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Many mathematical problems have been stated but not yet solved. 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.
Archimedes's cattle problem. Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes, the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.
Peter Stoner (June 16, 1888 – March 21, 1980) was a Christian writer and Chairman of the departments of mathematics and astronomy at Pasadena City College until 1953; Chairman of the science division, Westmont College, 1953–57; Professor Emeritus of Science, Westmont College; and Professor Emeritus of Mathematics and Astronomy, Pasadena City College.
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems.
B.H. Streeter. The two-source hypothesis (or 2SH) is an explanation for the synoptic problem, the pattern of similarities and differences between the three Gospels of Matthew, Mark, and Luke. It posits that the Gospel of Matthew and the Gospel of Luke were based on the Gospel of Mark and a hypothetical sayings collection from the Christian oral ...
To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a ...
Fermat–Catalan conjecture. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many ...
Smale's problems are a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold , then vice-president of the International Mathematical Union , who asked several mathematicians to propose a list of problems for the 21st ...