Jozef was the son of the schoolmaster Johann (Ján) Friedrich Petzval and his wife Susanna (Zuzana) Creutzman. Susanna, the daughter of Joseph and Susanna Creutzman, was baptised in Spisská Belá on 20 April 1776. Johann, born on 4 July 1775 in Lodenice, taught in the evangelical school in Spisská Belá and :-
... was a great influence on Joseph. A well-rounded man, Johann Friedrich was an incredibly gifted musician, composer, and hobby mechanic. He made a lasting musical contribution to the churches in their district, but also made pianos, improved the riding saddle for the Hungarian military, and even worked on the Perpetuum - an early flying machine. He was known for being very eccentric and would often be found directing the church choir in his pyjamas.Jozef was one of his parents' six children (actually seven but one died while a baby). He had a younger brother Otto Balthasar Petzval who was born on 6 January 1809. Note the coincidence that both brothers were born on the same day but an even greater coincidence is that the third brother Ján was only one day different, born on 7 January, or some say also on 6 January. The 6 January is the Christian festival of the Epiphany when the three Kings, Melchior, Caspar and Balthasar, visited the new born Jesus and hence the naming of Josef's brother as Otto Balthasar. Unsurprisingly the three brothers were known in their family as the "Three Kings". Let us note at this stage that Otto Petzval also became a professor of mathematics and published Elementary mathematics (Hungarian) (1856) and Higher mathematics (Hungarian) (1867). The other three children were girls, one of whom was Maria Mathilda.
Johann had to leave Spisská Belá because of problems in his church, and in 1815 the family moved to Késmárk. Joseph attended primary school in Késmárk (now Kezmarok in Slovakia) and, after that, the gymnasium at Podolin (now Podolinec). He completed his schooling in Levoca where the family moved in 1819. At first his best subjects were Latin and religious studies while he performed badly in mathematics having no interest in the topic. Petzval's teacher advised his father that he should leave school and take up a trade and the family considered having him become an apprentice to a cobbler. However, he found an interesting book on mathematics, namely Analytische Abhandlung der Anfangsgründe der Mathematik (1807) by Mathias Hauser. He studied this book over the summer and his performance improved markedly so that when he returned to school in the autumn he was now the best mathematics student in his class. After leaving school in 1823 he went to Kosice (named Kassa at the time) where he attended the Lyceum for a while but he was financially poor and was forced to undertake work as a tutor to earn money to survive. He spent two years studying with Professor Barlai, the Professor of Mathematics and Philosophy. After completing his studies, he took a one-year position as a tutor employed by Count Almássy.
In 1826 Petzval entered the Institutum Geometricum of the University of Pest (today the Eötvös Loránd University) to study philosophy and mathematics. Later, in 1872, the town of Pest was to join with the town of Buda on the opposite bank of the Danube to form Budapest. The main language of instruction at the university at this time was German and not until 1860 did Hungarian become the language of instruction. During his two years at the university he studied the works of Lacroix, Laplace and Lagrange. He also made quite a reputation for himself in the student body as a highly skilled fencer. After graduating from the University with an engineering degree in 1828, Petzval was appointed to the city of Pest as an expert in flood prevention and drainage. He undertook this work for seven years and showed real talents in his job.
Petzval taught mechanics and mathematics at the University of Pest from 1832 and he became a professor in Higher Mathematics at the University of Pest in 1835. Then, two years later, he accepted a chair of mathematics at the University of Vienna. We note that soon after Petzval left the University of Pest, his brother Otto Petzval was appointed as a professor of Higher Mathematics at the University of Pest in 1839, a position he held until his death in 1883.
