Guido Hoheisel published his foundational text on ordinary differential equations in 1926, establishing a career focused on the rigorous exploration of analysis. Operating within the German academic system throughout the mid-twentieth century, he contributed significantly to the study of prime number gaps and served as a university teacher across multiple institutions before his death in 1968.
Academic Foundations and Early Career
Born in 1894 in Wrocław, Hoheisel pursued his higher education at the Humboldt-Universität zu Berlin. In 1920, he completed his doctoral studies under the supervision of Erhard Schmidt. His professional trajectory included faculty appointments at the University of Wrocław, the University of Greifswald, and the University of Cologne, where he spent a significant portion of his career.
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Take the IQ test →Contributions to Prime Number Theory
Hoheisel addressed the distribution of prime numbers by examining the gaps between consecutive primes. He proved that a constant θ exists, where θ is less than one, such that the difference between the (n+1)-th prime and the n-th prime remains smaller than the n-th prime raised to the power of θ for sufficiently large values of n. He determined that this constant could be represented as 32999/33000.
Publications and Pedagogy
Throughout his life, Hoheisel authored several influential textbooks on differential and integral equations. His 1926 work, Gewöhnliche Differentialgleichungen, saw seven editions by 1965. He also authored Partielle Differentialgleichungen in 1928 and the 1933 collection Aufgabensammlung zu den gewöhnlichen und partiellen Differentialgleichungen. His 1936 text, Integralgleichungen, was later translated into English by A. Mary Tropper. During his teaching tenure, he supervised doctoral students, including Arnold Schönhage, and contributed research articles to the journal Deutsche Mathematik.
Fast facts
- Born: 1894, Wrocław
- Died: 1968, Cologne
- Citizenship: Germany
- PhD Advisor: Erhard Schmidt
- Notable Student: Arnold Schönhage
- Field: Analysis
- Primary Area: Theory of differential equations
Questions readers ask
What is Hoheisel's main contribution to prime number theory?
He proved the existence of a constant θ < 1 that bounds the gaps between consecutive prime numbers.
Which universities employed Guido Hoheisel?
He held positions at the University of Wrocław, the University of Greifswald, and the University of Cologne.
Achievements
- Held posts at University of Cologne, University of Greifswald and University of Wrocław
- Fields: mathematics and theory of differential equations
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