Luure graduated from the Moscow State University in 1983, majoring in mathematics. In 1998, he successfully defended his MA thesis titled "A combinatorial model of referring". In 2006, he successfully defended his Ph. D. thesis titled "Duality and sextets: a new structure of categories" in semiotics at the University of Tartu.
In 2008, Luure was recognised by Estonian Volunteering Development Centre as the Volunteer of the Year for his contribution to the Estonian Wikipedia. He received the Order of the White Star, 5th Class in 2013 for his contribution to the Estonian Wikipedia.
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