SCIENCE PROGRESS 



RECENT ADVANCES IN SCIENCE 



MATHEMATICS. By F. Puryer White. M.A., St. John's CoUege, 

 Cambridge. 



A FURTHER account of the work of the late H. G. Zeuthen on 

 Enumerative Geometry and on the history of mathematics, 

 together with a Hst of his writings, is given by M. Noether 

 (Math. Ann., 83, 192 1, 1-23). 



Adolf Hurwitz (i 859-1919) devoted himself in his earlier 

 years to the study of algebraic functions, and his paper, " "Qber 

 algebraische Correspondenzen und das verallgemeinerte Corre- 

 spondenzprinzip " {Math. Ann., 28, 1887, 561) remains a classic. 

 Later he turned to continued fractions, algebraic numbers and 

 arithmetical properties of certain transcendental functions. 

 A full appreciation of his life and work is given by D. Hilbert 

 {Math. Ann., 83, 192 1, 161-72). 



History. — G. A. Miller {Isis, 4, 1921, 5-12) discusses the merits 

 and defects of the various types of mathematical history, 

 including the treatises of Montucla and Cantor, the popular 

 works of Ball and Cajori, and the detailed reference work of 

 Dickson on the Theory of Numbers. 



D. E. Smith {Amer. Math. Monthly, 28, 1921, 296-300) prints 

 the will of Robert Recorde {d. 1558), the author of The Whet- 

 stone of Witte, and describes the one extant portrait, dated i 556. 



O. Mautz {Verhl. Basel, 32, 1920-21, 104-6) has a note on the 

 tables published in 1620 by Biirgi, which are practically a set of 

 antilogarithms. 



Cantor {Geschichte d. Math., t. 3, p. 368) states that Taylor's 

 Theorem, announced in 1 712 in a letter to Machin and published 

 in 1 71 5 in the Methodus Incrementorum, was anticipated by 

 John Bernoulli in the 1694 volume of the Acta Eruditorum. 

 G. A. Gibson {Proc. Edin. Math. Soc, 39, 1921, 25-33), combat- 

 ting this, calls attention to the fact that Bernoulli's theorem 

 consists only in repeated integration by parts, and that in his 

 illustrations the series obtained are not power series. Further, 

 Taylor's own account of his book in the Phil. Trans. (29, 1716) 

 shows that he appreciated the importance of his theorem. 



In his lectures on the integral calculus, published in 1742, 



