František Josef Gerstner

Quick Info

23 February 1756
Chomutov, Bohemia, now Czech Republic
25 July 1832
Mladejov, Bohemia, now Czech Republic

František Josef Gerstner was a Czech mathematician, astronomer and engineer. He is famed for transforming the Prague School of Engineers into the Prague Polytechnic Institute in 1806. It is now the Polytechnic University of Prague. He also produced a non-linear wave solution, known today as Gerstner waves or trochoidal waves.


Let us note first that František Josef Gerstner is also known as Franz Josef Ritter von Gerstner. František is the Czech version of his forename while Franz is the German version. He became Ritter von Gerstner when he was elevated to the nobility in 1810. The town of his birth is known in Czech as Chomutov but it was also known by the German name of Komotau; it is roughly equidistant between Leipzig and Prague. He was the son of Florian Gerstner (1730-1783), a leather worker, and Maria Elisabeth Englert, the daughter of a butcher. Frantisek was educated in his home town of Chomutov, attending the Jesuit Gymnasium from 1765. During 1771-72, he was taught by Ignaz Cornova (1740-1822), a Jesuit priest and historian who left Chomutov in 1773 to became a professor of Poetry and Classical Greek at the Jesuit college in Klatovy. At the Jesuit Gymnasium, Gerstner's [2]:-
... favourite subjects included mathematics and physics and where he learnt perfect Latin. He was very dexterous, and acquired technical skills in many different crafts (joinery, carpentry, locksmith work, smithing, bricklaying, dyeing, soap-making, etc.). He eventually put these practical skills to a good use during his pedagogical career.
In 1772 Gerstner graduated from the Jesuit Gymnasium in Chomutov and entered the Faculty of Philosophy at the Charles-Ferdinand University in Prague to study mathematics and astronomy. He studied elementary mathematics with Stanislav Vydra (1741-1804), higher mathematics with Jan Tesanek (1728-1788) and astronomy with Joseph Stepling (1716-1778). Stepling was a Jesuit priest who was an astronomer, physicist and mathematician. He founded the Clementinum Observatory in Prague in 1751 and was appointed to teach mathematics and physics at the University of Prague in 1753. He championed the ideas of Newton and Euler. Tesanek, also a Jesuit, was a student of Stepling at the University of Prague. He became an expert in the works of Newton and was appointed as Professor of Higher Mathematics at the University. Vydra was a student at the University of Prague where he was taught by both Tesanek and Stepling. He served as Professor of Mathematics at the University of Prague from 1772, teaching elementary mathematics. In 1776 Gerstner passed his astronomy examination and in the following year he was examined in Newton's Philosophiae Naturalis Principia Mathematica , again passing the public examination.

Gerstner's family were not well off, and so he had to earn money to support himself during his student years. He did this by earning money by playing the organ in various Prague churches, but he also gave private tutoring in mathematics in order to cover his living expenses. He completed his studies at the University of Prague in 1777, and in 1779 he was employed as an engineer with the Robot Abolition Commission. The Domains and Robot Abolition Commission was responsible for converting church and other land in crown control to peasant ownership. He did not find this occupation very pleasing, so in 1781 he decided to have a complete change of career and went to Vienna to study medicine. He rapidly decided this was not a good move, and returning to mathematics and astronomy, he spent the next three years working as an observer at the University Observatory in Vienna. This observatory was built in 1743-54 on the roof of one of the university buildings. Gerstner was an assistant of the director of the University Observatory, Maximilian Hell (1720-1792). Hell had been director of the Observatory since 1756, had published astronomical tables, and had been to Sweden in 1769 to observe the transit of Venus on 3 June of that year.

Antonín Strnad (1746-1799) was a Jesuit who, after the abolition of the Jesuit Order in 1773, studied mathematics, physics and astronomy under Joseph Stepling at the University of Prague. After the death of Stepling in 1778, Strnad was appointed as an extraordinary professor, and became director of the Clementinum Observatory in 1781. In 1784 Gerstner was appointed as Strnad's senior assistant. His publications were in German and began in the following year with On the determination of longitudes, correcting the longitudes of Marseille, Padua, Kremsmünster, Dresden, Berlin and Danzig. In 1786 he published Transit of Mercury in front of the Sun. Observed 4 May 1786.

When Gerstner's former teacher of higher mathematics, Jan Tesánek, fell ill in 1787, Gerstner provided him with careful care in his own apartment and at the same time taught Tesánek's students higher mathematics. Following Tesánek's death in 1788, Gerstner was employed as an assistant to take over his teaching commitments at the University of Prague. In the following year he become professor of Higher Mathematics, Astronomy, Mechanics and Hydraulics at the University in Prague. Let us record at this point that his most famous student was Bernard Bolzano who entered the Philosophy Faculty of the Charles University of Prague in 1796, studying philosophy, physics and mathematics. In 1799 Bolzano began undertaking research advised by Gerstner and was awarded a doctorate in 1804.

