Carl Theodore Heisel (1852–1937) [1] was a mathematical crank who wrote several books in the 1930s challenging accepted mathematical truths. Among his claims is that he found a way to square the circle. He is credited with 24 works in 62 publications. [2] Heisel did not charge money for his books; he gave thousands of them away for free. Because of this, they are available at many libraries and universities. Heisel's books have historic and monetary value. [3] Paul Halmos referred to one of Heisel's works as a "classic crank book." [4]
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems. These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
John von Neumann was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He had perhaps the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics. He was a pioneer of the application of operator theory to quantum mechanics in the development of functional analysis, the development of game theory and the concepts of cellular automata, the universal constructor and the digital computer. His analysis of the structure of self-replication preceded the discovery of the structure of DNA.
Martin Gardner was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature – especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton. He was also a leading authority on Lewis Carroll. The Annotated Alice, which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books.
Q.E.D. or QED is an initialism of the Latin phrase quod erat demonstrandum, meaning "which was to be demonstrated". Literally it states "what was to be shown". Traditionally, the abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete.
Theodore Sturgeon was an American fiction author of primarily fantasy, science fiction, and horror, as well as a critic. He wrote approximately 400 reviews and more than 120 short stories, 11 novels, and several scripts for Star Trek: The Original Series.
Underwood Dudley is an American mathematician and writer. His popular works include several books describing crank mathematics by pseudomathematicians who incorrectly believe they have squared the circle or done other impossible things.
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of lines and circles implied the existence of such a square.
Lester Randolph Ford Sr. was an American mathematician, editor of the American Mathematical Monthly from 1942 to 1946, and president of the Mathematical Association of America from 1947 to 1948.
Paul Richard Halmos was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis. He was also recognized as a great mathematical expositor. He has been described as one of The Martians.
Pappus of Alexandria was one of the last great Greek mathematicians of antiquity; he is known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.
In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "quod erat demonstrandum". It is inspired by the typographic practice of end marks, an element that marks the end of an article.
Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable areas. A person engaging in pseudomathematics is called a pseudomathematician or a pseudomath. Pseudomathematics has equivalents in other scientific fields, and may overlap with other topics characterized as pseudoscience.
Hao Wang was a Chinese-American logician, philosopher, mathematician, and commentator on Kurt Gödel.
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
In mathematics, two square matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that
The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative fiat. Despite its name, the main result claimed by the bill is a method to square the circle, although it does imply various incorrect values of the mathematical constant π, the ratio of the circumference of a circle to its diameter. The bill, written by a physician who was an amateur mathematician, never became law due to the intervention of Prof. C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote.
Nonstandard analysis and its offshoot, nonstandard calculus, have been criticized by several authors, notably Errett Bishop, Paul Halmos, and Alain Connes. These criticisms are analyzed below.
William Delbert Gann or WD Gann, was a finance trader who developed the technical analysis methods like the Gann angles and the Master Charts, where the latter is a collective name for his various tools like the Spiral Chart, the Hexagon Chart, and the Circle of 360. Gann's market forecasting methods are purportedly based on geometry, astronomy, astrology, and ancient mathematics. Opinions are sharply divided on the value and relevance of his work. Gann authored a number of books and courses on shares and commodities trading.
Mathematical Cranks is a book on pseudomathematics and the cranks who create it, written by Underwood Dudley. It was published by the Mathematical Association of America in their MAA Spectrum book series in 1992 (ISBN 0-88385-507-0).
Margaret Lee Alison Johansen was an American writer from Alabama. She received the Newbery Honor.