unit - 2 Mathematicians

List of Famous Mathematicians and their Contributions

Here is the list of those mathematicians whose theorems, results and inventions paved a path for deep research in mathematics. Here is some information about the same. There is certainly no end to the series of mathematicians whose works created the platform for others to produce seminal works in mathematics. But since it is indeed not possible to list every mathematician who has contributed to this great science, I have made a humble attempt to compile a list of some really well-known mathematicians whose great works revolutionized the scientific and mathematical world.

Mathematics has witnessed some of the most genius brains pondering over complex problems and solving them to unravel mysteries of Universe, science and life. The world salutes the great mathematicians and their contributions. Mathematics knows no religion, culture, color, creed or gender. There have been famous black mathematicians and at the same time, female mathematicians and their contributions, that have shaped the mathematical world, all across the globe.

Archimedes
           The greatest mathematicians of ancient era, Archimedes made phenomenal contribution in the field of mathematics. His works include integral calculus studies and finding various computation techniques to determine volume and area of several shapes including the conic section.

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
       Euclid, the 'father of Geometry', wrote the book,"Euclid's Elements", that is considered to be the greatest piece of historical works in mathematics. The book is divided into 13 parts and in it, Euclid has discussed in details about geometry (what is now called Euclidean geometry). His contributions are also famous in the fields of spherical geometry, conic sections and number theory.

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 of solid geometry

·       the last part throws light on the properties of five regular polyhedrons.

These Elements have an impressive clarity regarding the selection and order of the theorems and problems. There are minimum assumptions, less extraneous material and an excellent logic in the propositions. The Elements was first published in 1482. The other works of Euclid which survive are:

• ·       optics
• ·       phenomena
• ·       on divisions of figures
• ·       data

The works of Euclid that have not survived are:

• ·       elements of music
• ·       book of fallacies
• ·       conics
• ·       porisms
• ·       surface loci

Aryabhatta

The Indian mathematician and astronomer Arya bhata (476 A.D) is well known for his work. He was born at Pataliputra near Patna in Bihar. His most famous book is known as ―Aryabhrtia‖. In arithmetic, Algebra and place Geometry Aryabhata suggested humerons rules. A few important rules are enlisted below-

1. Area of triangle = base*height

2. The value of Pi =3.1456

3. Area of the circle (pi)2

4. Sum of AP =n/2[2a+(n-1)d

              Aryabhatta has been famous for his mathematical works and theorems on astronomical bodies that have been found to be very accurate in terms of modern calculations. "Aryabhatiya", his only work to have survived has given the world innumerable theorems and research subjects. His two other major contributions are the, introduction of zero to the world and calculating the approximate value of pie. His works are also spread in fields like include algebra, arithmetic, trigonometry, sine table and the quadratic equations.

To sum up Aryabhata was really one of the greatest genius of his time in the field of mathematics and astronomy. 

Brahmagupta

            The ancient Indian astronomer brahmagupta is credited with having put forth the concept or zero for the fist time: brahmagupta is said to have been born in the year 598 A.D. at Bhillamala in Gujarat, western Indian. Much is known about brahmagupta’s early life, we are told that his name as a mathematicians was well established when k.vyaghramukha of the chapa dynasty made him the court astronomer.

In the earlier Roman and Babylonian system of numeration , large number of characters were required to denote higher numerals. Thus enumeration and computation became unwieldy. For instance, as E the Roman system of numeration, the number thirty would have to be written as X; while as per the decimal system it would 30, further the number thirty three would be XXXIII as per roman system, would be 33 as per the decimal system. This also made computation easier. 

Ramanujam           

         Srinivasa Ramanujan Iyengar contributed immensely in fields like number theory, mathematical analysis, string theory and crystallography. His genius has been admired by some greatest contemporary mathematicians of his time. He is hailed to be one of the most famous mathematicians in the field of number theory. Although he lived for a short span of 32 years, he compiled nearly 3900 phenomenal results that leave even the best mathematical brains of today in sheer awe and wonder!

Ramanujan was born in Brahmin family on December 22, 1887 at erode madras. He got his school education at kumba koram. He won a scholarship in matriculation examination. His teacher were very much impressed by his injected and special gifted abilities in mathematics.

Hardy remarked: I had never seen anything the least like them before. A single look at them is enough to show that they could be written down by a mathematician of the highest class.

His work thrown light on divergent series. Hypergemetric series continued fraction, definite integrals. Partition functions, ecliptic functions the theory of numbers, fractional differentiation and highly composite numbers. 

