Input: Read this: 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.
Question: What area of classification leads to troublesome arithmetic?

Output: finite groups


QUES: Tuberculosis has been present in humans since antiquity. The earliest unambiguous detection of M. tuberculosis involves evidence of the disease in the remains of bison in Wyoming dated to around 17,000 years ago. However, whether tuberculosis originated in bovines, then was transferred to humans, or whether it diverged from a common ancestor, is currently unclear. A comparison of the genes of M. tuberculosis complex (MTBC) in humans to MTBC in animals suggests humans did not acquire MTBC from animals during animal domestication, as was previously believed. Both strains of the tuberculosis bacteria share a common ancestor, which could have infected humans as early as the Neolithic Revolution.

What period did the bison live in?
What is the answer?
ANS: unanswerable


QUES: The pointed arch, one of the defining attributes of Gothic, was earlier incorporated into Islamic architecture following the Islamic conquests of Roman Syria and the Sassanid Empire in the Seventh Century. The pointed arch and its precursors had been employed in Late Roman and Sassanian architecture; within the Roman context, evidenced in early church building in Syria and occasional secular structures, like the Roman Karamagara Bridge; in Sassanid architecture, in the parabolic and pointed arches employed in palace and sacred construction.
What is one defining characteristic of the Gothic architectural style?

ANS: The pointed arch


Chapter VII (of the first edition) addresses the evolution of instincts. His examples included two he had investigated experimentally: slave-making ants and the construction of hexagonal cells by honey bees. Darwin noted that some species of slave-making ants were more dependent on slaves than others, and he observed that many ant species will collect and store the pupae of other species as food. He thought it reasonable that species with an extreme dependency on slave workers had evolved in incremental steps. He suggested that bees that make hexagonal cells evolved in steps from bees that made round cells, under pressure from natural selection to economise wax. Darwin concluded:
If it is possible to answer this question, answer it for me (else, reply "unanswerable"): What did Darwin notice specifically about slave-making ants?
Ah, so.. some species of slave-making ants were more dependent on slaves than others


Question: The Empire was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty. The empire rose to prominence as a culmination of attempts by the southern powers to ward off Islamic invasions by the end of the 13th century. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India. The empire's legacy includes many monuments spread over South India, the best known of which is the group at Hampi. The previous temple building traditions in South India came together in the Vijayanagara Architecture style. The mingling of all faiths and vernaculars inspired architectural innovation of Hindu temple construction, first in the Deccan and later in the Dravidian idioms using the local granite. South Indian mathematics flourished under the protection of the Vijayanagara Empire in Kerala. The south Indian mathematician Madhava of Sangamagrama founded the famous Kerala school of astronomy and mathematics in the 14th century which produced a lot of great south Indian mathematicians like Parameshvara, Nilakantha Somayaji and Jyeṣṭhadeva in medieval south India. Efficient administration and vigorous overseas trade brought new technologies such as water management systems for irrigation. The empire's patronage enabled fine arts and literature to reach new heights in Kannada, Telugu, Tamil and Sanskrit, while Carnatic music evolved into its current form. The Vijayanagara Empire created an epoch in South Indian history that transcended regionalism by promoting Hinduism as a unifying factor. The empire reached its peak during the rule of Sri Krishnadevaraya when Vijayanagara armies were consistently victorious. The empire annexed areas formerly under the Sultanates in the northern Deccan and the territories in the eastern Deccan, including Kalinga, while simultaneously maintaining control over all its subordinates in the south. Many important monuments were either completed or commissioned during the time of Krishna Deva Raya. Vijayanagara went into decline after the defeat in the Battle of Talikota (1565).
Try to answer this question if possible: When was the Kerala school established?
Answer: 14th century


Context and question: The Constitution of the United States of America provides that the United States Congress has the power "To coin money". Laws implementing this power are currently codified at 31 U.S.C. § 5112. Section 5112 prescribes the forms, in which the United States dollars should be issued. These coins are both designated in Section 5112 as "legal tender" in payment of debts. The Sacagawea dollar is one example of the copper alloy dollar. The pure silver dollar is known as the American Silver Eagle. Section 5112 also provides for the minting and issuance of other coins, which have values ranging from one cent to 50 dollars. These other coins are more fully described in Coins of the United States dollar.
Coins are considered illegal tender for which type of transactions?
Answer:
unanswerable