![]() ![]() However, a generalization called the smooth four-dimensional Poincaré conjecture-that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures-is unsolved. The seventh problem, the Poincaré conjecture, was solved by Grigori Perelman in 2003. Of the original seven Millennium Prize Problems listed by the Clay Mathematics Institute in 2000, six remain unsolved to date: The Riemann zeta function, subject of the celebrated and influential unsolved problem known as the Riemann hypothesis Millennium Prize Problems ![]() Unsolved Problems on Mathematics for the 21st Century In some cases, the lists have been associated with prizes for the discoverers of solutions. Various mathematicians and organizations have published and promoted lists of unsolved mathematical problems. Lists of unsolved problems in mathematics Although this list may never be comprehensive, the problems listed here vary widely in both difficulty and importance. ![]() This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. Some problems belong to more than one discipline and are studied using techniques from different areas. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Many mathematical problems have been stated but not yet solved. You can help by adding missing items with reliable sources. By 1966, the one-room country school had become a thing of the past.This is a dynamic list and may never be able to satisfy particular standards for completeness. School districts consolidated, pooling their resources to provide more teachers, broader curriculum, and opportunity for extracurricular activities. Equipped with little more than a blackboard and a few textbooks, teachers passed on to their pupils cultural values along with a sound knowledge of the three Rs.īy the turn of the century, the population began to shift to the cities and country schools began to lose students and tax support. She had to be a nurse, janitor, musician, philosopher, peacemaker, wrangler, fire stoker, baseball player, professor, and poet for less than $50 a month. The school teacher, sometimes slightly older than her pupils, was a renaissance individual. ![]() When they arrived on their first day of school they may have only known how to speak a foreign language but they soon learned how to speak, read, spell, and write English. They got to school on foot, on horseback, or in a wagon. The children who attended ranged in age from five to 21 and endured dust storms, prairie fires, and cattle drives swirling past the school house in order to get an eighth grade education. They were called names like Prairie Flower, Buzzard Roost, and Good Intent. For a hundred years, white frame or native stone one-room schoolhouses dotted the section corners across Kansas. ![]()
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