9780945726050
Science Awakening I: Egyptian, Babylonian And Greek Mathematics - B.L. van der Waerden
Scholar's Bookshelf (2005)
In Collection
#7201

Read It:
Yes
Mathematics, Mathematics, Babylonian, Mathematics, Egyptian, Mathematics, Greek, Science

Why History of Mathematics?
Every one knows that we are living in a technological era. But it is not often realized that our technology is based entirely on mathematics and physics. When we ride home on the streetcar in the evening, when we turn on the electric light and the radio, everything depends on cleverly constructed physical mechanisms based on mathematical calculations. But more than that! We owe to physics not only these pleasant articles of luxury, but, to a large extent, even our daily bread. Apart from the fact that our grains come to us, chiefly by steamer from overseas, our own agriculture would be far less productive without artificial fertilizers. Such fertilizers are chemical products, and chemistry depends on physics.
But science has not brought us blessings only. The destructive armaments which mankind uses at the present time to knock its own civilization to pieces are also products to which the development of mathematics and physics have inevitably led.
Our spiritual life is also influenced by science and technology, in a measure but rarely fully understood. The unprecedented growth of natural science in the 17th century was followed ineluctably by the rationalism of the 18th, by the deification of reason and the decline of religion; an analogous development had taken place earlier, in Greek times. In a similar manner the triumphs of technology in the 19th century were followed in the 20th by the deification of technology.
Unfortunately, man seems to be overly inclined to deify whatever is powerful and successful.

Product Details
Dewey 973
Format Paperback
Cover Price 29,95 €
No. of Pages 306

Notes
This in an opinionated and confident history of Greek mathematics. On issues of interpretation and historiography, a few sections are original and many are based on the classical German literature, not readily available to the modern reader. The problem is with the mathematics, where van der Waerden is very unhelpful. He follows the standard practice of simply reproducing or lightly paraphrasing the original sources. A typical section on Archimedes, which almost entirely lacks commentary, simply reproduces a number of proof and ends "All this is found in Archimedes, in essentially the same words" (p. 220).

This is especially ironic since van der Waerden himself portrays as a main reason for the demise of Greek geometry "the difficulty of the written tradition" (p. 266): "An oral explanation makes it possible to indicate the line segments with the fingers; one can emphasize essentials and point out how the proof was found. All of this disappears in the written formulation of the strictly classical style. The proofs are logically sound, but they are not suggestive. One feels caught in a logical mousetrap, but one fails to see the guiding line of thought. As long as there were no interruption, as long as each generation could hand over its method to the next, everything went well and science flourished. But as soon as some external cause brought about an interruption in the oral tradition, and only books remained, it became extremely difficult to assimilate the work of the great precursors and next to impossible to pass beyond it." (p. 266). This is exactly how we feel. It seems obvious, then, that a good history of Greek mathematics will aspire to recreate the qualities here ascribed to the oral traditions. Unfortunately, van der Waerden is generally happy to reproduce the "logical mousetraps" and leave it at that.

One further point is important to remember in this context. Today's mathematics tends to be congenial to "logical mousetraps" and shun intuition and applications. In Antiquity it was probably the other way around: it was precisely the mathematicians who were striving for more intuition and applications, while philosophical and other prejudices were exactly opposed to such a development. This inversion of the current roles is indicated in Plutarch: "Plato himself censured those ... who wanted to reduce the duplication of the cube to mechanical constructions, because [it is based on] a non-theoretical method; for in this manner the good in geometry is destroyed and brought to naught, because geometry reverts to observation instead of raising itself above this and adhering to the eternal, immaterial images in which the immanent God is the eternal God." (p. 163). In other words: the surviving mathematical texts are "censured" by non-mathematicans on non-mathematical grounds, whereas the subject matter screams out for a less formalistic treatment.