February 5, 1920] 



NATURE 



601 



all of Natal, South Africa. The aviaries are of simple 

 wire-netting, in which are growing flowering shrubs 

 and weeds. Their dimensions are 12X9x6 ft. 



The food provided is Mellin's (baby) food, honey, 

 and Swiss milk (tin) in equal proportions, and pea- 

 flour one-quarter to the above. 



The brilliant scarlet borne by certain of the varieties 

 has changed in every case to a bright orange colour, 

 thus causing the bird to present a great contrast to 

 its original colour. Metallic green, which is borne bv 

 so many of the "sun-birds," is in no manner affected. 

 Other colours of these birds are also not affected. 



It would appear to be a case of change of plumage 

 caused by the feeding, for the condition of life is 

 almost natural. 



We are not aware of such variety of colour having 

 been observed previously. It would be of interest if 

 any contributor to Nature could give information of 

 examples of similar occurrences with respedt to cap- 

 tive wild birds, or offer an explanation of the physio- 

 logical causes which are at work. 



Harold Millar, 



Director. 



Zoological Gardens, Mitchell Park, Durban, 

 Natal, December 30, iqiq. 



MATHEMATICS IN THE UNITED STATES. 



TVfOT very long ago (perhaps fifteen or twenty 

 -'■ ^ years) an English lady, spending a visit in 

 Utrecht, met a distinguished Dutch professor of 

 mathematics. In the course of conversation the 

 lady asked the professor what he thought of con- 

 temporary English mathematicians and their work. 

 The answer was not calculated to flatter our 

 national vanity, for it was to the effect that he 

 rarely looked at English mathematical papers, 

 because they were so unconnected with the general 

 progress of the science, and written in such a 

 peculiar way that he could scarcely understand 

 them. Incredible as it seems, this opinion was 

 expressed when Salmon, Cayley, Sylvester, and 

 Clifford had published all their best work. Preju- 

 dices die hard, and thp professor's attitude would 

 have been intelligible in the earlier part of the 

 nineteenth century. 



One moral of the story is that, as there are 

 nationalities in drinks, so there are in mathematics, 

 in spite of the growing tendency towards universal 

 co-operation. The history of recent mathematical 

 progress in the United States presents many points 

 of interest. To a great extent, American mathe- 

 maticians may be regarded as the grown-up pupils 

 of Germany. From Germany they have acquired 

 habits of thoroughness, breadth of view, and col- 

 laboration. Rut they have clearly passed the time 

 of pupilage, as we see from their growing list of 

 original and eminent writers ; it is enough to refer 

 to such men as the two Peirces and ^^■illard 

 Gibbs. 



There are several features of the attitude of the 

 Americans towards mathematics which deserve 

 our careful attention. In the first place, it should 

 be noted that the State and private benefactors 

 encourage mathematics for its own sake, quite 

 apart from considerations of utility. Many Ameri- 

 NO. 2623, VOL. 104] 



can professors are allowed to devote themselves 

 to research in such things as group-theory, ab- 

 stract^ geometry of all kinds, function-theory, and 

 the higher arithmetic; the predominance of such 

 subjects in American journals and transactions is 

 quite remarkable. The Government and people of 

 the United States appear to be fully conscious of 

 the fact that special ability of every kind should 

 be encouraged. 



An excellent American institution, which might 

 well be adopted here, is that of the sabbatical year, 

 \\ hich gives the teacher an opportunity of bring- 

 ing his knowledge up to date, or of carrving out 

 some laborious research. As an example of what 

 can be done in such periods of leisure, we may 

 refer to the recently published first volume of 

 Prof. L. E. Dickson's "History of the Theorv of 

 Xumbers." With almost incredible industrv,' the 

 author has personally consulted and summarised 

 thousands of papers, notes, and memoirs; and if 

 the work is carried out on the same scale it will 

 fill four or five large octavo volumes, and be an 

 mdispensable guide to all who work in this field. 

 It may be remarked here that we owe to the States 

 many valuable works on the historv of mathe- 

 matics (especially from the teacher's point of 

 view), and reprints and translations of scarce and 

 valuable works. 



Collaboration, both in the composition of books' 

 and in that of papers, is more common than with 

 us. There are two sides to this question ; in some 

 ca.ses the advantages of joint authorship are 

 obvious, but those treatises which rank as master- 

 pieces (such as Salmon's "Conic Sections" or 

 H. Weber's ".Algebra ") are usuallv, if not alwavs, 

 the work of one man. 



-Vmerican mathematical colloquia are far more 

 serious affairs than anything we have here. They 

 are meetings of experts, lasting for a week or so, 

 at which a serious programme is carried out, and 

 carefully prepared addresses and short sets of 

 lectures are delivered on topics of outstanding in- 

 terest. In this matter we ourselves seem to 

 vibrate between two extremes ; either we have a 

 technical meeting where papers are read (or taken 

 as read), which seldom interest more than one or 

 two of the audience, or we indulge in a picnic, at 

 which a few casual notes are communicated, 

 mainly for the sake of securing priority. 



While thus directing attention to some things 

 in which we might well imitate the States, we 

 have no intention of carping at our own countrv- 

 men. The general condition of mathematics in 

 this country is probably better now than it has 

 been for many years, and we should be sorry to 

 see some of the old English characteristics dis- 

 appear. For instance, the view that mathematics 

 is a gentlemanly recreation has something to be 

 said for it, and we may avoid being needlesslv 

 solemn and serious in our study of it, however 

 conscious we may be of its vital importance for 

 national welfare. 



G. B. M. 



