Korteweg inspired many young mathematicians who wrote their doctoral thesis under his supervision. Besides G. de Vries, we mention Hk. de Vries, H.J.E. Beth (the father of the logician E.W. Beth) and last but not least, L.E.J. Brouwer.
The conscientiousness and the courage shown by Korteweg, albeit an applied mathematician, in supervising Brouwer's thesis 'Over de Grondslagen van de Wiskunde' ('On the foundations of Mathematics') is remarkable. The thesis was defended in 1907 and the negation of the 'principle of the excluded middle' followed in 1908. Ten years later the thunder was roaring between Göttingen and Amsterdam.
Korteweg's teaching duties concerned analytic and projective geometry, mechanics, astronomy and probability theory. He was meticulous in the preparation of his lectures and keenly interested in the progress of his students; a student could have a tough time when he was not applying himself.