aa r X i v : . [ m a t h . HO ] J a n Gotthold Eisenstein and Philosopher John
Franz Lemmermeyer
Abstract
Before the recent publication of the correspondence between Gaussand Encke, nothing was known about the role that John Taylor, a cottonmerchant from Liverpool, had played in the life of Gotthold Eisenstein.In this article, we will bring together what we have discovered about JohnTaylor’s life.
Eisenstein’s Journey to England
Gotthold Eisenstein belonged, together with Dirichlet, Jacobi and Kummer,to the generation after Gauss that shaped the theory of numbers in the mid-19th century, and like Galois, Abel, Riemann, Roch and Clebsch, Eisensteindied young. Today, Eisenstein’s name can be found in the Eisenstein series,Eisenstein sums, the Eisenstein ideal, Eisenstein’s reciprocity law and in hisirreducibility criterion, and he is perhaps best known for his ingenious proofsof the quadratic, cubic and biquadratic reciprocity laws. Eisenstein’s father Jo-hann Konstantin Eisenstein emigrated to England in 1840; Eisenstein and hismother followed in June 1842, although Eisenstein’s few remarks on this episodein his autobiography [3] belie the dramatic events that he experienced in Eng-land. On their journey to England, the Eisensteins passed through Hamburg;during the Great Fire in May 1842 about a third of the houses in the Altstadthad burned down. What we learn from Eisenstein’s account is that he wasimpressed by the sight of railroad lines running right under the foundations ofhouses (in London?) and by the Menai suspension bridge in Wales: Eisensteinmentions that he undertook six sea voyages, and that on one of them they sailedunder the tremendous suspension bridge in Anglesey, which was so high thatthe Berlin Palace would easily have fitted under its main arch.Eisenstein also writes that he later made the acquaintance of William Hamil-ton in Dublin (who would discover the quaternions in October 1843), as wellas that of the mayor of Dublin, Daniel O’Connell (who died in 1847 in Genoa,where he wanted to organise help for the Irish during the Great Famine).Eisenstein does not mention what happened after his arrival in England; thecorrespondence between Encke and Gauss reveals that he fell seriously ill andwas saved by the assistance of a certain Mr. Taylor from Liverpool. Encke firstmentions this story in his letter from 10 June 1844 (see [10, S. 1141]):1 have the honour, most esteemed Privy Counsellor, to send youthe second volume of the Berlin Observations, and I have encloseda collection of papers by a young local mathematician Eisenstein,whose assessment seems to me to be of importance in the interest ofscience, and for which no better judge could ever be found than you,the true head of this part of higher mathematics. I would not haveconcerned myself with this matter, but would have left it to Prof.Dirichlet, if the latter had not already been away for a year. YoungEisenstein went to the same Gymnasium as my sons, where he didnot excel at other subjects, but surprised his teacher in mathematics with a curious derivation of a series first developed by Lagrange,without having known this paper. He was then introduced to Prof.Dirichlet, who believed him to be an extraordinary genius. Owingto his family being in special financial circumstances, he followed hisparents to Liverpool two years ago, where illness and family relations(his father seems to have speculated unsuccessfully) reduced him tosuch a harassed state that his local acquaintances thought it necessaryto send him back home. Dirichlet told me of these circumstances andasked me to try to aid his return with the help of my English friends.Although I did not have any acquaintances in Liverpool, it turned outthat an important cotton merchant, Taylor, had submitted a bookon ancient Roman festivities and chronology to the Academy, andI learned that he published articles in journals on our comet and inparticular on the short-period comet . Based on this, I turned to thisgentleman, who was otherwise completely unknown to me, and askedfor his assistance. With a generosity that can perhaps only be foundin Englishmen, he sought out young Eisenstein, arranged for a doctorand medicine (Eisenstein was suffering from typhoid