Chang Tshang was a famous mathematician who lived in ancient China during the Han Dynasty (202 BC – 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.
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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.
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