Chang Tshang was a famous mathematician who lived in ancient China during the Han Dynasty (202 BC â€“ 220 AD). He is best known for his work on the mathematics of magic squares, which are squares that contain a set of numbers such that the sum of the numbers in each row, column, and diagonal is the same.

Chang Tshang was born in the year 179 AD and grew up in the province of Sichuan. He was a brilliant student from a young age and excelled in both mathematics and literature. He was particularly interested in the study of magic squares and spent much of his time researching and developing new methods for creating and solving them.

One of Chang Tshang's most famous contributions to mathematics was his work on magic squares of order three, which are squares with three rows and three columns. He was able to show that there were exactly eight different magic squares of this type, a result that was later generalized to magic squares of all orders by other mathematicians.

In addition to his work on magic squares, Chang Tshang also made important contributions to the study of Diophantine equations, which are equations that involve only integer solutions. He developed a method for solving these equations that is still used today, known as the "Chang Tshang Method."

Despite his many contributions to mathematics, Chang Tshang is not as well known as some of his contemporaries such as Archimedes or Euclid. This is likely due to the fact that much of his work was not recorded in written form, but was instead passed down through oral tradition. Nonetheless, his contributions to the field of mathematics have had a lasting impact and are still studied and revered by mathematicians today.

In conclusion, Chang Tshang was a brilliant mathematician who made significant contributions to the study of magic squares and Diophantine equations. Although he may not be as well known as some of his contemporaries, his work has had a lasting impact on the field of mathematics and continues to be studied and admired by mathematicians around the world.

GREAT MATHEMATICIANS & SCIENTISTS: vedic mathematics

His other accomplishments in physics include theories about the speed of sound and surface tension. Huygens had tremendous creativity, historical importance, and depth and breadth of genius, both in physics and mathematics. While Al-Biruni may lack the influence and mathematical brilliance to qualify for the Top 100, he deserves recognition as one of the greatest applied mathematicians before the modern era. For this reason, Desargues may not be important enough to belong in the Top 100, despite that he may have been among the greatest natural geometers ever. He developed an important new cosmology superior to Ptolemy's and which, though it was not heliocentric, may have inspired Copernicus. He proved theorems of great importance which had defeated all earlier attempts. His knowledge of Greek may have been poor but he supervised the translation into Arabic of Classical Greek works by Euclid, Aristotle and others; and edited and augmented them.

Another version has Hippasus banished for revealing the secret for constructing the sphere which circumscribes a dodecahedron. Several theorems or concepts are named after Witten, including Seiberg-Witten theory, the Weinberg-Witten theorem, the Gromov-Witten invariant, the Witten index, Witten conjecture, Witten-type Topological quantum field theory, etc. Though applied first to algebra, the notion of invariants is useful in many areas of mathematics. Archimedes was an astronomer details of his discoveries are lost, but it is likely he knew the Earth rotated around the Sun. Thales' writings have not survived and are known only second-hand.

Kummer was an inspirational teacher; his famous students include Cantor, Frobenius, Fuchs, Schwarz, Gordan, Joachimsthal, Bachmann, and Kronecker. Many would now agree this is due in large measure to Descartes' deliberate deprecations of competitors in his quest for personal glory. Langlands and others have applied these methods to prove several other old conjectures, and to formulate new more powerful conjectures. Although most of his paper designs were never built, Leonardo's inventions include reflecting and refracting telescope, adding machine, parabolic compass, improved anemometer, parachute, helicopter, flying ornithopter, several war machines multi-barreled gun, steam-driven cannon, tank, giant crossbow, finned mortar shells, portable bridge , pumps, an accurate spring-operated clock, bobbin winder, robots, scuba gear, an elaborate musical instrument he called the 'viola organista,' and more. He developed a new system of definitions and axioms for geometry, replacing the 2200 year-old system of Euclid. It is said he once leased all available olive presses after predicting a good olive season; he did this not for the wealth itself, but as a demonstration of the use of intelligence in business.

