## Some reviews of Wilhelm Ahrens' books

Wilhelm Ahrens wrote several books and we give extracts from reviews of four of these below.

**1. Mathematiker-Anekdoten (2nd edition) (1920), by Wilhelm Ahrens.**

**Review by: Robert Daniel Carmichael.**

*Bull. Amer. Math. Soc.*

**27**(5) (1921), 230-231.

Whether the telling of an anecdote shall provoke the interest of a pleased smile or the different amusement which leads to a shrug of the shoulders depends intimately and delicately upon the mental associations which arise involuntarily when a story is related; and the latter in turn depend upon the varied elements, and even the most minute, which make up the daily life and experience and environment. Hence it has always been, and perhaps always will be, difficult for one people to appreciate the humor of another. It is therefore natural that a book of anecdotes, containing humorous ones among others, shall be addressed by an author principally to his own countrymen.

These stories related by Ahrens of mathematicians and things mathematical are evidently intended primarily for his own countrymen; hence it is fitting that far the greater space should be given to men and things that are German. One of the pleasing features of the booklet is the inclusion of fifteen or more excellent likenesses of mathematicians. The stories range in excellence from some of high quality to some which are not pleasing. We do not find much of value in the story of the boys who convinced a simple old man that in their use of logarithm tables they were mastering the house numbers of Europe. We are only mildly interested when we are told of L Fuchs' surprise when a long computation in his lecture led to the result 0 = 0, that he first painfully suspected an error, but that he then regained his composure and said " 'Null = Null' ist ja ein sehr schönes und richtiges Résultat." But the story of the youth of Gauss will please every one who enjoys the activity of genius. An effective impression of the progress of mathematical instruction is made by a brief account of mathematical instruction in the "good old times." The account of the self-taught Arago's successes when examined on one occasion by Louis Monge and on another by Legendre is inspiring; any one who does not know these stories will be repaid if he looks up the booklet for them alone.

**2. Scherz und Ernst in der Mathematik. Geflügelte und ungeflügelte Worte (1904), by Wilhelm Ahrens.**

**Review by: Anon.**

*The Mathematical Gazette*

**3**(48) (1904), 118-119.

This entertaining volume consists of extracts, winged and otherwise, from the writings, addresses, letters, etc., of the most famous German, French, and English mathematicians. A few examples will give an idea of the miscellaneous nature of the contents. "Geometry is the only science which has produced no sects" (Frederick the Great). "D'Alembert, that great genius, seems to be far too ready to pull down everything he has not himself built up" (Euler to Lagrange). "I am delighted at the contrast between your modesty and the good opinion that other geometers have of themselves, although they have certainly nothing like the same claim. You are a living instance of what you said to me some time ago, that pretensions are ever in an inverse ratio to merit" (d'Alembert to Lagrange). "Leibniz never married. At the age of 50 he began to think about it, but the lady asked for time to reflect. This gave Leibniz time to reflect - and he did not marry" (Fontenelle). "My dear and illustrious friend - they write to me from Berlin that you are about to take what we philosophers call 'le saut perilleux,' and that you have married one of your relations. ... Accept my compliments, for a mathematician ought to have pre-eminent advantages in the calculations of his own happiness, and any calculations of yours are sure to lead to a solution - the solution in your case being marriage" (d'Alembert to Lagrange).

**3. Briefwechsel zwischen C G J Jacobi und M H Jacobi (1907), by Wilhelm Ahrens.**

**Review by: Anon.**

*The Mathematical Gazette*

**4**(71) (1908), 269-270.

To mathematicians the name of the younger brother, Carl Gustav Jacobi (1804-1951), is of course the more familiar. That of the elder, Moritz Hermann (1801-1875), occupies however an honoured place in the history of electrical discovery, and just now may have a revived attention given to it as that of the inventor of the first 'motor boat.' As the two brothers corresponded freely with each other about their occupations, and as from their influential positions they had a wide acquaintance, including practically all the 'scientific worthies' of Europe, to whose work they continually allude, the correspondence forms a mine of information for the future historian, especially as the editor has added a large number of explanatory notes with reference to other publications. One of the most interesting to an English reader is that dated Sept, 25, 1842, written by the mathematician, in which he describes his visit to England with Bessel to attend officially the Manchester meeting of the British Association. "In Manchester sprach Faraday viel mit mir von Dir. Er reiste ab als die eigentliche Versammlung anfing." We were puzzled to account for Faraday's journey to Manchester when he obviously did not intend to stay for the general meeting. Bence Jones does not allude to the matter, but the Schönlbein-Faraday correspondence makes it clear. Faraday had not intended to go to Manchester at all, but the Society of Sciences at Modena had appointed Herschel and him to represent them, and as the former had at first said that he could not go it fell to Faraday to attend a committee meeting and report the credentials of the Society. Herschel seems to have gone after all, and Jacobi's letter supplies the probable reason for his change of mind, viz. to meet Bessel, "if it were but to touch the garment of this gentleman." An elaborate index of the names of the writers and subjects mentioned in the correspondence and notes adds greatly to the value of the work. Portraits of the two brothers are given.

**4. Mathematische Spiele (3rd edition) (1916), by Wilhelm Ahrens.**

**Review by: Robert Daniel Carmichael.**

*Bull. Amer. Math. Soc.*

**26**(2) (1919), 86.

The principal new matter introduced in preparing the third edition of this booklet consists of an additional section (Magische Quadrate auf Amuletten) in the chapter on magic squares and the enlargement of the chapter on mathematical fallacies, the latter having been increased from seventeen to twenty-eight pages.