fever), providedhim with the means for travelling to Dublin (where Hamilton receivedhim very obligingly) and also gave him and his mother the necessaryfunds to return to Berlin. Here, Eisenstein occupied himself withinvestigations of the kind you will find among the enclosed papers andhas obtained, since other avenues were unsuccessful, a yearly sum ofmoney from the King (through the efforts of Mr. v. Humboldt, ashe told me), with which this young man is completely content (inhis own words). He would like to visit G¨ottingen in the near futurein order to present himself to you and, if the circumstances allow,profit from your teaching. Because of his young age (he cannot yetbe or must only just be 20) and his talent, which he certainly mustpossess, although I admittedly cannot tell whether it is as great asDirichlet’s remarks would have one believe, your judgement wouldbe of such importance for his future position that I entreat you withsome urgency not to deny my request. He seems to me to be pleasant This might have been Karl Heinrich Schellbach. Encke had computed the elements of the comet now named after him; it has an orbitalperiod of only 3.3 years. ompany, and his experiences do not appear to have weighed himdown, but rather shown him that he must pull himself together, andI believe I may hope that he will not be a burden to you. The mannerin which I am involved in these matters is not entirely comfortableto me, since I feel indebted to Mr. Taylor and must see how I canthank him. Gauss answers Encke’s letter on 23 June and writes:
I would be pleased to make the acquaintance of such a promisingyoung man, and I would be delighted [. . . ] if he would spend sometime in G[¨ottingen]. It would be my pleasure if I could be of anyassistance to him, if not by actual teaching, since he clearly hasby far surpassed this stage.
Gauss’s judgement on Eisenstein’s skills was based on the articles that Eisensteinpublished in Crelle’s Journal in early 1844. Gauss had only studied one of thesearticles in detail, namely Eisenstein’s proof of the quadratic reciprocity lawusing multiple Gauss sums (see [3, vol. I, pp. 100–107]), but this was sufficientto convince Gauss of Eisentein’s talent.On 13 August 1844, Encke writes to Gauss, asking him to reply to a letterfrom Taylor and reminding him what Taylor has done for Eisenstein:
Young Eisenstein, in whom you have shown so much interest, wentto Liverpool in early 1843 (unless I’m mistaken) with his (ratherworthless) father; there his family got into a serious plight, andin addition young Eisenstein became gravely ill with typhoid fever.Prof. Dirichlet told me about it and asked if I happened to have anacquaintance in Liverpool who could take an interest in the youngman, for otherwise he would perish.Although I did not know Mr. Taylor (I had only heard from Prof.Mitzscherlich that he was a wealthy cotton merchant and an am-ateur astronomer who published news about comets and was famil-iar with my name), I took the chance of approaching him about thematter. He immediately did a lot more than I had hoped, sendinga doctor to young Eisenstein, providing for him by a subscription,supplying him with money for travelling to Dublin in order to meetHamilton, and facilitating his return to Berlin. Eilhard Mitzscherlich (1799–1863) is a chemist and mineralogist from Berlin. ohn Taylor Who was this Mr. Taylor, cotton merchant from Liverpool, who saved Eisen-stein’s life and paid for his travels to Ireland and back to Germany? Enckewrites in a letter to Gauss from 15 August 1846:
I must confess that I think very highly of his actions, for which hereceived no compensation, and so I am sorry that he got into a bitterdispute with Sheepshanks concerning the building of the observatory,in which he (probably deservedly) drew the short straw, since he doesnot know much about modern astronomy. He knows more about an-cient astronomy, since he has translated the first four books of Ovid’sfastis and published them with explanations about the knowledge ofthe skies at that time.Should you thus feel inclined to answer his letter, I would sincerelyrequest that you make friendly mention of his truly noble behaviourtowards young Eisenstein, which he would value highly.