Although he never accepted non-Euclidean geometry, and had spent much time trying to prove the Parallel Postulate, his inspiring geometry text remained a standard until the 20th century. Other discoveries of the Pythagorean school include the construction of the regular pentagon, concepts of perfect and amicable numbers, polygonal numbers, golden ratio attributed to Theano , three of the five regular solids attributed to Pythagoras himself , and irrational numbers attributed to Hippasus. Some even suspect that Descartes arranged the destruction of Pascal's lost Essay on Conics. He was also an accomplished gambler and chess player and wrote an early book on probability. He may have been first to recognize proofs that parts of mountains had once been submerged under ocean. He invented improved accounting methods, and the equal-temperament music scale.

Al-Biruni's contemporary Avicenna was not particularly a mathematician but deserves mention as an advancing scientist, as does Avicenna's disciple Abu'l-Barakat al-Baghdada, who lived about a century later. Some of his other ideas were wrong; for example, he dismissed Kepler's elliptical orbits and notion of gravitation and published a very faulty explanation of tides. The earliest of these great Italian polymaths were largely not noted for mathematics, and Leonardo da Vinci began serious math study only very late in life, so the best candidates for mathematical greatness in the Italian Renaissance were foreigners. Dirichlet found a flaw in the proof of the Isoperimetric Theorem which was later corrected by Weierstrass. There are still debates about certain mathematical classics. He also did brilliant work in geometry, proving theorems about conic sections, the cycloid and the catenary. His name is associated with the Pascal's Triangle of combinatorics and Pascal's Wager in theology.

Michael Hartley Freedman 1951- U. Desargues' projective geometry may have been too creative for his time; Descartes admired Desargues but was disappointed his friend didn't apply algebra to his geometric results as Descartes did; Desargues' writing was poor; and one of his best pupils Blaise Pascal himself turned away from math, so Desargues' work was largely ignored except by Philippe de La Hire, Desargues' other prize pupil until Poncelet rediscovered it almost two centuries later. He was a great inventor: in addition to being first to conceive of the pendulum clock, he developed a new type of pump, and the best telescope, thermometer, hydrostatic balance, and cannon sector of his day. The very famous Kepler Equation relating a planet's eccentric and anomaly is just one tool Kepler needed to develop. William Kingdon Clifford 1845-1879 England Clifford was a versatile and talented mathematician who was among the first to appreciate the work of both Riemann and Grassman. I then found out what demonstrate means, and went back to my law studies. This record was subsequently broken by relative unknowns: a German ca.

Thales is ranked 38 on the Pantheon List of Most Popular and Productive Persons. Markov is best known as the founder of the theory of stochastic processes. Huygens is famous for his inventions of clocks and lenses. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. Like Nash, he had a habit of challenging colleagues to present him with their hardest unsolved problems. He was also an accomplished gambler and chess player and wrote an early book on probability.

Ramanujan may have had unrecorded proofs, poverty leading him to use chalk and erasable slate rather than paper. Constructing the regular 17-gon as a teenager was actually an exercise in complex-number algebra, not geometry. Joseph-Louis Comte de Lagrange 1736-1813 Italy, France Joseph-Louis Lagrange born Giuseppe Lodovico Lagrangia was a brilliant man who advanced to become a teen-age Professor shortly after first studying mathematics. Newton also designed the first reflecting telescope, first reflecting microscope, and the sextant. Another version has Hippasus banished for revealing the secret for constructing the sphere which circumscribes a dodecahedron.

Penrose is most noted for his very creative work in cosmology, specifically in the mathematics of gravitation, space-time, black holes and the Big Bang. Sixteen more born-after-1930 mathematicians are shown among slots 151- 200. He was a polymath: in addition to being a philosopher of far-ranging scope, he also wrote treatises on music, mechanics and natural science. Although incorporating work by Cardano, Diophantus and possibly Omar al-KhayyÃ¡m, the textbook was highly original and extremely influential. Fermat developed a system of analytic geometry which both preceded and surpassed that of Descartes; he developed methods of differential and integral calculus which Newton acknowledged as an inspiration. Pythagoras was very interested in astronomy and seems to have been the first man to realize that the Earth was a globe similar to the other planets. Hardy is especially famous and important for his encouragement of and collaboration with Ramanujan.