By Leo Corry

The area round us is saturated with numbers. they're a primary pillar of our sleek society, and accredited and used with hardly ever a moment suggestion. yet how did this situation end up? during this publication, Leo Corry tells the tale at the back of the belief of quantity from the early days of the Pythagoreans, up until eventually the flip of the 20 th century. He provides an summary of ways numbers have been dealt with and conceived in classical Greek arithmetic, within the arithmetic of Islam, in eu arithmetic of the center a while and the Renaissance, through the medical revolution, throughout to the maths of the 18th to the early twentieth century. concentrating on either foundational debates and useful use numbers, and displaying how the tale of numbers is in detail associated with that of the belief of equation, this e-book presents a priceless perception to numbers for undergraduate scholars, lecturers, engineers, expert mathematicians, and somebody with an curiosity within the background of arithmetic.

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The insight that integers and fractions can be written according to the same principles played a major historical role in allowing a broad, uniﬁed vision of number. Moreover, this insight teaches an important lesson about the developments we want to consider in this book, because the logic of numbers and the logic of history did not work in parallel here. Indeed, it was not the case that ﬁrst a clear idea developed of fractions and integers being entities of a same generic type (numbers) and thereafter a notational system developed for conveniently expressing this idea.

What is then the point in speaking about two separate ideas, cardinal and ordinal, if they always represent the same situation? Can they somehow be understood separately? The answer to these questions is that there may indeed be situations where one cardinal may be associated with more than one ordinal, but this will happen only in the inﬁnite case. Dealing with inﬁnite cardinals is a tricky business that has to be handled with extreme care, but I will give here a brief indication of some of the problems involved, CARDINALS AND ORDINALS | 15 so that the diﬀerence between ordinals and cardinals may at least be sensed.

It is habitual to refer to Hypatia of Alexandria (ca. 370– 415) as the last Greek mathematician (incidentally, Hypatia was also the ﬁrst woman mathematician in history to be known by name; her persona was brought to public attention in the 2009 Hollywood ﬁlm Agora, starring Rachel Weisz). Also in terms of NUMBERS AND MAGNITUDES IN THE GREEK TRADITION | 31 geography, the area of activity of Greek mathematicians spread from Asia Minor to the East, to Syracuse in Sicily to the West, and to Alexandria in Egypt to the South.