Problem: Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q["] An intermediate step is the classification of finite simple groups.r["] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s["] The JordanHolder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic groupthe "monster group"and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.
When was the Jordan-Holder theorem published?
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Answer: unanswerable

Problem: Northwestern fields 19 intercollegiate athletic teams (8 men's and 11 women's) in addition to numerous club sports. The women's lacrosse team won five consecutive NCAA national championships between 2005 and 2009, went undefeated in 2005 and 2009, added more NCAA championships in 2011 and 2012, giving them 7 NCAA championships in 8 years, and holds several scoring records. The men's basketball team is recognized by the Helms Athletic Foundation as the 1931 National Champion. In the 201011 school year, the Wildcats had one national championship, 12 teams in postseason play, 20 All-Americans, two CoSIDA Academic All-American selections, 8 CoSIDA Academic All0District selections, 1 conference Coach of the Year and Player of the Year, 53 All-Conference and a record 201 Academic All-Big Ten athletes. Overall, 12 of Northwestern's 19 varsity programs had NCAA or bowl postseason appearances.
How many women's intercollegiate athletic teams are fielded by Northwestern?
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Answer: unanswerable

Problem: Interracial relationships have had a long history in North America and the United States, beginning with the intermixing of European explorers and soldiers, who took native women as companions. After European settlement increased, traders and fur trappers often married or had unions with women of native tribes. In the 17th century, faced with a continuing, critical labor shortage, colonists primarily in the Chesapeake Bay Colony, imported Africans as laborers, sometimes as indentured servants and, increasingly, as slaves. African slaves were also imported into New York and other northern ports by the Dutch and later English. Some African slaves were freed by their masters during these early years.
What did traders and fur trappers do before European settlement increased?
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Answer:
unanswerable