Sophus Lie. 67 



Unhappily, recognition appears to have been, not merely slow in 

 coming, but almost too late when it came. There is no doubt that his 

 ceaseless activity in thought and work had undermined his strength, 

 and his spirit had brooded in its loneliness. He suffered from sleep- 

 lessness, and developed nervous symptoms : the result was a complete 

 breakdown in 1889. The direct interruption of his work lasted for a 

 large part of a year ; happily he was afterwards able to resume it, and 

 for a time was as fertile in production as he ever had been. But the 

 effect upon the man never completely passed off ; it seems to have 

 exercised, upon his attitude towards life and in his personal relations 

 with his friends, a morbid influence which lasted for the remainder of his 

 days. ' The brighter side of these years is to be seen in the record of 

 his continued work. How great that record is, may be gathered from 

 the tale of his published work.* It includes over 150 memoirs, many 

 of them of considerable length, and six volumes. Reference has already 

 been made to his three-volume treatise on groups of transformations. 

 In a couple of instances, his lectures in amplification and elucidation 

 of portions of his theory were edited and published in volume form by 

 his pupil, Scheffers, whose help is gratefully acknowledged : one of 

 these relates to differential equations that admit of known infinitesimal 

 transformations ; the other to continuous groups. 



Two other works were promised by him. One of these, to be written 

 in co-operation with Engel, was to deal with the theory of infinite con- 

 tinuous groups and the application of the general group-theory to the 

 integration of differential equations: this work has not appeared. 

 The other, to be written in co-operation with Scheffers, was to be 

 devoted to a systematic exposition of his geometrical investigations ; 

 the first volume has appeared under the title ' Geometric der Beriihr- 

 ungstransformationen.' 



As his fame grew, placing him in the forefront of the mathemati- 

 cians of his day, a strong desire was felt by his fellow-countrymen 

 that he should return to Norway, and that some professorship of 

 exceptional dignity should be created expressly for him in Christiania. 

 Such a post was made for him about 1896 ; but he only returned to 

 his native country to occupy it in September, 1898. The desire of his 

 fellow-countrymen was thus gratified honourably for Lie, but unhappily 

 too late to be effective. His broken health forbade any long tenure 

 of a chair in which, as had been hoped, he would be able to continue 

 his mathematical researches. He was almost a dying man on the day 

 of his return ; he lingered through part of the winter ; such little 

 strength as was left was undermined by pernicious anaemia; and he 

 passed away on the 18th of February, 1899. 



* A full bibliography is given by Engel in the article already quoted in ' Biblio- 

 theca Mathematical 3rd ser., vol. 1 ; see pp. 174 204. 



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