Archimedes is remembered as the greatest mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas as well as volumes of curved surfaces. His works expected integral calculus almost 2000 years before it was invented by Sir Isaac Newton and Gottfried Wilhelm von Leibniz. He also proved that the volume of a sphere is equal to two-thirds the volume of a circumscribed cylinder. He regarded this as his most vital accomplishment. So, he desired that a cylinder circumscribing a sphere ought to be inscribed on his tomb. He found an approximate value of pi by circumscribing and inscribing a circle with regular polygons of 96 sides. His works have original ideas, impressive demonstrations and excellent computational techniques. Some of these which have survived are:
- on the sphere and cylinder
- measurement of a circle
- on conoids and spheroids
- on spirals
- on plane equilibriums
- the sand reckoner
- quadrature of the parabola
- on floating bodies
- stomachion
Euclid is the most famous mathematician of all time. "Euclid's Elements" is divided into 13 books.
- the initial six are related to plane geometry
- seven, eight and nine are pertaining to number theory
- number ten is regarding Eudoxus's theory of irrational numbers
- eleven to thirteen comprise solid geometry
- the last part throws light on the properties of five regular polyhedrons and an evidence that there can be maximum five of these
- optics
- phaenomena
- on divisions of figures
- data
- elements of music
- book of fallacies
- conics
- porisms
- surface loci
Newton created the basis for elementary differential and integral calculus during the plague years. This occurred several years prior to its independent discovery by the German mathematician Gottfried Wilhelm von Leibniz. He called it as the method of fluxions. He proposed that the integration of a function is the opposite procedure of its differentiation. Using differentiation as a basic operation, he developed simple analytical methods concerning issues like finding areas, lengths of curves, areas, maxima and minima. Newton is credited for development of a potent problem solving and analysis tool in pure mathematics and physics.
Pythagoras
He was a Greek mathematician. His belief was that all relations could be expressed as number relations i.e. all things are numbers. He deduced this conclusion due to observations in mathematics, music and astronomy. The Pythagorean theorem is thought to be first proved by the Pythagoreans. However, it is thought that this was known in Babylonia, where Pythagoras traveled in his young days. The Pythagoreans also observed that vibrating strings created harmonious tones if the ratios of the length of the strings are whole numbers. These ratios could be extended to other devices also. The important discovery was that the diagonal of a square was not an integral multiple of its side. This led to the proof of existence of irrational numbers.
Blaise Pascal
The French mathematician had been involved in imaginative and subtle work in geometry and other branches of mathematics. In 1645, Pascal invented the first calculating machine and sold it. His work in hydrostatics led to the invention of the syringe and hydraulic press. In 1647, he published an essay on conic sections using the methods of Gerard Desargues and deserted the field of mathematics. However, later he developed an interest in probability due to his involvement in gambling.
Carl Friedrich Gauss
Gauss was a German mathematician. While he attended Caroline college from 1792 to 1795, he formulated the least-squared method and a surmise on the distribution of prime numbers amongst all numbers. In 1795, he discovered the basic theorem of quadratic residues relating to the concept of congruence in number theory. In 1796, he proved the possibility of constructing a 17-sided regular polygon with the help of a ruler and compass only. In 1799, his dissertation revealed the first evidence of the fundamental theorem of algebra. In 1801, his treatise - Disquisitiones arithmeticae set a basis for future research and enabled Gauss to have a major recognition amongst mathematicians. He became very popular when he correctly predicted where the asteroid Ceres would reappear by calculating the orbit by an improved theory.
Aryabhatta
"Aryabhatiya" is the name of Aryabhatta's work. There are an introductory 13 verses followed by 108 verses, all of them divided into 4 chapters. Aryabhatta found out the approximate value of pi and writes about it in the second part of his works (Ganitapada 10). It is possible that he found out that pi is irrational. In Ganitapada 6, he mentions the formula to calculate the value of a triangle. He developed the "Kuttaka" method to solve first order Diophantine equations. This is termed as the "Aryabhatta algorithm". The number place-value system was obviously present in his work. Later, this system was noticed in the 3rd century Bakhshali manuscript. Georges Ifrah, the French mathematician, states that the number "zero" was implicit in this system.
Ramanujam
Srinivasa Ramanujan Iyengar contributed to number theory, mathematical analysis, infinite series and continued fractions. He was a great Indian mathematical genius of the 20th century. He compiled about 3900 results that were original and highly unconventional. The Ramanujan prime and the Ramanujan theta function have led to a tremendous further research. A few major discoveries entered the mathematical mainstream a bit slowly. After his death, his formulae were found useful in string theory and crystallography. The Ramanujan Journal is an international publication that publishes his works concerning those areas that have been influenced by them.
Some other famous mathematicians are Stefan Banach, Georg Cantor, Joseph Fourier, John von Neumann, and Brook Taylor.
Reference:http://www.buzzle.com/articles/famous-mathematicians.html
