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THE HONGKONG DAILY PRESS, MONDAY, MAY DTH, 1924
THE BEGINNINGS OF MATHEMATICS.
GREEK SUPREMACY.
CHINA'S CONTRIBUTION, IN 3,000 14.C.
The Hon. Bertrand Russell, reviewing a recently published book on this sul ject, writes ia a Home paper:--
Mathematicians are less interested than other learned men in the history of their subject, because it is possible to arrive at truth in mathematics, and the truth arriv
dat is not historical. The chronological order of discovery corresponds only very loosely with the logical order, which is the one to be adopted in exposition, or with the order of difficulty, which is the one to be adopted in teaching. "Neverthe less, the history of mathematics, espe cially of early mathematies, has consider- able interest on its own nessunt, and 15 a part of the general history of culture. Various things surprise one about it-the way discoveries are forgotten if they come too seen, the slowness with which im- provements travel from one nation to another, and the small number of in- dividuals upon whom fundamental ad vances depend.
The pre-eminence of the Greeks wAS regarded as indubitable by our grand. fathers, but was based upon their literary and artistic achievements. Modera cons noisseurs, who know far more than was formerly known of Egyptian art, early Chines art, and even the art of the cave-man, are inclined to dispute Greek supremacy. In fact, however, it exists, but in a different sphere, the sphere of mathematics. Many ancient nations pro- duced good art and good literature. but the Greeks alone invented deductive roying Burlid is a far mere astonish: ing product than Aeschylus. Without Greek literature the world would to-day be pretty much what it is; without Greek mathematics our Western virilisation would not exist, since science and indus trialism could not have arisen. It is true, of course, that mathematics existed elsewhere-in Egypt, in Babylonia in India. aul China. But what existed in these countries, as compared with what the Greeks created, was no more than the Balding of infants. Mr. Sinith in his, history remarks, for example, that that Hindus enatelated the theorem of Patha- goras, but adds that there is no reason. for believing that the Hindu had the slightest idea of the nature of geometric proof." In all likeblood the same true of the Egyptians, from whom Pythagoras is supposed to have learnt.
PREMATURE DISCOVERIES.
As an example of a discovery coming too 5000, wo ny mention Aristarchus Ord ventury, B.C), who discovered that the earth goes round the sun, and in yented methods of measuring the dis tance of the sun and moon from the earth which, in the hand of Eratosthenes, gave very fairly accurate results (Eratos- then, by the way, calculated the earth's diameter at 7.500 miles--a sult so near the truth that it must have owed a good deal of luck.) But to revolution in men's general outlook resulted from this anti- cipation of Copernicus, which was spou forgotten. The inuence of Copernicus depended upon, Kepler, Galileo, Newton, And the Inquisition: without their help he would have been as ineffective as Aristarchus.
Mr. Smith's history is so written as not to require any knowledge of mathematics beyond what most people, learn at school.
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8.8.
192. to.
aldressed as foildiya:
attributed to n presumably mythical per- son named Fu Hai, supposed to have ived about 3,000 B.Ct Leibniz; who came to know the diagrams through a Jesuit tricod. suggested that they represented the numbers from 6 to in the binary senle. As to this. Mr. Smith remarks merely that the Leibniz theory. " that these symbols had some connection with binary numerals, has no historical foundation in the King as originally written." Per contra, Mr. Arthur Waley, departing for once from the realms of poury, has written an article (Bulletin of the School of Oriental Studies, 1021) suggesting a possibility that Leibniz maj have been right. He remarks that "per- haps the most interesting point is that the diagrams employ the method of
It is illustrated by portraits and enliven-value by position, which is the dis- ed by occasional biographical curiosities. tinguishing feature of pur Arabic' nota- There is room for debate as to the best tion": If so, this method was invented method of arranging the narrative in a in China long before any other country history of mathematics, and it may Le knew of it. questioned whether Mr. Smith has been
There is one all error in Mr. Smith's altogether wise in this respect. He first account of China. He states that Marcus takes a period for instance, 30 BC. to Aurelius sent an Embassy to that conn
A.D. and then divides his account of try. The fact is that certain Syrian the period by untions. This has several merchants arrived, and said they came drawbacks. There is usually no natural as Ambassadors from the Roman Em- division of the subject-matter at the peror" An-Tun" (Antoninu); but there dates chosen, and after the Renaissance was nobody to examine their credentials, there is no object in classifying European so there is no reason to believe that they mathematicians by, their nationality. The
were speaking the trath." reason given for choosing the dates 300 B.C. and 500 D. is that these dates ranrk, approximately, the period of ine fluence of the greatest mathematical school of ancient times, the school of Alexandria.' But this school was-per- fectly continuous with previous Greek Diathematics, its separation from which is quite artificial, and in the East the dates in question to not mark any sort | of epoch. It would have been better to treat early mathematics by nation-first, those that iofuenced Greece (Egypt and Babylonia): then Greece: then Fodia, Chinn, etc; each down to the period when European influence (other than that resulting from Alexander's conquest) began. Then should come Mathometan mathematics, and then that of modern Euro, treated as one development, not divided by nations.
VALUE BY POSITION. Although the Greeks surpassed all other ancients in deductive reasoning, there was one inatter of great importance in which many others surpassed them, namely, the method of numeration. Tho Greeks and Romans never discovered the plan of making the value of a digit depend upon its position, which requires a symbol for zero. The Indians, perhaps the Babylonis and (some say) the Chinese had such a plan. The Arabs seem to have derived it from the Indian." Medieval Europe. derived it from the Arabs, owing to the accident that. Leonardo Pisano (13th century) was the son of a man in charge of an Italian warehouse in North Africa, and was taught arithmetic by a Moorish school- master. Commerce has been at all times. the chief cause of the spread of ideas from one civilisation, to another; our in- tellectual debt to cupidity can hardly be exaggerated
Whether the system of wine by posi
tion" was ever discovered in China in z | moot point, of considerable interest. One of the five sacred books of Confucianism, the "I King," or Books of Changes, which is generally accepted as more or less unintelligible, contains exty-four diagrama, derived from eight diagrams
·(Continued on next column.)"tem
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