282 
of mathematical writers; this number is 2.6 
times greater than that for 1830-1840, in- 
dicating an annual production of 2.6 times 
165.9 or 431.3. The average annual produc- 
tion for the sixth period 1835-1875, is the 
average of 165.9 and 481.3, or 298.6. 
From Professor White’s statistics it appears 
that the annual output was in 1905 about 2.1 
times greater than in 1875, or 905.8. From 
these data it follows that during the seventh 
period, 1875-1905, the average yearly quantity 
of mathematical literature was 668.8. Our 
results, put in tabular form, are as follows: 
Average Production 
Annual during 
Production Period 
J. Period, 2000 B.c—1200 ap. 1 3,200 
II. Period, 1200-1668 ........ 6.9 3,149 
III. Period, 1668-1758 ........ 35.3 3,177 
IV. Period, 1758-1799 ........ 95.8 3,928 
V. Period, 1799-1835 ........ 140.1 5,044 
VI. Period, 1835-1875 ........ 298.6 11,944 
VII. Period, 1875-1905 ........ 668.8 20,064 
The tremendous increase is shown strikingly 
also by the two charts. They give emphasis to 
the biblical declaration, “Of making many 
books there is #o end.” 
The total literary production during the last 
three periods is 37,052 and for the interval 
1799-1901 it is 34,377. How long would it 
take to survey this field and write the history 
of mathematics of the nineteenth century? 
Moritz Cantor published his first historical 
paper in 1856 and completed the third volume 
of his well-known history in 1898. Perhaps it 
would not be fair to claim that all of these 42 
years were given to the three volumes. Three 
smaller historical books from his pen preceded 
the three volumes in question. The early years 
were years of necessary preparation. The first 
volume appeared in 1880, the second in 1892, or 
12 years later. If we assume that the prepara- 
tion of the first volume required the same time 
as that of the second, then 30 years is the 
time Cantor devoted to the three volumes. 
In the tabular view given above the first three 
volumes are the history covering mathematical 
material amounting to 9,526. At this rate it 
would take a man 108.3 years, or 20 men 5.4 
years, to write the history of mathematics of 
SCIENCE 
[N. S. Vou. XLVIII. No. 1238 
the nineteenth century, provided that these 
men gave, as did Cantor, a liberal amount of 
time to research and confined their efforts to 
this particular project. If only one third of 
their research time were given to it, then 65 
men would be needed for 5 years. 
Let us estimate the number of men from a 
different set of data. Wolume IV. of Cantor’s 
history was prepared by 10 men, each working 
about one year and a half. Some of these 
prepared short chapters and probably com- 
pleted their parts in less time. On the basis 
of 14 years and on the supposition that each 
worker will give one third of his research time 
to the enterprise, it will take 79 men 5 years 
to write the mathematical history of the nine- 
teenth century. If this history is written with 
the elaborateness of Cantor’s “ Vorlesungen,” 
it will embrace 14 or 15 volumes of the size 
of the Cantor volumes; it will contain 54 mil- 
lion words. Probably it would be wise to plan 
a considerably smaller. number of volumes. 
Considering the magnitude and difficulty 
of the undertaking, it is quite evident that 
American mathematicians alone would find 
the task excessive. If the services of English, 
French and Italian mathematicians could be 
enlisted, the enterprise would be compara- 
tively easy. In past years it has been Europe 
that has initiated organized efforts among 
scientists. In proof of this I need only men- 
tion the “Encyklopadie der mathematischen 
Wissenschaften,” the “ Encyclopédie des sci- 
ences mathématiques,” the “Royal Society 
Catalogue of Scientific Papers,” as also the 
publications of Euler’s complete works, of 
the Fortschritte der Mathematik, of the Revue 
semestrielle. It would seem to be our turn to 
take the initiative. The history of mathe- 
matics of the nineteenth century might very 
well be planned and financed by America. 
The magnitude and difficulty of the task would 
exert a healthful stimulus upon our 550 col- 
leges and universities. Such an ambitious 
scheme would require the exercise of energies 
now latent. 
Let us hope that the places where mathe- 
matical research is carried on will cease to be 
limited to a small number of localities on the 
