Guido Hoheisel
Encyclopedia
Guido Hoheisel was a German
mathematician
, a professor of mathematics at the University of Cologne
. He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt
.
Hoheisel is known for a result on gaps between prime numbers. He proved that if π denotes the prime-counting function, then there exists a constant θ < 1 such that
as x tends to infinity, implying that if pn denotes the n-th prime number
then
for all sufficiently large n. In fact he showed that one may take θ = 32999/33000.
During World War II
, as one of the few remaining competent mathematicians in Germany, Hoheisel was required to teach classes simultaneously at three universities, in Cologne
, Bonn
, and Münster
.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, a professor of mathematics at the University of Cologne
University of Cologne
The University of Cologne is one of the oldest universities in Europe and, with over 44,000 students, one of the largest universities in Germany. The university is part of the Deutsche Forschungsgemeinschaft, an association of Germany's leading research universities...
. He did his PhD in 1920 from the University of Berlin under the supervision of Erhard Schmidt
Erhard Schmidt
Erhard Schmidt was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia . His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905...
.
Hoheisel is known for a result on gaps between prime numbers. He proved that if π denotes the prime-counting function, then there exists a constant θ < 1 such that
- π(x + xθ) − π(x) ~ xθ/log(x),
as x tends to infinity, implying that if pn denotes the n-th prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
then
- pn+1 − pn < pnθ
for all sufficiently large n. In fact he showed that one may take θ = 32999/33000.
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, as one of the few remaining competent mathematicians in Germany, Hoheisel was required to teach classes simultaneously at three universities, in Cologne
Cologne
Cologne is Germany's fourth-largest city , and is the largest city both in the Germany Federal State of North Rhine-Westphalia and within the Rhine-Ruhr Metropolitan Area, one of the major European metropolitan areas with more than ten million inhabitants.Cologne is located on both sides of the...
, Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
, and Münster
Münster
Münster is an independent city in North Rhine-Westphalia, Germany. It is located in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also capital of the local government region Münsterland...
.