories, religions, philosophical and mathematical taught by the Pythagoreans, were known in India in the sixth century B.C., and the Pythagoreans, like the Jains and the Buddhists, refrained from the destruction of life and eating meat and regarded certain vegetables such as beans as taboo" "It seems that the so-called Pythagorean theorem of the quadrature of the hypotenuse was already known to the Indians in the older Vedic times, and thus before Pythagoras."

"If we consider the results obtained together, we will not be able to doubt the conclusion to be drawn from them. The ancient priestly geometry of the Indians not only knew the Pythagorean theorem, but it even played the main role in their calculations; with its help, they constructed elements that the Greeks found in a completely different way; with its help, they also found the irrational quantities. And it was precisely these two things that Pythagoras introduced into the Greek-Italian world; these two things, according to the Greeks, he invented. Indeed, even more! The way in which Pythagoras proved his theorem was also, in all likelihood, the same as that which we find in the Vedic Shulba Sutras. After examining the Shulba Sutras, we could have said: If Pythagoras really was in India, as we previously suggested, and initiated himself into the priestly wisdom of the Brahmins, then he could have brought precisely these theorems of geometric science to Greece; — and history has been telling us for several millennia now that this was indeed the case!"

"Aging gracefully, I stay away from toxic people or stress. I try to keep my private life really private. I focus on my family. We all know about eating well and drinking water. But I think it's more internal. It's what happens in your mind."

"Aging is representative of all the wisdom one gains through the years. I am not afraid of it. Instead, I embrace it."

"When you are happy and you give back to the people, the feeling you get from there is something you cannot equate from receiving luxuries or getting external validation."

"I try to keep my private life private and I focus on my family."

"My first priority, first and foremost, is my family, especially my children who are the be-all and end-all.”"

"I don't believe in cosmetic surgery. I believe in aging gracefully and I can do that with healthy living, and of course, having a good choice in your skin regimen."

"If you are happy, you’re content, you know you’re doing something purposeful in your life, it doesn’t matter if you’re not wearing any concealer, and your hair is not blow-dried or just tied in a bun. Invest more in friends. Invest in relationships and your own character."

"I’ve always, always dreamed of a daughter that could dance. When she was in my tummy, I hoped, you know, she would like to dance the way I like to dance, and fortunately she does. She is so much better than me."

"I’m quite conservative in disciplining our child, We want to raise them in a way that they do not forget the important values."

"For me, [my rule] is always [to choose] what’s comfortable for you to wear and you will always look elegant."

"What cancer has given me ... is time. It has given me time to think about my mortality and what my life is worth. At the end of the day, what makes your life worth it is not so much what you’ve done but whom you loved."

"In Fukuoka, more than anywhere else in Japan or in the world where I have been in the company of Sato-sensei for the last two decades, I have learned my most important lessons as a filmmaker. The first is to work on each film as if it were my last. The second, to be unafraid of failure. The third, and above everything else, is to detach from both pain and glory."

"I hope to have a body of work on women, children and religion."

"Together, let us dream of peace and let us each waking day be an occasion to say yes….., let us dream, let us hope, let us act together."

"This time, let's learn from our mistakes."

"I think so. It's not mine. It's God’s. It's for everybody. Or else, I wouldn't be teaching, if I don't want to share myself."

"Friendship. Before, during, and after [marriage]"

"It's for the country! And this is the first time that I'm asked to do a film that's for the country! It's not my film!"

"“It’s not what people think it is. It’s a lot of hard work because it’s not a common job. It’s not the normal path to success.”"

"I’ve learned to accept that life has passed. It’s not going to come back, but I can come back to it and relish it. I can share it. I can still enjoy it by remembering it. What’s in front of me right now is the challenge to trust in the goodness of life na (that) it’s worth it."