Person: Strassen, Volker
Volker Strassen is a German mathematiican who can be considered the founding father of algebraic complexity theory.
Mathematical Profile (Excerpt):
- At this stage Strassen's interests were more on the arts side rather than science and he decided to study music and philosophy at university.
- Jacobs, who had been an assistant at Munich before taking up the chair of mathematical statistics at Göttingen in 1959, had not previously been a thesis advisor so Strassen became his first student.
- Strassen was awarded his Diploma in Mathematics from Göttingen in 1961 and his doctorate in the following year for his thesis Messfehler und Information Ⓣ(Measurement error and information).
- After the award of his doctorate, Strassen went to the University of California, Berkeley in the United States.
- Volker's Ph.D. adviser, Konrad Jacobs, was eager to entertain us - rather, to entertain Julia.
- It was clear that Volker had scored a coup with his "Doktorvater" by bringing her to Göttingen.
- The baby was born while we were still in Göttingen but turned out to be a boy, so Volker named him Tyko after Tycho Brahe, which showed me the class Julia was in as far as Volker was concerned.
- At Berkeley, Volker Strassen took up an appointment as an Assistant Professor in the Department of Statistics and was later promoted to Associate Professor there.
- Strassen wrote a highly influential paper in 1964, namely An Invariance Principle for the Law of the Iterated Logarithm.
- This paper contains what today is called 'Strassen's law of the iterated logarithm', showing scale invariance in random walks.
- The importance of the results was quickly realised and Strassen was invited to lecture at the International Congress of Mathematicians held in Moscow in 1966.
- A postdoctoral grant from the Deutschen Mathematiker-Vereinigung (German Mathematical Society) allowed Strassen to habilitate in 1966 at the University of Erlangen where Konrad Jacobs had moved in 1965 to set up a centre for probability with Hans Bauer who had moved there from Hamburg.
- In 1968 Strassen took up an appointment at the Institute of Applied Mathematics at the University of Zürich.
- Strassen's discovery touched off an intensive search for asymptotically better matrix multiplication algorithms.
- Strassen spent twenty years at the University of Zürich during which time he made many more highly significant discoveries including, in 1977, his test for whether a number is prime using a randomised algorithm.
- We will quote from the citations of prestigious awards made to Strassen to give further details of his contributions.
- In 1999 Strassen was awarded the Cantor medal by the Deutsche Mathematiker Vereinigung (German Mathematical Society).
- Strassen received the 2003 Association for Computing Machinery Paris Kanellakis Theory and Practice Award (jointly with Gary Miller, Michael Rabin, Robert Solovay).
- Solovay and Strassen (1977) proved that, if nnn is composite then, for their predicate, at least half the possible choices of bbb are witnesses to its compositeness.
- The Solovay-Strassen and Miller-Rabin tests demonstrate the power of randomized algorithms and make it possible to generate large random prime numbers and thus construct candidate instances of the RSA cryptosystem.
- The Association for Computing Machinery Special Interest Group on Algorithms and Computation Theory presented Strassen with the 2008 Knuth Prize at their 'Symposium on Discrete Algorithms' held in New York in January 2009.
- Strassen's innovations enabled fast and efficient computer algorithms, the sequence of instructions that tells a computer how to solve a particular problem.
- Strassen's algorithms include fast matrix multiplication, integer multiplication, and a test for the primality of integers.
- For thirty five years, the Schonhage-Strassen integer multiplication method algorithm held the world record for the fastest multiplication algorithm.
- In 1969, Strassen discovered a novel way to multiply two matrices, a critical element of linear algebra that is pervasive throughout the sciences.
- Using this new matrix multiplication routine, Strassen was able to show that Gaussian elimination (an efficient algorithm for solving systems of linear equations) is not an optimal solution.
- Few students in computer science have not encountered Strassen's multiplication algorithm in their undergraduate program.
- In addition to his very practical work, Strassen has proved fundamental theorems in statistics, including "Strassen's law of the iterated logarithm" and the principle of strong invariance.
- We mentioned above that Strassen was an invited speaker at the International Congress of Mathematicians held in Moscow in 1966.
- At the International Congress of Mathematicians at Berkeley in 1986 the Nevanlinna Prize was awarded to Leslie Valiant and Strassen was invited to give a lecture explaining the significance of Valiant's work.
- This was not the only time that Strassen was involved with the presentation of the Nevanlinna Prize for he was on the committee that chose Alexander Razborov as the winner of the award at the International Congress of Mathematicians at Kyoto in 1990.
- Let us also mention that Strassen was an invited speaker at the First European Congress of Mathematics held in Paris in 1992 when he gave the lecture Algebra and complexity.
Born 29 April 1936, Düsseldorf-Gerresheim, Germany.
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
