**Gustav de Vries** was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterises travelling waves.

- However, few know anything else about de Vries.
- He was a classical geometer who, after teaching at secondary school level in Kampen and Haarlem, taught at a technical college in Delft.
- After high school studies in Amsterdam, Gustav de Vries entered the University of Amsterdam where he was taught by the professor of physics Johannes Diederik van der Waals and the professor of mathematics Diederik Johannes Korteweg.
- After completing his undergraduate studies, Gustav de Vries worked for a doctorate under Korteweg's supervision.
- He earned sufficient money to make this possible by teaching at the Koninklijke Militaire Academie (Royal Military Academy, Netherlands) during 1892-1893.
- The Academy, located in the castle of Breda, trained officers of the Dutch Air Force and the Dutch Army and had not been operating for long when de Vries began to teach there.
- In the following academic year, 1893-1894, de Vries again taught at a military school, this time at the Cadet School at Alkmaar.
- The study of the literature concerning your subject-matter must serve solely as a means for arriving at a more independent treatment, expressed in your own words and in accordance with your own line of reasoning, prompted, possibly, by the literature, which should not be followed so literally.
- When you have mastered your subject-matter to the extent that you can do this, then naturally you will also be confronted with the questions raised by Rayleigh and McCowan, which will provide you with the opportunity to display your strength.
- It is obviously a disappointment for you who must have deemed to have already almost completed your task, to discover that you have apparently only completed the preparatory work.
- Now both Korteweg and de Vries were under considerable pressure at this time.
- The position at the HSB was filled by Gustav de Vries who found the position very time consuming.
- De Vries had studied work on the theory of waves by John Scott Russell, George Biddell Airy, John William Strutt (Lord Rayleigh), John McCowan, Alfred George Greenhill, and Joseph Valentin Boussinesq.
- But, as we note below, both Korteweg and de Vries failed to pay enough attention to the work of Boussinesq.
- On 1 December 1894 de Vries had an oral examination on his thesis Bijdrage tot de kennis der lange golven Ⓣ(Contribution to the knowledge of long waves) which contained the famous Korteweg-de Vries equation.
- The results of this thesis were written up for publication in a paper authored jointly by Korteweg and de Vries On the Change of Form of Long Waves advancing in a Rectangular Canal and on a New Type of Long Stationary Waves published in the Philosophical Magazine in 1895.
- They found explicit, closed-form, travelling-wave solutions to the Korteweg - de Vries equation that decay rapidly.
- These waves take the form of one or several waves propagating with a velocity which is proportional to their amplitude.
- Korteweg and de Vries proved John Scott Russell was right and produced the necessary mathematical justification.
- We now know that this work by Korteweg and de Vries is extremely important, but sadly this was not recognised at the time and it was over seventy years before this fundamental research led to the rapidly expanding research topic of 'solitons'.
- However, both Korteweg and de Vries seem to have completely missed the fact that the equation, now called the Korteweg-de Vries equation, had already appeared in the work of Joseph Valentin Boussinesq.
- The equation appears as a footnote in Boussinesq's 680-page treatise Essai sur la théorie des eaux courantes Ⓣ(Essay on the theory of flowing water) (1885), but this should not in any way diminish the importance of de Vries's contribution.
- Although he found it difficult to work in his home at Ripperdapark 45, de Vries published two further papers in 1900.
- These concern cyclones and were published in the Proceedings of the Royal Netherlands Academy.
- However, despite many attempts, he failed to get a better position for himself.
- Although at first his teaching at the five-year HBS had gone well, things began to go much less well and de Vries felt that he was not getting the support that he deserved from his principal.
- This was not an isolated event for the HSB annual reports of 1902, 1903 and 1904 all note that de Vries had been "absent for a considerable period because of illness".
- It gives me the impression that the author has accidentally noticed a quite natural and unexceptional phenomenon, of whose true nature he makes no correct representation, and now more or less raises the status of what actually amounts to a commonplace thing to a miracle.
- Korteweg showed this letter of rejection to de Vries and this was yet another blow to add to his unhappiness.
- From the documents it appears that De Vries perhaps made too high demands on his pupils in the higher classes, but that he did distinctively well in the lower ones.
- This signifies that he as yet did not expect much from the younger students, but that he perhaps looked for spiritual affinity with the older ones.
- Also, from the long, even printed, open letter to the Alderman it appears that there were many colleagues who found him socially incompetent in dealing with punishing pupils, but also in regard to teaching itself.
- The picture is that of a man with considerable communication problems.
- This lower level school made much less demands on de Vries and his situation seems to have improved.
- That his life was now more stable is shown by the fact that, in 1912, de Vries published two further papers on his 'calculus rationis' in the Proceedings of the Royal Netherlands Academy of Sciences.
- De Vries taught at the three-year HBS in Haarlem until he retired in 1931, when he reached the age of 65.
- However, he developed new interests in freemasonry and spiritualism.
- He also entered a long and deep discussion concerning Goethe's Faust.
- In December 1934 he attended a séance in Haarlem-Noord.
- to commemorate the centennial of the equation by and named after Korteweg and de Vries.

Born 22 January 1866, Amsterdam, The Netherlands. Died 16 December 1934, Haarlem, The Netherlands.

View full biography at MacTutor

Origin Netherlands

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive