Franz Mertens facts for kids
Quick facts for kids
Franz Mertens
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| Born | 20 March 1840 Schroda, Prussia
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| Died | 5 March 1927 (aged 86) Vienna, Austria
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| Nationality | Polish |
| Alma mater | University of Berlin |
| Known for | Mertens conjecture Mertens function Meissel–Mertens constant Mertens's theorems |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Vienna Graz Polytechnic Jagiellonian University |
| Doctoral advisor | Ernst Eduard Kummer Leopold Kronecker |
| Doctoral students | Ernst S. Fischer Eduard Helly |
Franz Mertens (born March 20, 1840 – died March 5, 1927) was an important Polish mathematician. He was also known as Franciszek Mertens. He was born in a place called Schroda, which was part of Prussia at the time. Today, this place is known as Środa Wielkopolska in Poland. He passed away in Vienna, Austria.
Mertens made many contributions to the world of mathematics. He was especially known for his work with numbers. He studied how numbers behave and how they relate to each other.
Contents
Mertens's Discoveries in Math
Franz Mertens is famous for several ideas in mathematics. These ideas are often named after him.
Mertens Function
One of his ideas is the Mertens function. This function helps mathematicians understand how certain types of numbers add up. It is used in a part of math called number theory.
Mertens Conjecture
Mertens also made a guess, or "conjecture," about how the Mertens function grows. He thought it would always stay below a certain value. This idea was very important because it was linked to another big math problem called the Riemann hypothesis. However, later on, other mathematicians found out that his guess was not completely correct.
Meissel–Mertens Constant
Another thing named after him is the Meissel–Mertens constant. This number is similar to another famous math constant called the Euler–Mascheroni constant. It helps mathematicians study prime numbers. Prime numbers are numbers that can only be divided by 1 and themselves, like 2, 3, 5, 7, and so on.
Mertens's Theorems
In 1874, Mertens published three important results. These results are now known as Mertens's theorems. They helped explain how often prime numbers appear. They showed how common prime numbers are as you look at bigger and bigger numbers.
Teaching and Legacy
Franz Mertens was also a teacher. He taught at several universities, including the University of Vienna and the Jagiellonian University. One of his famous students was Erwin Schrödinger, who later became a very important physicist. Mertens taught Schrödinger about calculus and algebra.
Franciszek Mertens Scholarship
To honor his memory, a special award was created in 2017. It is called the Franciszek Mertens Scholarship. This scholarship helps talented high school students from other countries. It allows them to study mathematics and computer science at the Jagiellonian University in Kraków, Poland.
Students can get this scholarship if they have done very well in math or computer science competitions. This includes national math olympiads or big international competitions. Some of these international competitions are the International Mathematical Olympiad (IMO) and the International Olympiad in Informatics (IOI).
See also
- Cauchy product
