Sophus Lie (1842-1899) often went on long, physically demanding hikes. Sometimes he got himself into trouble because of this. In August 1870, after the outbreak of the Franco-Prussian war, he attempted to travel on foot from Paris all the way to Milan, to visit Luigi Cremona and enjoy the scenery of French and Swiss Alps along the way. Unfortunately, he travelled with an expired Norwegian passport, so in Fontainbleau (about 50 kilometers south of Paris) he was taken for a German spy and imprisoned. Of course being in possession of strange-looking notes with some German names here and there did not help him. At the intervention of Gaston Darboux he was released after a month and continued his itinerary on a train. But this incidents did not deter him from hiking. Two years later, when courting his future wife in Norway, he visited her a few times on foot, going about 35-40 kilometers each way. In a letter to her he wrote:
``I have used my Legs in a decent manner during these Days (...). People think that I have very strange Tastes; but this strengthens the Muscles and Nerves, and besides, I find myself with such good feelings, as I roam the Countryside as a Hobo. By habit, I am always deep in my own Thoughts, and building Castles in the Air for the Future: and You quite understand who it is that plays the Main Role..."
(citation after Arild Stubhaug,
The Mathematician Sophus Lie.
It was the Audacity of My Thinking. Springer 2002
https://www.springer.com/us/book/9783540421375)
He was trying to pass on his passion for outdoors to his children. His daughter recalled that the family went on on a long tour every Sunday. The children were taught skating and had skis imported from Norway, which were still a novelty (and created a sensation) in the German city of Leipzig, where Lie was appointed a professor of mathematics.
