Perhaps we should look a little at the political situation at this time in order to understand the times in which Banachiewicz lived. Poland had ceased to become an independent country in 1795 when it was divided between Russia, Prussia and Austria. Warsaw was controlled by the Russians and, after various unsuccessful uprisings by Polish nationalists, a period of Russification followed. In particular, Warsaw University became a Russian university and much was spent on building a new campus. However, various underground groups were set up by the students most of whom were Polish and wanted to see Poland re-established. It was in this atmosphere of Russian domination but underlying Polish nationalism that Banachiewicz grew up. Banachiewicz was a firm Polish patriot.
While he was still an undergraduate, studying astronomy, Banachiewicz published his first paper in Astronomische Nachrichten in 1903. The paper contained a mathematical description based on observations of an eclipse of a star by the planet Jupiter. He graduated from the University of Warsaw with a bachelor's degree in physical and mathematical sciences in the following year, 1904, having submitted a dissertation discussing certain heliometric measurements that had been made at Pulkovo Observatory with a heliometer made in the workshop of the famous German company Repsold & Sohnes. The instrument was specially designed to allow accurate measurements to be made of the distance from the earth to the sun during a transit of Venus. This dissertation was awarded a gold medal by the Warsaw University Senate. Banachiewicz continued to undertake research at the University. The first comet to be discovered in 1905 interested him for he had developed methods to compute orbits. He started to make calculations but problems at the University forced him to stop. Protests and strikes which marked the beginnings of the 1905 Russian revolution took place from January of that year. This prompted unrest among the Polish students at Warsaw University and the authorities closed the University. In 1906 Banachiewicz had important papers published by the Paris Academy of Sciences after being presented to the Academy by Poincaré: Sur un cas particulier du probléme des n corps Ⓣ; and Über die Anwendbarkeit der Gyldén-Brendelschen Störungstheorie auf die Jupiternahen Planetoiden Ⓣ. The second paper studied the three-body problem applied to small bodies near Jupiter. Over the years 1905-07 the authorities considered moving Warsaw University to Russia but eventually decided to keep it in Warsaw with an even stronger Russian character. Not only was the teaching conducted in Russian but also only Russian professors were to be employed. However, Banachiewicz had already left.
He arrived in Göttingen in 1906 to begin studying astrophysics under Karl Schwarzschild who was both an ordinary professor at Göttingen and the director of the University Observatory. At this time Schwarzschild was studying the transport of energy through a star by radiation and published an important paper on radiative equilibrium of the atmosphere of the sun. After spending a year at Göttingen, Banachiewicz went to the Pulkovo Observatory which was situated 19 km south of St Petersburg on the Pulkovo Heights. The Observatory had been founded in 1839 and quickly gained fame under its first director, Friedrich Georg Wilhelm von Struve. In 1878 a 76-centimetre (30-inch) refractor was built there which was the largest telescope in the world at the time. During the year he spent studying at the Observatory (1907-08), Banachiewicz studied under Oskar Backlund (1846-1916), who was head of the Pulkovo Observatory from 1895 to 1916. Backlund was an expert in celestial mechanics, working on planetary perturbations and calculating orbits of comets. He had also carried out geodesic studies in Spitsbergen from 1898 to 1900 so his interests were very close to those of Banachiewicz who spent his time both making astronomical observations and also deepening his knowledge of mathematics. At Pulkovo, Banachiewicz also learnt from Aristarkh Apollonovich Belopolsky (1854-1934) who was a fine instrument maker.
The Russian authorities had decided not to move the University of Warsaw to a Russian city, but to reopen it in Warsaw. So Banachiewicz was able to return there, being appointed as an assistant astronomer for the academic year 1908-09. He then returned to the family estate at Cychry where he worked towards his Master's Degree. He took two examinations in Warsaw in 1909 and, in the following year, he went to Moscow where he took another two examinations. He was then employed at the Engelhardt Observatory near Kazan where he spent five years (1910-1915) making a series of heliometric observations. This Observatory was founded in 1901 with instruments gifted to Kazan University by Vasily Pavlovich Engelhard from his private observatory in Dresden. During these five years, Banachiewicz took part in a scientific expedition to the Volga River Basin to make accurate measurements of terrestrial gravity. In 1915 he submitted an habilitation thesis to Kazan University but it was in Dorpat (now Tartu, Estonia) in November 1915 that he defended his habilitation thesis on refraction theory and became a docent at Dorpat University. Two years later he again defended a thesis at Dorpat, this time on the Gauss equation, and was promoted to assistant professor. In March 1918 he was promoted to full professor and became director of the famous Dorpat Observatory.
