MATHEMATICS 



3697 



MATHER 



Story of Mathematics. As long ago as 3000 

 B.C. the Egyptians knew a great deal about 

 mathematics. Many of their methods, to be 

 sure, were cumbersome, but arithmetic, algebra 

 and geometry were all understood to some 

 extent. The Babylonians, too, knew some- 

 thing of the science, of which they made 

 use in their studies in astronomy. But only 

 with the Greeks was the real science of mathe- 

 matics developed. Though they worked out 

 to a certain extent a theory of numbers, it 

 was in geometry that they were chiefly inter- 

 ested, and some of their great geometers left 

 little to be discovered in certain phases of that 

 subject (see GEOMETRY). It seems strange 

 that the practical Romans should have made 

 so little contribution to the subject, but not so 

 strange that the theorizing, mystical scholars 

 of the Middle Ages should have neglected it. 



Meanwhile, however, the Oriental nations 

 had taken up mathematics, and the Hindus 

 and Arabs developed to a creditable degree 

 arithmetic, algebra, geometry and even as- 

 tronomy. It is not fair to give, as is usually 

 done, the credit for the modern system of 

 numbers to the Arabs, for the Hindus in- 

 vented it, and the Arabs merely borrowed it. 

 Interesting to note is the fact that the Persian 

 Omar Khayyam, whose Rubaiyat is world- 

 famous, was not only a poet but an authority 

 on algebra. The results of much of this Ori- 

 ental study and discovery were carried by the 

 Arabs to Spain, and thus Europe was roused 

 to a new interest in mathematics. 



The Renaissance (which see) gave new birth 

 to mathematics, and from that time onward 

 development was fairly rapid. Descartes, who 

 lived in the seventeenth century, gave a great 

 impetus to the science, helping particularly to 

 make elementary algebra what it is to-day. 

 Other great names in the history of mathemat- 

 ics are those of Kepler, whose contributions to 

 geometry were epoch making; and of Newton 

 and Leibnitz, who practically remade higher 

 mathematics by their discovery of the princi- 

 ples of calculus. 



The work of these masters left little to be 

 done in regard to the fundamental theories and 

 principles, but the later centuries have been by 

 no means idle. They have evolved a multitude 

 of new methods and new applications, some 

 very difficult and abstruse, and beyond the 

 reach of any but scholars, others which have 

 as their object the simplifying and illuminat- 

 ing of the lower branches. All in all, it may 

 be said that the constant tendency is to make 

 232 



mathematics as studied in the schools more 

 practical ; to give problems which are not mere 

 abstractions but have a relation to the life of 

 the pupils. Many of the theories and reason- 

 ings which used to be looked upon as a.n inte- 

 gral part of the subject are now taught only to 

 those students who expect to do advanced work 

 in mathematics, and elementary pupils are not 

 compelled to study principles which they can- 

 not possibly use in their later life. 



Mathematics is universally taught in the 

 schools. The articles in these volumes on the 

 various branches discuss the value, both prac- 

 tical and disciplinary, of the subject in all its 

 departments. A.MC c. 



Related Subjects. The reader who is inter- 

 ested in mathematics is referred for wider and 

 more detailed treatment to the following articles 

 in these volumes. Some of these also contain ex- 

 tensive indexes, so that the list referred to is a 

 wide one. 



Algebra Geometry 



Arithmetic Mensuration 



Calculus .Trigonometry 



The lives of the following eminent mathema- 

 ticians are also treated in these volumes : 



Archimedes 

 Descartes, Ren6 

 Dodgson, Charles L. 

 Euclid 



Kepler, Johann 

 Laplace, Pierre Simon 

 Legendre, Adrien M. 

 Leibnitz, Gottfried 

 Wilhelm 



Napier, John 



Newton, Sir Isaac 



Omar Khayyam 



Plato 



Ptolemy 



Pythagoras 



MATH'ER, the family name of two very 

 notable clergymen, father and son, of colonial 

 times in America. 



Increase Mather (1639-1723) was born in 

 Dorchester, Mass. His unusual name was be- 

 stowed upon him "because of the never-to-be- 

 forgotten increase of every sort wherewith God 

 favored the country about the time of his na- 

 tivity." He was a precocious boy, for he was 

 graduated from Harvard at the age of seven- 

 teen, after which he went to Dublin for further 

 study. Certain sermons which he delivered in 

 England were favorably received, and at the 

 time of the Restoration he was urged to settle 

 there, but he returned to Massachusetts and in 

 1664 was made pastor of the North Church of 

 Boston. His influence was great on State as 

 well as Church questions, and in 1688 he was 

 sent to England to regain the colonial charter 

 which had been revoked by Charles II. He 

 failed to do that, but accepted from William II 

 a new charter which was in most respects satis- 

 factory. It was while he was in England that 