In 1792 Gerstner married Gabriele von Mayersbach, the daughter of the medical doctor Moritz Adolph Mayer von Mayersbach and his wife Maria Greger von Ehrenberg, in Prague. They had five sons and four daughters. One of their sons was Franz Anton Gerstner (11 May 1796 - 12 April 1840) who achieved fame as a civil engineer and railway pioneer. We will say a little about his career at the end of this article.

A commission was set up in 1795 with the aim of improving higher technical education in the Austrian empire. As a member of this commission, in 1798 Gerstner drafted a memorandum. He began by stressing the importance of mathematics and physics in technical advances (see [3] and [13]):-
Wherever natural sciences, physics and mathematics are not successfully practised, industry cannot be elevated from its backwardness. New forces and new laws of nature have been discovered, giving rise to new production ... However, even momentous discoveries of science and technology have never been made by a few isolated ingenious minds. First of all, the overall level of general education has to be raised to a high degree of technical knowledge, and a passionate desire has to be aroused for education ... The emerging polytechnic should be designed for the nascent higher technical intelligentsia. Specialised training will be given to owners of iron works, glass works, dye works, to watchmakers, mechanics and builders. It will educate chief officers and foremen at private plants, manufactories and workshops.
He argued that a polytechnic should be established (see [3] and [13]):-
The first draft for the foundation of a polytechnic for the entire Habsburg monarchy, submitted in 1798, displayed more or less the following structure. Gerstner intended to set up a school providing two different types of courses, elementary and higher. The elementary course was designed to match subjects taught at Prague University's Faculty of Philosophy, while the higher course offered solely technical subjects. The higher course was expected eventually to form the basis for an independent school - a polytechnic. The elementary course was based on mathematics and natural science subjects (the project reckoned on the establishment of collections including exhibits on natural sciences, physics and machinery, and a botanical garden). Gerstner's higher course also covered the so-called professional sciences, based on industrial and generally technical studies.
Having set out the details of what should be taught and how professors should be appointed, Gerstner gave a list of the advantages:-
... in addition to teaching students, the school could also train teachers of technical subjects, take over supervision of the emerging secondary technical and industrial schools, devote itself consistently to practical work, prepare expert opinions on technical projects, and, last but not least, train graduates for the civil service (including military careers).
Gerstner's proposals, which were made at the time of the Napoleonic wars, did not find favour, so, in 1803, he made a second proposal involving converting the Prague School of Engineers, which had been founded in 1707, into a polytechnic school. Emperor Franz Joseph I issued a decree confirming this on 14 March 1803, naming the new polytechnic the Gerstner Polytechnic. Gerstner, however, did not give up on his original proposal and, with a change of emphasise to the more practical sides of the subjects, this was approved by decree on 22 August 1805. The Polytechnic Institute in Prague was officially opened on 10 November 1806 with Gerstner as its first director. The Polytechnic was highly successful with 106 students in 1806 raising to over 400 by 1825. It had exceedingly high standards with only around a quarter of the students who entered successfully graduating. We can also judge the success of Gerstner's concept of a polytechnic by the fact that over the following years many similar polytechnics were founded in cities across central Europe.

In 1804 Gerstner published the book Theorie der Wellen: samt einer daraus abgeleiteten theorie der deichprofile . This contained a description of what today are known as Gerstner waves or trochoidal waves. He had first described these in a work of 1802, and his brilliant work was well ahead of its time. Only in 1863 did Rankine independently discover these waves. The basic idea is as follows. When a wave moves across water, the water itself is not moving along with the wave. But the water cannot remain only moving up and down, for there must be more water under the crest of a wave and less under at a trough. In the Gerstner model, a water particle basically moves in a circle about a fixed point. David Henry writes [7]:-
... Gerstner's flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.
Another important work by Gerstner is Handbuch der Mechanik in three volumes: 1. Mechanik fester Körper (1831); 2. Mechanik flüssiger Körper (1831); and 3. Beschreibung und Berechnung grösserer Maschinenanlagen (1834). Gerstner's son Franz Anton Gerstner wrote a Preface to the work which begins as follows:-
The great advances which the mechanics of the heavens made in the last century with the help of higher analysis, already in my father's student years, aroused a keen desire that the same enlightenment would also like to be given to the mechanical trades, to guide them with equal certainty in the progress of industry, and keep them from those cliffs where so many promising enterprises have found their downfall.

