June 1, 1917] 



SCIENCE 



557 



become more pronounced with its develop- 

 ment. 



In view of the age of this language and 

 its contact with various sciences it may be 

 readily understood why mathematical his- 

 tory occupies a prominent place in the his- 

 tory of science. In fact, the history of sci- 

 ence cotastitutes one of the fields where 

 scientists may find common interests most 

 fully represented, even if the past is too 

 rich in events to be studied completely. It 

 may therefore be appropriate on this occa- 

 sion to refer to a few recent developments 

 relating to the history of mathematics, espe- 

 cially since the interest in the history of 

 science has increased rapidly during recent 

 decades, as is partly evidenced by the ef- 

 forts that are now being made to establish 

 an institiite of historical scientific research 

 in our land. 



One of the most interesting questions 

 relating to the early history of mathe- 

 matics is the use of positional values of 

 numbers and the closely connected use of 

 a symbol for zero. Until a decade or two 

 ago it was commonly assumed by mathe- 

 matical historians that the use of zero as a 

 positional number symbol originated in 

 India, and this view has not yet been en- 

 tirely abandoned, notwithstanding the fact 

 that the Babylonians employed numbers 

 with positional value and a symbol which 

 seems to have fulfilled the main function 

 of our zero several centuries before the 

 Christian era. On the other hand, the 

 fii-st definite evidence of the use of zero 

 among the Hindus falls in the second half 

 of the first millennium of this era. 



In view of these facts it is extremely 

 interesting to note the early use of zero, in 

 connection with numbers having positional 

 value, by the Maya, a people inhabiting the 

 Atlantic coast plains of southern Mexico 

 and northern Central America. One of the 

 worthy alumni of your university recently 



referred to this matter in the columns of 

 Science in the following words: 



Special interest attaches to the occurrence of 

 lero-symbols and the principle of local value 

 among the inhabitants of the flat lands of Central 

 America, at a period as early as the beginning of 

 the Christian era, if not much earlier. It would 

 seem that in this invention, the Maya in Central 

 America possessed priority over Asiatic people by 

 a margin of five or six centuries.? 



If further investigation wiU lead mathe- 

 matical historians to agree that the zero as 

 a symbol in a numerical notation with posi- 

 tional value was actually first used in 

 America, according to the preserved rec- 

 ords, it will effect a very fundamental 

 change as regards interest in the early 

 mathematical attainments of the American 

 aborigines. Unfortunately these early 

 mathematical attainments failed to become 

 the source of extensive further develop- 

 ments on American soil. They exhibit 

 clearly that central concepts may be dis- 

 covered independently and they direct at- 

 tention to the danger in trying to establish 

 one source for a particular concept in his- 

 torical investigation. They also show that 

 the small strip of country marked now by 

 Boston has not always been the intellectual 

 hub of America. 



The history of some of the mathematical 

 attainments of the Maya people hasrecently 

 been made more easily accessible through 

 the publication of ' ' An Introduction to the 

 Study of the Maya Hieroglyphs," pre- 

 pared by S. G. Morley and published as 

 Bulletin 57 of the Bureau of American 

 Ethnology, Smithsonian Institution of 

 Washington. On page 92 of this bulletin 

 a dozen different symbols for zero are 

 noted and on page 131 numbers varying 

 from 21 to 12,489,781, and involving the 

 use of zero, are represented in the Maya 

 notation. It is of interest to note that the 



TF. Cajori, Science, N. S., Vol. 44 (1916), 

 p. 715. 



