**Piers Bohl** was a Latvian mathematician, who worked in differential equations, topology and quasi-periodic functions.

- Piers received his first lessons from private tutors and studied at the municipal elementary school in Walka (also known by the German name of Walk).
- Perhaps at this point it is worth briefly looking at the history of the region where Bohl was brought up and educated.
- Although it was part of the Russian Empire during the time Bohl was growing up, it was an autonomous region ruled by German nobles and the language of the people was German.
- Piers was ill for half a year and had trouble making up for what he had missed in class.
- From the archive records it can be seen that Piers found mathematics easy from the start and that he was one of the best students in class in this subject.
- Nothing further seems to be known about Edgar Bohl.
- At the Fellin Grammar School, Bohl was taught mathematics by Edward Hugo Weidemann (1854-1887), known as Hugo.
- Tragically, he died when only 32 years old, just three years after giving Bohl his passion for mathematics.
- In 1884 Bohl graduated from the Fellin Grammar School with the Maturity Certificate and remained in, what today is Estonia, entering the Mathematics and Physics Faculty of the University of Dorpat in August of that year.
- When Bohl studied there, the three year course was examined with oral examinations by the lecturers at the end of each year.
- The Professor of Pure Mathematics at this time was Peter Helmling (1817-1901) and the Professor of Applied Mathematics was Ferdinand Minding, but neither had much influence on Bohl.
- At the end of the first year, on 9 December 1895 Bohl completed his examinations on the theory of equations and determinants, differential calculus, integral calculus, analytical geometry and the theory of curves and surfaces.
- Bohl's schooling had been in German, and students with this language background were required to write an essay in Russian at the end of their second year.
- This was rather a challenge for Bohl who had not performed particularly well in his school studies in Russian.
- Bohl's essay was, not surprisingly, the poorest of his examined works, graded "satisfactory".
- On 17 August 1887, Bohl made a request to the Mathematical and Physical Faculty of the University of Dorpat to be examined in these five topics.
- After the five oral examinations were carried out in the week after his request by those who had taught the courses, Bohl was awarded "very good" in each of the five subjects.
- After graduating with his Candidate's Diploma, a few weeks later Bohl passed the examinations which qualified him to teach in High Schools.
- As the titles of the works show, Bohl turned to physical questions during this period, but from today's perspective, some of his results and conclusions are incorrect.
- By 1889 Bohl was registered as a research student at Dorpat University, where he was advised by Adolf Kneser who had been appointed to the chair of Applied Mathematics at Dorpat in that year.
- In 1893 Bohl was awarded his Master's Degree (equivalent to a Ph.D. degree) for the thesis Über die Darstellung von Funktionen einer Variablen durch trigonometrische Reihen mit mehreren, einer Variablen proportionalen Argumenten Ⓣ(On the representation of functions of a variable by trigonometric series with several arguments proportional to a variable).
- Although Bohl was the first to study these functions the name is not due to him but is due to Ernest Esclangon who studied them later.
- He communicated this to P Painlevé and probably sent him a copy of his dissertation, and in 1903 Esclangon's second note in the "Comptes Rendus" acknowledged Bohl's priority in discovering the new class of functions.
- In the same note, Esclangon said that he had reached his results independently of Bohl, discussed the differences between the two works, and cited several new results.
- Bohl was very pleased with this reaction; in the subsequent correspondence between him and Esclangon, he in turn shared various new research results and was very benevolent about Esclangon's scientific projects.
- It is worth noting that the examining committee for Bohl's thesis had not realised the importance of his introduction of quasi-periodic functions.
- Bohl taught at Riga Polytechnic Institute from 1895.
- Bohl's doctoral dissertation applied topological methods to systems of differential equations.
- Grave was one of the examiners of Bohl's doctoral thesis and he claimed it was not worthy of the degree.
- Eventually, despite Grave's objections, Bohl was awarded his doctorate in September 1900.
- The Russification had another impact on Bohl.
- Although Bohl was able to do this he had never been particularly happy with that language and this must have presented him with difficulties.
- As well as being an outstanding mathematician, Bohl was a top quality chess player.
- Mikhail Botvinnik, World Chess Champion from 1948 to 1963, was an admirer of Bohl's chess playing.
- When it came to protecting himself, Bohl did so reluctantly and without much thought.
- Piers Bohl had a thorough knowledge of variations - no doubt he was studying them specifically.
- In terms of Bohl's practical level of play, in modern terminology he would probably be on the border between Category 1 and Candidate Master.
- Bohl went to Moscow with his colleagues.
- Bohl also studied questions regarding whether the fractional parts of certain functions give a uniform distribution.
- In his paper 'Über ein Dreikörperproblem' Ⓣ(On a Three-Body Problem) (1906) Bohl proved a famous theorem about quasiperiodic functions, as well as some important results about differential equations with quasiperiodic coefficients.

Born 23 October 1865, Walka, Livonia (now Valka, Latvia). Died 25 December 1921, Riga, Latvia.

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Origin Latvia

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