## Axel Thue writes from Berlin

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

*Selected mathematical papers of Axel Thue*(Universitetsforlaget, 1977). Before giving this text we note that Palmström, mentioned in the text, is Arnfinn Palmström (1867-1922) who became professor of actuarial mathematics. Professor Hettner, who gave lectures on e and π, is Georg Hermann Hettner (1854-1914) Hettner who was an associate professor of mathematics at the Technical University of Berlin. Here is Thue's letter:I liked Berlin enormously from the very first, streets broad with plenty of light, big parks, plenty to see and hear. I have thrived here continuously. It was congenial to have Palmström living here too ...

In the first semester Palmström and I attended Kronecker's lectures on the theory of algebraic equations. He is remarkable for his great depth and thoroughness, but has the bad habit in the grip of his enthusiasm to impart definitions and other absolutely essential information altogether too rapidly. It is very easy to miss the point under such circumstances. He is an extremely likeable man, but prefers to do the talking himself, and at considerable length. I have therefore only been able to communicate my own erudition in minimal quantities. His knowledge of books is astonishing. There seems to be nothing he hasn't looked into. He praises Abel and sundry other potentates to the skies, but he appears to nourish an antipathy towards mediocre talents, and in such cases he can be severely critical. Kronecker has a particularly lively style of lecturing and knows how to present things with taste, so that one has the feeling that he himself has a real appreciation of the fare which he is serving to his students.

Fuchs, whom I heard lecture on analytical mechanics, did not at first make much of an impression on me. The concepts he employed were, as far as I could see, surrounded by a mist of vagueness. When I heard him in a seminar, however, I got a strong presentiment that he can excel when he wants to do so. He lectures with his eyes shut and looks thoroughly tired and peevish. He can also be rather absent-minded. I remember how he was once talking about differentials, and quite unconsciously he picked up a handful of bits of chalk which he waved in illustration before our wondering eyes. Afterwards he carefully laid his differentials down again on his desk, with his eyes still closed. Professor Fuchs, like Kronecker, is a very prepossessing man, but not overly talkative. I was at a ball at his home this winter. It was a delightful affair. We danced so energetically that the floor cracked in a couple of places.

This semester I am again attending Kronecker's lectures on definite integrals, and those of Helmholtz on hydrodynamics and the theory of elasticity. The problems associated with this latter subject are of increasing interest to me. As you know, we ought not to be too cocksure that space is infinite. The following thought has struck me, that the assumption that space is finite and that the straight line recoils upon itself will explain the fact that there is still warmth and life on earth and that all the warmth has not been radiated away into "infinite space" long ago, let us say 1000000

^{10000999}years ago. If the straight line was no more than 230 kilometres and a bit, perhaps the sun would be able to shine on itself if it stood still, or if one postulated certain other "ifs". In general, it is a problem of the greatest interest. When I get home, I will certainly try first of all to discover that geometry of space in order subsequently to solve the problem of the movement of a fluid which fills that space etc. I'd like to talk to Helmholtz about this. I haven't visited him yet. He is certainly a thinker of rare genius, perhaps the greatest in Germany, but his lectures, as far as presentation goes, are far from being first rate. I have long since given up any attempt to write them down. Fortunately, his most famous works in this field are available in print.

Professor Hettner in his lectures about e and π is dealing with the same matters with which I at one time gladdened the seminar. He talks like a book, distinctly and correctly. Palmström, who heard his lectures about determinants, was finally moved to praise him to the skies.

The mathematical seminar down here functions in much the same way as yours does in Oslo. It is an established university institution. Fuchs and Kronecker preside in turn. Meetings are held between 5 and 7. No report is circulated. I have requested Kronecker to permit my highly attractive voice to be heard at the aforementioned place, but so far he hasn't paid any attention. This is annoying because in this way I have missed a valuable opportunity of acquiring practice: it is all the more annoying because many Germans have been allowed to lecture many times on different topics. In the mathematical society on the other hand, I have lectured twice to an eagerly listening audience, once on a stereometric subject, once on something relating to theory of numbers.

I haven't had as many ideas as in Leipzig. I have written about 500 pages, but most of them can be scrapped. There are indeed some discoveries which will be a great boon to our society, but I can't exactly employ the number I have used above, in counting them.

Yours faithfully,

Axel Thue.