January 5, 191 1] 



NATURE 



o'o 



vie of decoration with glazed bricks was borrowed 

 V the Persians, and we see it in the splendid decora- 

 tion from Persepolis now in the Louvre at Paris. 



It is to be hoped that Dr. Koldewey has still more 

 important discoveries in store. H. R. Hall. 



IHE NEGLECT OF GROL P-THEORY. 



THE volume of " Proceedings of the London 

 Mathematical Society," second series, vol. vii., 

 contains twenty-six papers by such well-known mathe- 

 maticians as Bateman, Bromwich, Burnside, Dick- 

 son, Dixon (A. C, and A. L.), Hardy, Harrison, Hob- 

 son, Lamb, Littlewood, Macdonald, Pidduck, Sommer- 

 ille. and Young. While these are mainly of tootech- 

 cal a character to admit of discussion in this notice, 

 detention should be directed to some remarks in Prof. 

 Burnside 's address on the "" Theory- of Groups of Finite 

 Order," as affordint^T an object-lesson on the important 

 question of " England's neglect of mathematics." 

 Prof. Burnside states : — 



" It is undoubtedly the fact that the theory of groups 

 of finite order has failed, so far, to arouse the interests 

 of any but a very small number of English mathe- 

 maticians ; and this want of interest in England, compared 

 with the amount of attention devoted to the subject both 

 on the Continent and in America, appears to me ven," 

 : markable." " So far as I have been able to learn, no 



urse of lectures has ever been delivered either at Oxford 

 Cambridge on the theon,- of groups of finite order." 



In fact, so far as the teaching of the subject in England 



concerned, one may say that it does not exist." 



It appears that during the twenty-one years of the 

 \v, alas I defunct "Part II." of the Mathematical 

 ripos, questions on finite groups have only appeared 

 ur times, and that it is doubtful whether four candi- 

 ites have seriously studied the subject. 

 On the other side we have the following statement : 



"In Paris M. Jordan gives a course on the theor}' of 

 oups of finite order at the College de France at regular 

 ervals to an average class of six students, while the 

 ilois theory of equations is lectured on at the Sorbonne 

 J the Ecole normal, as well as at one or two of the 

 ovincial universities. 



In most German universities, the regular course of 



lectures on algebra, attended by large classes of students, 



f^ntains an exposition of the more elementary parts of 



r theory of groups of permutations. In addition to this 



ere are, in all the larger universities, special courses 



devoted to groups of finite order and to discontinuous 



groups, which attract a considerable number of students. 



" ir instance, such special courses last year were attended 



Gottingen by thirty students, and at Freiburg by twelve. 



In the United States all the leading universities offer 



:^ular courses in the theory of groups of finite order, 



ih the exception of Harvard, where a course is given on 



V Galois theory of equations. In some cases the course 



a yearly one, and in the others it is biennial. These 



courses attract from two or three up to ten or twelve 



students, who in general have already taken the B.A. 



■degree." 



Prof. Burnside offers some explanations for this 

 neglect, but probably the reason is a \ety simple one. 

 If any English mathematician specialises in the theory 

 of groups (and at least one instance is known to the 

 reviewer) no university will offer him adequate re- 

 muneration for a course of lectures on the subject ; on 

 the other hand, the mathematical departments of 

 English institutions of university rank are deplorably 

 understaffed in comparison with those in foreign 

 countries, and their teachers are far too overburdened 

 with elementary- work to be able to start courses or 

 a subject like " groups," in addition to meeting the 

 necessan,- requirements of their examination svllabuses. 

 Prof. Burnside suggests that the cause may parily be 



NO. 2149, VOL. 85] 



a lack of demand for instruction in the subject on the 

 part of senior university students. But is it not the 

 fact that such students are induced to give up advanced 

 mathematical study and to take to experimental 

 science in order to qualify for "research student- 

 ships?" If they persist in specialising in higher 

 mathematics of any kind, they not infrequently do so 

 at the risk of injuring their future prospects of obtain- 

 ing appointments. 



NOTES. 

 Political services and commercial prosperity appear to 

 be the claims to distinction of most of the people whose 

 names are to be found in the list of New Year Honours. 

 The list includes the names of few men of eminence in 

 the intellectual world — whether of science, art, or litera- 

 ture. One Fellow of the Royal Societ>- — Dr. David 

 Ferrier — has been knighted ; and among the twenty-four 

 other new knights are Dr. H. B. Donkin, Mr. G. 

 Laurence Gomme, and Dr. G. Newman. Even in these 

 cases, however, the honour appears to have been conferred 

 for public services rather than in recognition of scientific 

 w^ork. The list has been received with the usual chorus 

 of congratulation by the daily papers, but it can in no 

 way be regarded as truly representative of the men who 

 are rendering the best ser\-ices to the nation. 



The Oceanographical Institute provided by the Prince of 

 Monaco at Paris will be inaugurated on Monday, 

 January 23. 



It is announced that an association for the promotion 

 of science, to be called the " Kaiser Wilhelm Gesell- 

 schaft, "will shortly be formed in Germany. The first 

 meeting of the association is to be held within the next 

 week or two under the presidency of Prof. Emil Fischer, 

 and the German Emperor proposes to be present. 



The Paris Academy of Sciences, at a meeting on 

 December 29, 1910, discussed the question of the election- 

 of women as members of the Institute of France. We 

 learn from the Times that the academy eventual!}- came; 

 to the conclusion that each section of the institute has 

 complete independence with regard to the election of 

 members, and that each academy has the right to decide 

 the question of the election of women to its membership. 

 The subject is being discussed at a general meeting of the 

 academies as we go to press. 



We regret to see the announcement of the death of one 

 of the best known supporters of amateur astronomy in 

 Germany, Dr. M. Wilhelm Meyer, who died recently at 

 Meran, at the comparatively early age of fift}--eight. Dr. 

 Meyer's astronomical career began at Geneva, of which 

 observatory he was for a short time director. He 

 signalised his connection with that obser\'ator3- bv an 

 attempt to determine the densit>- of the material near the 

 nucleus of a comet by observing the displacement of stars 

 over which the comet passed ; but he is better known 

 from his relations with the Urania Gesellschaft in Berlin 

 and his efforts to encourage astronomical studies in those 

 who frequented the observatory-. He was successful in 

 attracting those who were capable of using the equipment 

 provided wiseh' and well. Among his pupils or followers 

 may be mentioned Herr Witt, who discovered the planet 

 Eros in the Urania Observatory. Many of ' his popular 

 works have had a wide circulation, among which mav be 

 mentioned " Das Weltgebaude, " a work addressed to 

 those who were capable of following the detailed explana- 

 tion of the more diflScult problems in astronomy, and the 