Banachiewicz's time in Dorpat was one of political upheaval. Konstantin Päts, who had been forced to flee from Estonia in 1905 when sentenced to death by the Russians, had returned to the country in 1910. Following the 1917 Russian Revolution, Estonia decided to declare itself to be an independent country and Päts became the head of a provisional government in October 1917. However, the Russians tried to keep control and appointed a puppet Communist government. While Estonia struggled to free itself from Russian domination, German troops entered the country in February 1918. So Estonia failed to gain independence, control simply changing from Russian domination to German domination. The Russians, however, having lost control of Estonia, moved Dorpat University from Dorpat to Voronezh in western Russia in the summer of 1918. In July Banachiewicz was invited to become the Professor of Astronomy at Voronezh, but a few months earlier, in May, he had been invited to take the chair of astronomy at Kraków University.
Poland, after 120 years of partition between Russia, Prussia and Austria, became an independent country again in 1918. In March of that year the Soviet government relinquished control of their part of Poland. This, of course, did not by itself unite Poland since World War I was still in progress. In October 1918 Banachiewicz returned to Poland and, until March 1919, acted as assistant professor of geodesy at the Warsaw Polytechnic High School. In March 1919 he went to Kraków to take up the position of Professor of Astronomy at the Jagiellonian University. He was also appointed as Director of the Astronomical Observatory. On 17 March 1931, Banachiewicz married Laura (or Larysa) Solohub Dikyj, a Ukrainian poet, in St Nicolas Church in Kopernika Street, Kraków; they had no children. In 1936 Banachiewicz organised a series of expeditions to Japan, Greece and Siberia to make solar observations. His highly successful career was temporarily put on hold with the German invasion of Poland in 1939. He was arrested by the Nazis, along with other members of the Faculty of the Jagiellonian University, on 6 November 1939. He was taken to the Sachsenhausen Concentration Camp near Berlin where he spent three months before being allowed to return to Kraków. He was allowed to resume his astronomical work at his Observatory, which had been renamed 'Die Krakauer Sternwarte' by the Germans.
After World War II ended in 1945, the Jagiellonian University was reestablished. As well as his position at the Jagiellonian University, Banachiewicz also accepted the position of professor of higher geodesy and astronomy at the Kraków University of Mining and Metallurgy. What might have been a very happy time was, however, one of great personal sadness since his wife Laura died on 28 May 1945. Banachiewicz threw himself into his administrative role, aiming to return Kraków Observatory to a leading centre. Observing conditions had not been good in Kraków so, in 1922, Banachiewicz had set up an observing station at Mount Lubomir south of Kraków. This, however, had been burnt down by the Germans on 15 September 1944, so after he took up his duties again after the war, Banachiewicz began to look for another solution. In 1953 he obtained permission to set up a new observing station at Fort Skala, a former military site. This project was incomplete at the time of his death in 1954 but it continued and, following Banachiewicz's plans, it became the first site of a Polish radio telescope.
Jan Mietelski writes in  about Banachiewicz's scientific contributions:-
The areas of Banachiewicz's scientific interest were wide, so one finds his contributions in astronomy, geodesy, geophysics, mathematics, and mechanics.In 1925 Banachiewicz introduced the Krakowian calculus which involved a column-by-column multiplication of matrices. The authors of  write:-
To simplify matrix computations, Banachiewicz introduced the Krakowian calculus, which greatly simplified and improved computations on calculating machines, which was his principal goal. Theoretically, Krakowians are not as rich in properties as matrices, since they do not involve the associative law. The results obtained by Krakowians can also be obtained by matrices. The Krakowian notation provides formulas that are very easy to remember, which in the conventional form are unwieldy and difficult to memorize. In computations, the Krakowian method makes it possible to obtain results faster and to control the succession of computations. Krakowians reached their zenith of popularity at the start of the 1950s, when calculating machines began to flourish. They found applications in many fields of the natural sciences and technology and simplified many algorithms, freeing formulas from logarithmic ballast.The Krakowian calculus was used by Banachiewicz in many computational techniques that he developed for astronomical purposes, mainly aimed at orbit calculations. For example: An outline of the Cracovian algorithms of the method of least squares (1942); On the accuracy of least squares solution (1945); Sur la résolution des équations normales de la méthode des moindres carrés Ⓣ (1948); Sur l'interpolation dans le cas des intervalles inégaux Ⓣ (1949); A general least squares interpolation formula (1949); Les cracoviens et quelques-unes de leurs applications en géodésie Ⓣ (1949); On the general least squares interpolation formula (1950); and Résolution d'un système d'équations linéaires algébriques par division Ⓣ (written much earlier by only published in 1951 due to World War II) :-
One of Banachiewicz's great achievements in theoretical astronomy was the simplification [using the Krakowian calculus] of Olbers' method of determining parabolic orbits.Banachiewicz made so many contributions to both theoretical and observational astronomy that one cannot give here more than a quick overview. An important contribution which must be mentioned, however, is the work he did on the planet Pluto (in 2006 Pluto was down-graded to dwarf planet status). Pluto was discovered by Clyde Tombaugh at the Lowell Observatory in Flagstaff, Arizona, on 18 February 1930. Banachiewicz was the first person to compute an orbit for Pluto publishing Chronique de l'Observatoire Astronomique de Cracovie concernant Pluton 1930 mars-août Ⓣ (1930) and Sur la détermination de l'orbite de Pluton Ⓣ (1930). Other astronomers, such as the American Charles Hugh Smiley (1903-1977), visited Kraków to learn about Banachiewicz's method of computing the orbit of Pluto.
