- From an article by Vilhelm Bjerknes which appeared in Aftenposten:
Everyone who came in close contact with him received a strong impression of his gifts in the areas which occupied his thoughts. In the ease and speed with which he grasped the most difficult questions, in creative imagination no less than in rigorous logic, he was far superior to his fellow students He acknowledged only one law: The resolute demand that his intellectual work must satisfy himself. For that reason, he never progressed very far with the reading of a mathematical work before he jettisoned it in order to rebuild its whole intellectual construction according to his own Ideas. This prevented him from ever becoming a deeply learned man. He was incapable of following the beaten track which by a systematic acquisition of the fruits of earlier work leads one to the special fields of work of the present day.
- From a speech by Fredrik Lange-Nielsen in the Students' Union In Oslo:
As a university teacher, Thue occupied a unique position, altogether unlike others I have heard His courses of lectures were exceptionally well thought out and organised. They were vastly different from the standard text-book presentations, every word being wholly and entirely his own original work. Everyone who has come into contact with Professor Thue will always retain the impression of his rare personality. He was impervious to fashion, he cared nothing for what was considered to be scientifically in vogue or out of date. As a thinker and as a person, he possessed qualities which have eternal value.
- From an article by Ralph Tambs Lyche, a student of Thue's, written on the 100th anniversary of his birth:
There was something paradoxical about the fact that Axel Thue, when he finally became a professor in Oslo, was appointed to the chair of Applied Mathematics. But one would be seriously mistaken in supposing that Thue would neglect "applied mathematics" (i.e. rational mechanics, according to the university's traditional interpretation of the term), merely in order to occupy himself with number theory and other "non-applied" mathematical subjects. On the contrary, he took his professorship very seriously, but of course, in his own characteristic fashion. His lectures on mechanics were models of their kind as regards their overall strategy and the logical rigour of their construction.
- From an article by Viggo Brun, his student during 1903-5 and his substitute 1920-22:
Thue gave his first lectures on mechanics at the University of Oslo during my first semester as a science student. He dictated his lectures to us, and I was astonished that he could do so without referring to a manuscript, proof of the unique capacity of his memory. Among these lectures, his treatment of the principle of virtual velocity was of especial importance. He wrote a monograph about this principle In 1912 which begins as follows: "Among the most beautiful and significant achievements of mechanical science is the principle of virtual velocity, or more precisely displacement. The principle normally approached through dynamics, is however fundamentally geometrical in character. It should therefore preferably be described in terms of vectors, and can thus be constructed on geometrical premises without introducing irrelevant physical relationships. In what follows, I shall briefly and schematically outline and in part prove a set of propositions on which a kinematic theorem can be based which covers the most important aspects of the principle under discussion." As far as I know, the theorem has the interest of novelty. A later, more detailed description of this principle is to be found in the excellent report of Thue's lectures which we owe to one of his pupils. A copy of the report is to be found in the university library in Oslo along with the large collection of unpublished papers previously mentioned. After the formulation of this principle the reporter has added: "Thue himself has shown that by means of this principle one can prove all theorems in absolute geometry. Also the main heads of the calculus of variations. The impossibility of a perpetuum mobile (which we saw) etc. An exceptionally profound principle." Thue never lectured on the theory of numbers. There was never any question of cooperation of a mathematical character between Thue and myself. He only once asked me to investigate whether a theorem he had discovered was new. I had to disappoint him by telling him it was already known. Thue once told me that in Leipzig he had discovered a proof of the existence of transcendental numbers, but it turned out that Liouville had already come up with the same proof. "When I went into the library and saw the book which contained Liouville's proof, which was almost identical with mine, I was so struck that I can still see before me the place on the shelf where the book stood," he said. (Compare the footnote after Thue's article . Über Annäherungswerte algebraischer Zahlen: "Vergleiche den Beweis von Liouville für die Existenz transzendenter Grössen; Journ. de Math. t. XVI, 1851.) It was as hard for him to read other people's work as it was easy for him to think things out for himself. Thue dictated his lectures. When I deputed for him during his final illness, he asked me to dictate the lectures he had prepared. I asked him whether I might be allowed to abbreviate a few things. "No", he replied, "I've discovered that if it is possible for anything one has written to be misunderstood, then it always is."
- From the commemorative speech by Carl Stürmer at the Norwegian Academy of Science and Letters on 21 April 1922:-
With the death of Professor Thue on 7 March this year, the Academy of Science has lost one of its most illustrious members, a mathematical genius who united the gift of extraordinary originality with a rare perspicacity and sense of logic.