When visiting several mechanical workshops, larger state factories and completed buildings, he found the opportunity to draft several essays on such subjects through his own reflection and soon after taking up his post as a teacher of higher mathematics in 1788 with the intention of publishing some smaller writings in the field of architecture and hydrodynamics.
He wanted to draw the attention of the heads of agricultural and civil trades to the advantages of mathematical studies and to recommend the study of higher mathematics for their pupils and successors in particular. Precisely his writings were the reason why he was frequently consulted about larger industrial establishments, improvements in the most important Bohemian ironworks and other state factories, and he was thus given the opportunity to become acquainted not only with the advantages and defects of these establishments, but also with the causes of the absorption and decay of other similar factories.
In 1807, Gerstner was commissioned by the Bohemian Hydrotechnical Society to calculate possible salt transport routes between Budweis and Linz and to draw up a transport route solution with cost estimates. He investigated a route, partly by water and partly by horse-drawn railway. This would have required making the river Vltava navigable from Budweis to Joachimsmühle, and building a railway line from Joachimsmühle to Katzbach, near Linz. He found a cheaper solution, however, with a good route for a horse-drawn railway for the whole journey. His plan was accepted in 1808 but the Coalition Wars between the Austrian Empire and the French under Napoleon delayed the start of the project. In fact, only in 1824 did work start with Gerstner's son Franz Anton Gerstner in charge.

In 1808 Gerstner's wife Gabriele died and in 1809 he married Maria Stark. Also in 1808, Franz Joseph Gerstner was awarded the Austrian Order of Leopold and he was elevated to the hereditary nobility in 1810. In 1811 the Emperor appointed him director of hydraulic engineering in Bohemia. His health began to deteriorate and he gave up teaching mathematics in 1822 but continued as director of hydraulic engineering and teaching mechanics. As his health became poorer, he felt forced to resign as director of hydraulic engineering in 1828 and gave up teaching mechanics in 1831. At this point he continued as director of the Polytechnic Institute but retired from this position in April 1832. He died in Chateau Mladejov, which he visited frequently after it was acquired by the family Pabstmann in 1792, only three months after he retired and was buried in the cemetery in Mladejov.

Karl Karmarsch writes in [9]:-
Not only through the educational institution he founded and the other branches of his activity already mentioned did Gerstner render great services to Bohemia; his advice in matters of industrial enterprise was sought after and influential; Indeed, one can rightly say that for almost half a century few such larger undertakings came into being on Bohemian soil without his direct or indirect participation.
On 25 May 1957 Czechoslovakia issued a series of four stamps to commemorate the 250th anniversary of the creation of the School of Engineering in Prague. The 30 haler stamp had a portrait of Josef Bozek (1782-1835), the 60 haler stamp had a portrait of F J Gerstner, the 1 koruna stamp had a portrait of J Skuhersky, and the 1.40 koruna stamp had a picture of the School of Engineering building. In 2006, the Czech Republic issued an 11 koruna stamp for František Josef Gerstner. See THIS LINK.

We promised to give some further details of Gerstner's son, Franz Anton Gerstner [6]:-
Franz Anton grew up in a household of upward mobility, engineering practice, and scholarly research and instruction. He studied at the University of Prague and then at the Standing Technical Institute in Prague, which his father helped to establish. In 1817, he was entrusted with a teaching post in practical, or engineering, geometry at the new Polytechnic Institute at Vienna. Eventually he became professor of mathematics there. Franz Anton's credentials as a professor of engineering knowledge were thus well established. The young nobleman had both the education and the social status to become the leading civil engineer of railroads on the European continent.
Franz Anton constructed railways in Russia, then went to the United States, arriving in New York on 5 November 1838. He toured the railroads of America but died of pneumonia a year later in Philadelphia.

References (show)

  1. F Balada, Frantisek Josef Gerstner, Matematika ve škole 7 (1957), 129-132.
  2. M Efmertova, Czech Technical Education: The Educational Reforms of Franz Joseph Von Gerstner and his Relationship with the Paris Ecole Polytechnique, Icon 3 (1997), 202-223.
  3. J Folta and P Sisma, Frantisek Josef Gerstner, Department of Mathematics and Statistics of the Faculty of Science, Masaryk University.
  4. Frantisek Josef rytir Gerstner (Franz Josef Ritter von Gerstner), Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague.
  5. Franz Josef von Gerstner, (May 2021).
  6. F C Gamst, Franz Anton Ritter von Gerstner, Student of America's Pioneering Railroads, Railroad History 163 (1990), 13-27.
  7. D Henry, On Gerstner's Water Wave, Journal of Nonlinear Mathematical Physics 15 (Supplement 2) (2008), 87-95.
  8. F Kaderavek, Frantisek Josef Gerstner a prazska polytechnika, Pokroky matematiky, fyziky a astronomie 1 (1956), 443-446.
  9. K Karmarsch, Gerstner, Franz Josef Ritter von, Allgemeine Deutsche Biographie 9 (1879), 67-69.
  10. P Mechtler, Gerstner, Franz Josef Ritter von, Neue Deutsche Biographie 6 (1964), 328-329.
  11. J Psota, Frantisek Josef Gerstner, Pokroky matematiky, fyziky a astronomie 1 (1956), 317-319.
  12. J Psota, Frantisek Josef Gerstner jako matematik a astronom, Pokroky matematiky, fyziky a astronomie 1 (1956), 446-449.
  13. A V Velflik, A History of Technical Teaching in Prague (Czech) (Prague, 1906).

Additional Resources (show)

Other pages about František Josef Gerstner:

  1. Miller's postage stamps

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update March 2022