Adam Strzalkowski was a student of Banachiewicz after he took up his teaching position in Krakow after World War II. He writes :-
Banachiewicz delivered excellent lectures, not only for their content, good preparation and delivery, but also because in them Banachiewicz put in front of his audience new scientific problems to solve. Often, immediately after the lecture, we ran into our room and tried to attack these problems. A lot of research work at the Astronomical Observatory in Krakow arose in this way. ... The Professor treated his lectures very seriously. He always taught on Thursdays and on Saturdays, 6 to 8. On those days under no circumstances was anyone allowed to bother him. He taught very neatly and systematically. I remember that once he made a mistake in deriving a method and was extremely upset. He did not like questions interrupting the course of his lecture, but he always tried to answer them. If he did not know the answer he postponed the explanation to the next lecture when he could have the answer ready. ... As the professor lectured only twice a week, it was not possible for him to cover all the necessary examinations material on astronomy in lectures. We had to learn from the notes taken in previous years by one of the listeners.... In the first years after the war the subject of Banachiewicz's lectures were: geodesy, practical and spherical astronomy, determination of orbits and celestial mechanics. ... Banachiewicz's examinations were not pleasant. The professor believed that the student should be given a chance, so he asked a question and waited. He could wait a very long time but he did not help, did not try to guide the student to the correct answer.Banachiewicz received many honours for his contributions to astronomy and to Polish science. He was elected a corresponding member of The Polish Academy of Arts and Sciences (28 May 1920), he was awarded the Finnish Medal, The White Rose (1926), he was elected a full member of The Polish Academy of Arts and Sciences (1927), he was awarded an honorary doctorate by Warsaw University (1928) and from Poznań University (1938). From 1932 to 1938 he was vice-president of the International Astronomical Union. In 1938 he received a bronze medal from the Jagiellonian University for long-service, receiving their silver medal for long-service in the following year. Also in 1939 he was elected to the Padua Academy of Sciences. He was elected to the Royal Astronomical Society in 1946 and, three years later, received an honorary degree from Sofia University. The Polish Academy of Sciences (Polska Akademia Nauk) was founded in 1952 and Banachiewicz became a member in its year of founding. He was awarded the Medal of Labour First Class in 1954, shortly before his death. The lunar crater Banachiewicz is named after him, as is the minor planet Banachiewicza discovered in 1933. Other minor planets named by Banachiewicz include: Lorcia (discovered 1933 and named in honour of his wife); Wawel (discovered in 1935 and named after the castle in Kraków); and Varsavia (discovered in 1933 and named after the Latin name for Warsaw).
Allow me [EFR] to end this biography with a personal note. In the years immediately preceding World War II a student Tadeusz Boleslaw Slebarski studied mathematics and astronomy at Kraków under Banachiewicz. He fled from Poland in 1939 when the German armies invaded and made a life in Scotland. He was my father-in-law. He always spoke in the highest possible terms about Banachiewicz, as a scientist, as a teacher and as a human being. After the war ended and Tadeusz Slebarski had been awarded an M.A. from the University of St Andrews with honours in mathematics and astronomy (1947), Banachiewicz tried to persuade him to return to Kraków, offering him a position there. Family commitments did not allow my father-in-law to accept, but for the rest of his life he regretted that he had not been able to return to work again with Banachiewicz.
Article by: J J O'Connor and E F Robertson
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