Marienus Johannes Hendrikus Heule (born March 12, 1979 at

Rijnsburg Rijnsburg () is a village in the eastern part of the municipality of Katwijk, in the western Netherlands, in the province of South Holland. The name means Rhine's wikt:Special:Search/burg, Burg in Dutch. History The history starts way before the ...

The Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...

) is a Dutch computer scientist at

Carnegie Mellon University Carnegie Mellon University (CMU) is a private research university in Pittsburgh, Pennsylvania. One of its predecessors was established in 1900 by Andrew Carnegie as the Carnegie Technical Schools; it became the Carnegie Institute of Technology ...

who studies

SAT solvers The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Schol ...

. Heule has used these solvers to resolve mathematical conjectures such as the

Boolean Pythagorean triples problem The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members. The Boolean Pythagorean triples problem w ...

, Schur's theorem number 5, and

Keller's conjecture In geometry, Keller's conjecture is the conjecture that in any tiling of -dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire -dimensional face with each other. For instance, in any tiling of the pla ...

in dimension seven.

Career

Heule received a PhD at

Delft University of Technology Delft University of Technology ( nl, Technische Universiteit Delft), also known as TU Delft, is the oldest and largest Dutch public technical university, located in Delft, Netherlands. As of 2022 it is ranked by QS World University Rankings among ...

, in the

Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...

, in 2008. He was a research scientist, later a research assistant professor, at the

University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

from 2012 to 2019. Since 2019, he has been an associate professor in the Computer Science Department at

In May 2016 he, along with Oliver Kullmann and Victor W. Marek, used SAT solving to solve the

. The statement of the theorem they proved isTo prove this theorem, the possible colorings of were divided into a trillion subcases using a

heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...

. Each subclass was then solved a

Boolean satisfiability In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfie ...

solver. Creating the proof took about 4 CPU-years of computation over a period of two days on the Stampede supercomputer at the

Texas Advanced Computing Center The Texas Advanced Computing Center (TACC) at the University of Texas at Austin, United States, is an advanced computing research center that provides comprehensive advanced computing resources and support services to researchers in Texas and acr ...

and generated a 200 terabyte propositional proof (which was compressed to 68 gigabytes in the form of the list of subcases used). The paper describing the proof was published in the SAT 2016 conference, where it won the best paper award. A $100 award that

Ronald Graham Ronald Lewis Graham (October 31, 1935July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He ...

originally offered for solving this problem in the 1980s was awarded to Heule. He used SAT solving to prove that Schur number 5 was 160 in 2017. He proved

in dimension seven in 2020. In 2018, Heule and

Scott Aaronson Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing an ...

received funding from the

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National I ...

to apply SAT solving to the

Collatz conjecture The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integ ...

References

External links

Official website

Old official website at UT Austin
{{DEFAULTSORT:Heule, Marijn Dutch computer scientists Delft University of Technology alumni University of Texas at Austin faculty Carnegie Mellon University faculty 1979 births Living people