Petzval worked for much of his life on the Laplace transform. He was influenced by the work of Liouville and wrote both a long paper and a two volume treatise on the Laplace transform and its application to ordinary linear differential equations. His study is thorough but not entirely satisfactory since he was unable to use contour integration to invert the transform. But for a student of Petzval we might today call the Laplace transform the Petzval transform. Petzval fell out with this student who then accused Petzval of plagiarising Laplace's work. Although this was untrue, George Boole and Henri Poincaré, influenced no doubt by the quarrel, called the transformation the Laplace transform. Szénássy writes :-
... in the [19th] century [Hungarian] scientists obtained particularly nice results in the theory of differential equations. ... special mention must be made of Józef Petzval who, after a whole range of articles on remarkable results of his own, around the middle of the [19th] century published a two-volume monograph on differential equations that was the only guide in the field for a long time [Integration der linearen Differentialgleichungen (Vol. 1, 1853; Vol. 2, 1859)]. Decades later it will still be referred to as a major source. Among his original results, the most important ones concern the singular solutions to linear differential equations with a complex variable. He went deeper into this subject than Riemann and was ahead of Poincaré in several respects. The nowadays fairly complete theory of Riccati's differential equations owes a lot to him.Today Petzval is best remembered for his work on optical lenses and lens aberration done in the early 1840's (Petzval curvature is named after him) which allowed the construction of modern cameras. Petzval produced an achromatic portrait lens that was vastly superior to the simple meniscus lens then in use. In  his work in optics is described as follows:-
[At the University of Vienna] he studied in detail L M Daguerre's invention, the so-called daguerreotype, and took on shortening its exposure time from minutes to seconds. In 1840, his extraordinary mathematical talent allowed him to assess and build an anastigmatic with six times greater luminosity. This Petzval highly luminous early form of photo lens was used by the enterprising Viennese optician Voigtländer, who launched its mass production and won a silver medal at the World's Exhibition Fair in Paris. Petzval also perfected the telescope and designed the opera glasses.This description actually hides a lot of the difficulties that Petzval encountered. After he was appointed to the chair of mathematics at the University of Vienna he rented an abandoned monastery on the Kahlenberg mountain in the Vienna Woods and there set up his own glass workshop. The portrait lens he designed was a great improvement on previous lenses and Petzval had completed the calculations by May 1840. He handed the design over to the company Voigtländer & Sohn run by Peter Wilhelm Friedrich Voigtländer (1812-1878) and received a small sum for them. Voigtländer's company, which had been founded by his grandfather Johann Christoph Voigtländer in 1756, marketed a camera using Petzval's lens design in 1841 and it revolutionised portrait photography. Voigtländer made a fortune but Petzval had not taken out patents and received no royalties. He fell out with Voigtländer and attempted to construct his lens at his workshop on the Kahlenberg. He was approached by the Military Geographic Institute and they asked him to design a landscape lens. He did so and produced the design of a lens which again vastly improved on what was in current use. In collaboration with the optician Carl Dietzler they discussed marketing the lens around 1854. He presented his lens at a meeting of the Academy of Sciences Leopoldina in 1856, but, although his work was received with great enthusiasm, Dietzler's firm went bankrupt in 1862. Voigtländer again used Petzval's designs to market his own cameras, further increasing the enmity between the two men.
Although Petzval is now recognised for his remarkable work on optics, he was so disillusioned by how things turned out that he gave up all his work on optics and even stopped lecturing on the subject. The last straw came in 1859 when his home was burgled and the manuscript of a treatise on optics which he was writing was destroyed. After that he turned to research in acoustics but he still was a founder of the Photographische Gesellschaft in 1861 but declined the offer of the presidency, preferring instead to be awarded an honorary membership.
Petzval seems to have been entirely in the right over his arguments with Voigtländer but, unfortunately, he also had an argument with Christian Doppler where he was totally incorrect. The problems arose for a number of reasons. First Petzval considered photography as an art form for portraits and landscapes, not as a tool in scientific research. Secondly, he was a firm believer in scientific discoveries being firmly mathematically based and only if one could describe the science via differential equations was it, for him, proper science. It was these beliefs that led to his completely incorrect attack on Doppler's theories regarding light.
The Austrian Academy of Sciences was founded in Vienna in 1846. Christian Doppler was elected to the Academy in 1848 and Petzval in 1851. The first sign of trouble between the two occurred in 1851 when, at the 27 May meeting, Doppler proposed that the Academy offer a prize for improvements in the Daguerre photographic process. Petzval objected to this proposal and it was not taken further. It is a little unclear what Petzval objected to. Perhaps he considered he was the expert and Doppler should not stray into his area. Perhaps he considered that his work had already overtaken the basic premise of the competition.
