Prize status records whether a conjecture carries a formal reward for solving it. Wikipedia notes "the Clay Mathematics Institute, having included the Poincare conjecture in their well-known Millennium Prize Problem list, offered Perelman their prize of US$1 million in 2010," which he then declined. This dimension separates conjectures with a standing prize from those pursued for reputation alone.
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1. Wikipedia: Combinatorics
Wikimedia FoundationHistory sectionQuote, History section
In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right.
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