# Piers Bohl

### Quick Info

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

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

### Biography

Piers Bohl's father was a merchant and his background was not an academic one. He first studied at Walka, then he went to the German school in Viljandi in Estonia. In 1884 Bohl remained in Estonia, entering the Department of Physics and Mathematics of the University of Dorpat. He graduated in 1887 with a degree in mathematics having won a Gold Medal for an essay he wrote on The Theory of Invariants of Linear Differential Equations in 1886.

In 1893 Bohl was awarded his Master's degree. This was for an investigation of quasi-periodic functions. Although Bohl was the first to study these functions the name is not due to him but is due to Esclangon who studied them later. Esclangon's work was in fact completely independent of Bohl's. The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost periodic functions.

Bohl taught at Riga Polytechnic Institute from 1895. In 1900 he received his doctorate from the University of Dorpat and, in the same year, he was promoted to professor at Riga Polytechnic Institute. The doctorate was a high qualification being essentially that required for a professorship, the Master's Degree being the passport to a university post. Bohl's doctoral dissertation applied topological methods to systems of differential equations. In this topic he was following earlier work by Henri Poincaré and A Kneser.

Latvia had been under Russian imperial rule since the 18th century so, in 1914, World War I meant that the Institute at Riga was evacuated to Moscow. Bohl went to Moscow with his colleagues. However after the Russian Revolution of 1917 and the end of World War I in 1918, Latvia regained its independence (although this was to be short-lived) and in 1919 Bohl was to return to Riga to fill a chair at the University of Latvia which had just been established. Sadly he was only to hold the chair for two years before his death due to a stroke.

Among Bohl's achievements was, rather remarkably, to prove Brouwer's fixed-point theorem for a continuous mapping of a sphere into itself, see [6]. Clearly the world was not ready for this result since it provoked little interest.

Bohl also studied questions regarding whether the fractional parts of certain functions give a uniform distribution. His work in this area was carried forward independently by Weyl and Sierpiński. There are many seemingly simple questions in this area which still seem to be open. For example it is still unknown whether the fractional parts of $(\large\frac{3}{2}\normalsize )^{n}$ form a uniform distribution on (0,1) or even if there is some finite subinterval of (0,1) which is avoided by the sequence.

### References (show)

1. A P Youschkevitch, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
2. A D Myskis and I M Rabinovic, Mathematician Piers Bohl from Riga: With a commentary by the grand master M M Botvinnik on the chess play of P Bohl (Russian), Izdat. Zinatne (Riga, 1965).
3. Yu M Gaiduk, Evaluation of the scientific work of Piers Bohl by his contemporaries (Russian), Tartu State University, History of development, training of personnel, and scientific research II (Tartu, 1982), 28-39.
4. A Kneser and A Meder, Piers Bohl zum Gedächtnis, Jahresberichte der Deutschen Mathematiker-Vereinigung 33 (1925), 25-32.
5. L L Kul'vetsas, P Bohl's fourth thesis and Hilbert's sixth problem (Russian), Studies in the history of physics and mechanics, 1986 (Moscow, 1986), 62-93.
6. A D Myskis and I M Rabinovic, The first proof of a fixed-point theorem for a continuous mapping of a sphere into itself, given by the Latvian mathematician P G Bohl (Russian), Uspekhi matematicheskikh nauk (NS) 10 (3) (65) (1955), 188-192.