Of course, this need not stop one from thinking about the best itinerary for such a mission. The question is: How can the estimated 15 billion stars in three-dimensional space be approached one after the other taking the shortest route? U.S. mathematician William "Bill" Cook has set this question for his third research residency in Bonn, after slowly but surely running out of practical examples for his specialty of integer optimization on Earth.

Cook, who was born in 1957 in the U.S. state of New Jersey, has spent his academic life at California's elite Stanford University, Columbia University in New York and Cornell University in Ithaca. Currently, he holds a professorship at the University of Waterloo in the Canadian province of Ontario. But he has always found decisive professional (and personal) impulses in Bonn, the scientist says during a walk along the banks of the Rhine.

He has spent a good eight years of his life in Bonn during three longer stays in the 1980’s and early 1990’s and now since July of 2022. As a Senior Fellow of the Alexander von Humboldt Foundation, the 65-year-old is now here until May of 2023.

Every morning, Cook walks from his small rented house in Küdinghoven across the South Bridge to the Institute for Discrete Mathematics on the edge of the Hofgarten. In the evening, he walks back across the Kennedy Bridge. Even a master of combinatorics is not immune to coincidences. The fact that the "Rheinnixe" no longer has a helmsman after the death of its long-time skipper, leaving the iconic ferry out of operation permanently, was not something Cook had calculated. "But this way I just keep walking a bit further," says the passionate hiker with a chuckle.

Cook is a welcome guest at the Bonn Institute, where it is hoped that he will make valuable contributions to current research. After all, the scientists there led by the institute's long-time director, Professor Bernhard Korte, are still working on route optimization - Cook's area of expertise. "We call the traveling salesman problem a hard mathematical problem," Korte explains. In it, a traveler is supposed to visit a number of defined locations over the shortest possible distance, but each one only once.

Using an algorithm, Cook was able to calculate the verifiably shortest route through 85,900 cities in 2006. Later, he tried his hand at the two million stars from the Hubble telescope surveys. "For such a problem, we cannot calculate an optimal solution. The number of combinations eventually increases exponentially and would overwhelm any computing power," Cook explains.

The unpretentious mathematics star approaches the best possible solution with a trick: He disregards less relevant possibilities and constraints. In this way, he reduces the possible combinations and arrives at solutions that are not guaranteed to be optimal, but they are close. In the case of the two million stars, his calculated route is provably a maximum of 0.0074 percent away from the optimum.

And even if no one travels to the stars with this navigation aid, it does help science. For example, it can be used to optimize the costly observations of moving telescopes, which in turn, focus their attention on as many passing stars as possible. Three-dimensional routes and the time plane are combined.

With the Concorde App for Apple, Cook is making his computational methods available to everyone. He recently used it, for example, to calculate an optimized hiking route through the Siebengebirge mountains and then walked it - from Küdinghoven via the Dollendorfer Hardt, the Weilberg, Stenzelberg and Nonnenstromberg to the Petersberg and back. "There's Bill's beer garden up there, named after Bill Clinton," Cook enthuses about his excursion.

For his 65th birthday a few days ago, Cook took on all seven peaks of the Siebengebirge. His wife came along. She was born in Bonn and works as a programmer at Princeton University. Cook will also see his daughter again after a year and a half in Bonn. She is coming from South Korea, where she also works as a mathematician.

The Institute for Discrete Mathematics is dedicating a week-long symposium to the visiting scientist on his birthday, with international participation. The routes may be convoluted, but in truth they all lead to Bonn.

THE SERIES

In the series "Bonn International" we regularly introduce people from Bonn or the region who come from abroad or have lived in other countries for a long time. The stories offer other perspectives on living and working on the Rhine.

Original text: Martin Wein

Translation: ck