Bhaskara

Bhaskara or bhasharacharya is the most well known ancient Indian mathematician. He was born on 1114A.D. at bijjada bida in the sahyadari hill. He is famous for his book siddhanta shiromani (1150 A.D). it is divided into four sections-leelavati (a book on arithmetic), bijaganita(algebra), goladnayaya(chapter on sphere- celestial globe), and granoganita (mathematics of a planets), leelavagti contains many interesting problems and was a very popular text book. He gave an example idea of what is now called ―Rolle’s theorem.‖ Unfortunately, later Indian mathematics did not take any notice of this. Five centuries, later newton and Leibnitz developed these subjects. As an astronomer bhaskara is renowned for his concept of tatakalikagati. 

Rene Descartes

          The French philosopher and mathematician, Rene Descartes was famous for his method of expressing geometric shapes in the form of algebraic equation. It was because of Rene Descartes that we got introduced to the beautiful branch of co-ordinate geometry. The Cartesian coordinates, in fact, refer to his name. Besides this Rene made valuable contributions in the field of optics and energy conservation.

Leonhard Euler

          Euler, a Swiss mathematician and physicists is widely acclaimed for his contributions in the field of function notation. His mathematical genius has been proved by his contribution in the fields of infinitesimal calculus and graph theory. His mathematical works and research in optics, mechanics, fluid dynamics have been hailed to be very influential.

Fibonacci

          Leonardo of Pisa, the greatest European Italian mathematician, popularly known as Fibonacci, was the first mathematician to introduce Hindu - Arabic system in Europe, that is the positional system of using ten digits with a decimal point and zero. He is popular for using Fibonacci number sequence, that is, 1, 1, 2, 3, 5, 11....in the book authored by him, known as Book of Calculation, the Liber Abaci.

John Carl Friedrich Gauss

          Carl F. Gauss, a German mathematician, known as Princeps mathematicorum meaning, "the Prince of Mathematicians" or "the foremost of mathematicians" was a child prodigy and a genius. Even as a teenager, he is believed to have made remarkable mathematical contributions. Carl F. Gauss made path breaking contributions in fields like set theory, statistics, differential analysis, geophysics, electrostatics, number theory and astronomy. He proved the fundamental theorem of Algebra and made various contributions in number theory.

Sir Isaac Newton

          Sir Isaac Newton was one of the greatest mathematician and physicist, the world has ever produced. His contributions in mathematics are spread in almost every field. However, he developed Calculus, both differential and integral, that are, still the most important aspects of higher mathematics. Using Calculus, he made it easier to find the area bounded by closed curves. In physics, his most famous and world changing contribution was the discovery of existence of gravitation force in our surrounding.

Blaise Pascal

          Blaise Pascal, French philosopher, mathematician, and physicist, contributed in several areas of mathematics, but he is widely known for Pascal's triangle. He invented the first mechanical adding machine in the year 1642. The unit of atmospheric pressure, Pascal (Pa) has been named in his honor. He also made contributions in the field of computer and the programming language Pascal was named after him, in 1972.

Pythagoras
         The Greek mathematician and philosopher, known as the 'father of numbers', is famous for the discovery of Pythagorean theorem formula, which states that in a right angled triangle, the square of the hypotenuse (z), is equal to the sum of the squares of the other two sides, x and y - that is, x² + y² = z².

Benjamin Banneker

          A child prodigy, a watch designer and a mathematician, Bannerker discovered many puzzles in fields of trigonometry. He was a genius in logarithms and used them extensively in trigonometry. He is still regarded as the most popular black mathematician.

 John Von Neumann

          The Hungarian-American mathematician, physicist, John made valuable contribution in several fields like set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry and statistics. His operator theory in mechanics is still regarded as one of his most pioneering works. He was also a key figure in the development of game theory.

Joseph Fourier

          The Fourier's law and Fourier transform are named after him. He is also accredited with the discovery of the green house effect. He is popular for discovering Fourier series and its uses in determining its application of real life examples in heat transfer and vibrations.

Sophie Germain

                   Especially known for her work on 'Fermat's Last Theorem', Sophie was one of the initiators of the elasticity theory and also contributed to number theory and philosophy. She was regarded as the 'the revolutionary mathematician' of her times.

Amalie Emmy Noether

          She gave path breaking theorems in algebra field. The most popular, "Noether's Theorem" connects symmetry and conservation laws in Physics. She also made valuable contributions to the theories of algebraic invariants and number fields.

Albert Einstein

     The scientific world was amused by the Einstein's theory of relativity. Although Albert Einstein was physicist, his applied mathematical theorems to reach to apt conclusions. Known as "father of Physics", he can be best described as a mathematical physicist. He also won the Nobel Prize in 1921 for his contributions to physics and the discovery of law of photoelectric effect.

         Certainly, talking in detail about contribution of each of these geniuses is not possible right here as a book can be compiled about contributions made by each of these mathematicians. The mathematical world has immensely benefited from the works of these geniuses!