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After years of work, mathematics researchers have answered a mysterious half-century-old riddle. The mystery was all but forgotten until a Danish researcher heard about, and then decided to tackle it.
Is there a lottery ticket that always wins?
So goes the popular version of a theoretical conundrum posed in 1969 by
English mathematician Adrian R.D. Mathias within the field of set
theory, an area dealing with infinity in mathematics.
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| Photo: courtesy of Graphics Mouse at FreeDigitalPhotos.net |
The problem remained a mystery throughout the 70's, 80's and 90's, as
set theorists the world over tried their best to solve it. Associate
Professor Asger Dag Törnquist of the University of Copenhagen's
Department of Mathematics was introduced to the problem in 2002 while
completing his doctoral dissertation at the University of California,
Los Angeles (UCLA).
"Research in the area had gone dormant from the 1990's on because no one was making any progress towards a solution. I was fascinated because it was an old problem that dealt with our understanding of infinity in mathematics. Even then, it became a dream of mine to solve the mystery, even though I had no idea of how to accomplish what had been elusive for others over decades," he says...
The 'baby-mystery' proved decisive
Asger Dag Törnquist's shouldered his dream of solving Mathias' question for several years abroad until he began working at the University of Copenhagen's Department of Mathematical Sciences in 2011. This marked the beginning of a period during which Törnquist and David Schrittesser, his Austrian postdoctoral researcher, would gradually approach the solution.
"In 2014, I decided to rethink the problem from scratch and found a whole new way of tackling it. Alongside the original mystery, Mathias had formulated a sort of baby-version of the mystery. Neither had been solved. I managed to solve the baby version of mystery, which I then wrote an article about," explains Törnquist.
Read more...
Additional resources
Journal Reference:
David Schrittesser, Asger Törnquist. The Ramsey property implies no mad families. Proceedings of the National Academy of Sciences, 2019; 201906183
DOI: 10.1073/pnas.1906183116
Source: Science Daily