The information that we can glean from Encke’s letter suffices for identifyingTaylor as the cotton merchant John Taylor from Liverpool: both his
Poems andTranslations including the English translation of Ovid’s fastis [9] as well as hisheated exchanges with Reverend Sheepshanks in [7] can be found online.Richard Sheepshanks (1794–1855) was a Fellow of the Royal Society in Lon-don since 1830. The list of persons he quarreled with is long; his dispute withJames South, in which later Charles Babbage and his difference engine gotdrawn into, is described in Hoskin’s article
Astronomers at War [5].The dispute with Taylor was about the best position for the future oberva-tory in Liverpool. In a letter to the Liverpool Mercury, Taylor heaps scorn uponSheepshanks’ choice: according to the writers of this Royal Astronomical Report, the propersituation for our Observatory is in the lowest point of land that can befound, surrounded by hills that cut off the true horizon, and where,in fact, there is no horizon at all, although, to be sure, when thetrough of the river is filled with smoke and fog, which is commonlythe case, there may seem to be a horizon at a few yards distance[. . . ] where nor sun, nor moon, nor star is ever seen, or was everseen, to rise or set, and where no meridian line can ever be drawnor determined [. . . ]
Sheepshanks prevailed, but 20 years later the observatory got closed due to anextension of the harbor, and in 1868 the new observatory was erected on BidstonHill, the position that had been suggested by Taylor.Another source of information on John Taylor comes from the diary of theAmerican astronomer Maria Mitchell. In 1857 she traveled through Europe; onAugust 3, 1857 (see [6, S. 86]) she delivered a letter to John Taylor and observedthat he must have been around 80: 4 brought a letter from Professor Silliman to Mr. John Taylor, cottonmerchant and astronomer; and to-day I have taken tea with him. Heis an old man, nearly eighty I should think, but full of life, and talksby the hour on heathen mythology. He was the principal agent in theestablishment of the Liverpool Observatory, but disclaims the honor,because it was established on so small a scale, compared with his owngigantic plan. Mr. Taylor has invented a little machine, for showingthe approximate position of a comet, having the elements. [. . . ] Hestruck me as being a man of taste, but of no great profundity.
If Taylor was about 80 years old in 1857, then he must have been born around1777. His cometarium was studied by Beech [2]. The information that Taylordied in 1857 can be found in [4, S. 191]:
One of Mr. William Ewart’s strongest political supporters duringthe stirring times which preceded the passage of the first ReformBill (of which Mr. Ewart became an energetic advocate) was Mr.John Taylor, who, along with his brother Richard, had commencedbusiness as cotton broker in 1821, but who since 1826 had been byhimself. He was commonly called “Philosopher John”, for besidesbeing an active politician, both as writer and speaker, he was alsonoted as a poet and as an astronomer. He was the first to propose theerection of an Observatory in Liverpool, and out of this suggestionoriginated the present establishment at Bidston Hill. He was oneof the original members of the Cotton Brokers’ Association, andcontinued in business until his death, which occurred in 1857.
William Ewart (1798–1869) was a liberal politician from Liverpool fighting forthe abolition of capital punishment; he voted for the legalization of the metricsystem in England in 1864.
References [1]
A description of the grand suspension bridge , L. E. Jones 1842[2] M. Beech,
The Cometarium by John Taylor , Bull. Scientific InstrumentSociety (2006), 2–6[3] G. Eisenstein, Mathematische Werke , 2 B¨ande, Chelsea 1975[4] Th. Ellison,
The cotton trade of Great Britain , London 1886; s. S.[5] M. Hoskin,
Astronomers at war: South vs. Sheepshanks , J. Hist. Astr. (1989), 175–212[6] Ph. Mitchell Kendall (Hrsg.), Maria Mitchell. Life, letters, and journals ,Boston 1896 57] Rev. R. Sheepshanks,
Correspondence respecting the Liverpool observatorybetween Mr. John Taylor and the Rev. R. Sheepshanks , 1845[8] Rev. R. Sheepshanks,
A letter to the Board of visitors of the Greenwichroyal observatory in reply to the calumnies of Mr. Babbage at their meetingin June 1853, and in his book entitled The exposition of 1851 , London 1860[9] J. Taylor,
Poems and Translations , Liverpool 1839[10] A. Wittmann,
Obgleich und indeßen: Der Briefwechsel zwischen CarlFriedrich Gauß und Johann Franz Encke , Kessel Verlag 2018