Problem: Extract the answer to the question from the following context. Question: What did Borcherds study? Context: 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 Jordan–Hölder 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 group—the "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.

A: contemporary group theory


Problem: Extract the answer to the question from the following context. Question: Which places had similar Neolithic cultures? Context: Not all of these cultural elements characteristic of the Neolithic appeared everywhere in the same order: the earliest farming societies in the Near East did not use pottery. In other parts of the world, such as Africa, South Asia and Southeast Asia, independent domestication events led to their own regionally distinctive Neolithic cultures that arose completely independent of those in Europe and Southwest Asia. Early Japanese societies and other East Asian cultures used pottery before developing agriculture.

A: Europe and Southwest Asia


Problem: Extract the answer to the question from the following context. Question: Which were there more of at the Olympic torch relay, spectators or police? Context: Hong Kong: The event was held in Hong Kong on May 2. In the ceremony held at the Hong Kong Cultural Centre in Tsim Sha Tsui, Chief Executive Donald Tsang handed the torch to the first torchbearer, Olympic medalist Lee Lai Shan. The torch relay then traveled through Nathan Road, Lantau Link, Sha Tin (crossed Shing Mun River via a dragon boat, which had been never used before in the history of Olympic torch relays), Victoria Harbour (crossed by Tin Hau, a VIP vessel managed by the Marine Department) before ending in Golden Bauhinia Square in Wan Chai. A total of 120 torchbearers were selected to participate in the event consisting of celebrities, athletes and pro-Beijing camp politicians. No politicians from the pro-democracy camp were selected as torchbearers. One torchbearer could not participate due to flight delay. It was estimated that more than 200,000 spectators came out and watched the relay. Many enthusiastic supporters wore red shirts and waved large Chinese flags. According to Hong Kong Chief Secretary for Administration Henry Tang, 3,000 police were deployed to ensure order.

A: spectators


Problem: Extract the answer to the question from the following context. Question: Which is not a last name, Darwin or Christian? Context: In later editions of the book, Darwin traced evolutionary ideas as far back as Aristotle; the text he cites is a summary by Aristotle of the ideas of the earlier Greek philosopher Empedocles. Early Christian Church Fathers and Medieval European scholars interpreted the Genesis creation narrative allegorically rather than as a literal historical account; organisms were described by their mythological and heraldic significance as well as by their physical form. Nature was widely believed to be unstable and capricious, with monstrous births from union between species, and spontaneous generation of life.

A:
Christian