# Piers Bohl

### Born: 23 October 1865 in Walka, Livonia (now Valka, Latvia)

Died: 25 December 1921 in Riga, Latvia

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**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 18

^{th}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 (

^{3}/

_{2})

^{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.

**Article by:** *J J O'Connor* and *E F Robertson*

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**List of References** (6 books/articles)

**Mathematicians born in the same country**

**Other Web sites**

- Dictionary of Scientific Biography
- D Taimina & I Henina (A history of Latvian mathematics)
- Mathematical Genealogy Project
- MathSciNet Author profile
- zbMATH entry
- ERAM Jahrbuch entry