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An enigma mathematician proposed in 1969 by Adrian R. D. Mathias wondered if it was possible the existence of a lottery ticket that always proves to be awarded. Unfortunately we can not give the fortunate combination: the response to the theoretical approach of Mathias you can only resolve by resorting to the theory of sets , an area of mathematics that deals with the infinite. Therefore, the answer to the enigma of Mathias is unknown.
At least until now. The theorists were trying to solve the enigma for 30 years, to be finally defeated. But, after starting from zero, the mathematical Asger Dag Törnquist, researcher at University of Copenhagen (Denmark), has just come up with a solution to the conundrum. Unfortunately, his conclusion is that such a ticket would not exist. His advances have just been published in the journal Proceedings of the National Academy of Sciences (PNAs). Despite its success, it probably will not become a millionaire.
“The research in the area fell into oblivion since 1990 because no one was approaching a solution,” said Dag Törnquist in a press release. “But I was fascinated with this, because it is an old problem that has to do with our understanding of the infinite in mathematics. So to solve the mystery became a dream for me, even though you had no idea of how to get what they had not been able to do for decades.” As is well known, the drop didn’t he pierces the rock by your strength but by perseverance.
four decades Ago, the mathematician Adrian R. D. Mathias he studied the structure and order , two properties that appear in mathematical systems very large, as set out in the Theory of Ramsey. As there is nothing larger than infinity, Mathias connected this theory with this concept. It did so through a concept known as families MAD. In English, “mad” is crazy, but, what are these families MAD?
“A family MAD may be likened to a kind of lottery ticket that it is always award-winning in a game of keno peculiar: infinite one”, explained Dag Törnquist. “In this game, the lottery tickets have an infinite number of series, and each series has an infinite number of numbers”.
And now is when we can understand the enigma of Mathias. This mathematician is asked: Can the order and the structure (properties that emerge in large systems, according to the Theory of Ramsey) to avoid the existence of very strange things in that family MAD, like a lottery ticket that is always rewarded?
After five years, in which Dag Törnquist raised the issue in an entirely new way, she finally gave up with a solution to the old riddle, with the help of the researcher David Schrittesser.
“we found the numbers of our lottery ticket is added of a form that leads to no certainty of a winner”, says Törnquist. “This was what Mathias suggested that would happen, but until now had not been able to prove.”
This implies that it is impossible to create a type of lottery ticket without the emergence of regularities and patterns in the numbers, so that there is not a ticket that always wins the game of lottery Mathias, as has been concluded Asger Dag Törnquist.