Soon Petzval launched another attack on Doppler, attacking the Doppler principle which relates the frequency of a source to its velocity relative to an observer. Doppler had proposed this in his 1842 paper Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels . Doppler derived the principle in a few lines treating both light and sound as longitudinal waves in the ether and matter, respectively. Although, of course, the Doppler principle is correct and extremely important for astronomical research, nevertheless much of Doppler's paper is incorrect, in particular his belief that the Doppler principle explained the different colours of binary stars. Petzval's attack came at the meeting of the Austrian Academy of Sciences on 15 January 1852 where he presented his paper Über die Unzukömmlichkeiten gewisser populärer Anschaungsweisen in der Undulationstheorie und ihre Unfähigkeit des Princip der Erhaltung der Schwingungsdauer zu ersetzen . It was published later in 1852 in Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Classe . His attack was based on the fact that Doppler derived the principle in a few lines using only simple equations. Petzval claimed in his paper:-
Without the application of differential equations, it is not possible to enter the realms of great science.The minute of the Academy's meeting of 15 January 1852 reads :-
... the full member, Professor Petzval held a lecture 'On the unsuitability of certain popular ways of looking at the undulation theory and their inability to replace the principle of maintenance of the wavelength'. He presented the manuscript for the report on the meeting. The full member, Professor Doppler, hereupon read a note entitled 'Remarks on the essays: on a general principle of the undulation theory' and presented this for the report on the meeting. The full member Director van Ettingshausen also read some remarks on the essay referred to which are also intended for the report.Alec Eden writes :-
In these objections Petzval confused two completely different cases: one in which there is relative movement between the sound source and the listener, and the other in which the medium is in motion but the sound source and listener are stationary. In the second case there is, according to the Doppler principle, no change in tone. In fact, Petzval's protracted and hard attacks, which came to a head during the meeting of the Austrian Academy of Sciences under the presidency of Andreas von Baumgartner on 21 May 1852, were eventually shown to be the best mathematical proof of Doppler's theory.A third meeting of the Academy on 21 October 1852 again saw Petzval attack Doppler but by this time Doppler was too ill to defend himself and had travelled south hoping to restore his health. Petzval's attack was vicious (see for example ):-
One cannot say exactly that Doppler's theory is of no value because it points to the facts of a phenomenon in a way that is definitely incorrect. On the contrary one has to say it has negative value because it has caused so many interested in that science to be misled through an illusion of simplicity and clarity which, however, is nothing more than superficial and lacks depth of understanding.The result of all this was that the Academy supported Petzval belief that Doppler's theory was incorrect despite the fact that it had been verified experimentally many times since it was first proposed.
The dispute was summed up by Egon von Opplzer in 1901 at a speech he gave of the unveiling of a statue of Doppler in the University of Vienna :-
His opponent [Petzval] bandied with such expressions as 'great science' and 'small science' in the Austrian Academy of Sciences, being of the opinion that great truths could not be found in a few lines and through an equation with only one unknown, and that at least one differential equation is necessary - and in this way he believes to have shown the incorrectness of the Doppler principle. Whoever probes somewhat deeper will find in these attacks, not a purely scientific motive, but a more personal goal. It is the old contradiction between genius and talent which must lead to a struggle when, on the side of the talent there is no understanding of intuitive action and individual brilliance. For Doppler, surveying his principle, it is of clear certainty, and for him - a true natural researcher - the attack on a law that has already been confirmed through experiments is completely incomprehensible. He responded in a factual and decisive manner.As a teacher, Petzval was well-liked by his students :-
As Professor of Mathematics at the University of Vienna, he was known for his lively lectures and incredibly unique teaching style. He lectured on optics, linear and differential equations, analytical mechanics, acoustics, ballistics and mechanical vibrations. Petzval was very critical of academic teaching methods - a feat he probably developed out of his own experience with the limited teaching styles which he encountered as a child. He was very outspoken against his department and the university administration and strove to bring imagination and creativity into his classes.In January 1869 Petzval married his housekeeper Katarina Schlegl. He was 62 years old at this time but we have been unable to find out Katarina's age. Sadly, she died three years later. In 1877, on reaching the age of 70, Petzval retired from his professorship at the University of Vienna. After this, he retired to the Kahlenberg where he lived essentially alone for the final 14 years of his life. His only company on the Kahlenberg seems to have been his horse. When he died there were no family members at his funeral, only a few students, a couple of old friends and a representative of the University of Vienna. In 1905 the mayor of Vienna recalled that Petzval had been a great man and a great scholar who brought glory to the city of Vienna and glory to the University of Vienna. Because of him, said the mayor, Vienna had become a world centre for photography. However, he said that although Petzval had lived in Vienna for 54 years he had remained faithful to his native country, he remained Hungarian.
Petzval won many distinctions for his work. In addition to those mentioned above, he was elected a member of the Hungarian Academy of Sciences in 1873, an honorary member of the Union of Czech Mathematicians and Physicists in 1881, and he received the platinum medal of Charles Chevalier from France. A street in Vienna bears his name as does a crater on the far side of the Moon.
Szénássy writes :-
Students liked Petzval and considered him a true firm and helpful friend, but his colleagues suffered much from his strong criticism.
Article by: J J O'Connor and E F Robertson