# Axel Thue writes from Leipzig

In 1891-92 Axel Thue held a travelling scholarship which enabled him to spend time at Leipzig and at Berlin. Sophus Lie had been on the faculty in Oslo and had known Thue from that time. Thue visited him in Leipzig in 1891. He wrote a letter to Elling Holst, who was in Oslo, while he was in Leipzig. Here is the text of this letter as given in T Nagell, A Selberg, S Selberg and K Thalberg (eds.),

*Selected mathematical papers of Axel Thue*(Universitetsforlaget, 1977). Let us not first that the Professor Mayer mentioned in the text is Adolph Mayer who, although giving lectures in his home city of Leipzig, was on the faculty at Heidelberg. Here is the text of Thue's letter:In the first few months my hands were so full that everybody at home thought I was dead and buried, and in the last three months I have enjoyed a deep yellow complexion, hair grown grey and other kind gifts of providence which have so entirely absorbed all my attention and all my thoughts that only the loudest complaints have been able to extract any communication from me. I have received a number of letters from my friends and acquaintances, and as you can well Imagine this has given me encouragement and amusement. But generally speaking I haven't sent any reply ....

My work with Lie has not led to any positive and conclusive result. Before the vacation the important thing was simply to get a general idea of his profound theory of transformation, his contact transformations and whatever was connected with it, so that afterwards in the vacation I could acquire a solid foundation which would make it possible for me to obtain a full comprehension. As you will readily understand it was by no means easy for me to taste so many things at the same time after so exhausting an examination period. During the first few days of the vacation we calculated together a large number of examples, and Lie did all he could to ensure that I got the maximum profit out of my stay down here. When I began to show signs of fatigue I took a brief recreational trip to Prague via Dresden, and came back looking like a full-blooded Chinese. Since then I have been preoccupied only with my own transformations. As far as Lie's material is concerned (which seems to be of increasing interest to the world of science) my stay down here has not been entirely wasted. Even if much of what I learned during the summer is now only a dim memory on account of that sudden interruption, I have nevertheless got a sufficiently good grasp of the material to be able to acquire a full understanding of it fairly quickly.

On the other hand I was lucky enough to be able to attend a complete lecture on the calculus of variations by Professor Mayer, who is by all accounts the world's leading authority. Generally speaking, it is odd how the prevailing mathematical climate here has an inspiring effect. I had plenty of new ideas, and to Lie's great dismay, I put together a great deal of nonsense. Amongst other things I made the most pertinent discoveries in the field of number theory: it has been pioneered here. I have also been concerned with other matters, but every time I came to a significant result, it turned out to be one well known already. It is to be hoped that there is still something left which can be said to be novel, and which learned mathematical palates will relish. I am of a mind to take your advice about coming home at once. The disease can come to last for another three months, and in that case my grant will be used up entirely.

Yours faithfully,

Axel Thue.

Last Updated July 2014