Biography-World Famous Mathematicians

WORLD FAMOUS MATHEMATICIANS

AGNESI, MARIA GAETANA

Italian Mathematician and Philosopher (1718-1799)

Maria Gaetana Agnesi was born in Milan, Italy. By the time she was 5 years old, she could speak both Italian and French. Her father was a professor of mathematics in Bologna, and Agnesi enjoyed a childhood of wealth and privilege. Her father provided her with tutors, and she participated in evening seminars, speaking to the guests in languages as varied as Latin, Greek, Hebrew, and Spanish. In her teens, Agnesi mastered mathematics. She became a prolific writer and an advocate for the education of women. After her mother died, Agnesi managed the household of eight children, and educated her brothers. Her father remarried and after her stepmother died, Maria became housekeeper for twenty siblings. Agnesi continued studying mathematics, mostly at night, and often to the point of exhaustion. In 1748 her mathematical compendium, Instituzioni analitiche ad uso delta gioventii italiana (Analytical Institutions), derived from teaching materials she wrote for her brothers, was published in two volumes. In this work, Agnesi had not only written clearly about algebra, precalculus mathematics, differential calculus, and integral calculus, but she had also added her conclusions and her own methods. Analytical Institutions remains the first surviving mathematical work written by a woman. So successful was Agnesi's textbook that it became the standard text on the subject for the next 100 years. Her book was studied and admired not only in Agnesi's native Italy but also in France and Germany, and was translated into a number of other languages. In his 1801 English translation of Agnesi's work, John Colson, the Cambridge (England) Lucasian Professor of Mathematics, made the mistake of confusing the Italian word for a versed sine curve, aversiera, with another Italian word for witch or wife of the devil, avversiere. Although 200 years have passed, the curve Colson misnamed the "Witch of Agnesi" still bears that name in many calculus texts as an illustration of an "even" function with a "maximum" value. For a = 2, for example, the maximum value of у will be 2. The curve illustrates many basic concepts in calculus.

Recognition

Agnesi was recognized during her lifetime with election to the Bologna Academy of Science. The Pope at the time was interested in mathematics and in 1750 made certain that Agnesi was invited to be an honorary lecturer in mathematics at the University of Bologna. However, Agnesi turned down the appointment and instead adopted a religious life, spending much of her time working among the elderly poor and sick women of Milan.

Although a hospice Agnesi founded has become famous throughout Italy, and Italian streets, a school, and scholarships have been named in her honor, Agnesi is perhaps best known today for her contributions to mathematics.

APOLLONIUS OF PERGA

Greek Geometer (262 B.C.E.-190 b.c.e.)

Apollonius, known as "The Great Geometer" to his admirers was born in 262 B.C.E. in the Greek colonial town of Perga in Anatolia, a part of modern Turkey. Apparently Apollonius's intellectual ability was recognized early, and as a young man he attended the university in Alexandria, Egypt, where many of the great scholars of that time were gathered.

Apollonius's teachers had studied with Euclid (c. 330-c. 260 B.C.E.), who is regarded as the most outstanding mathematician of ancient times. Apollonius quickly gained a reputation for his thorough and creative approach to mathematics and was made a professor at the university. Apollonius wrote a number of books on mathematics, especially geometry. He gathered, correlated, and summarized the mathematics of his predecessors. More importantly, he extended their work and made many creative and original contributions to the development of mathematics. His best known work is contained in the eight volumes of Conies. Volumes I—IV survive in the original Greek, and volumes I—VII, like many other Greek intellectual works, survive in medieval Arabic translation. Volume VIII is lost but is known from references made to it by later Greek scholars.

Conies addressed the four types of curves that result when a solid cone is cut into sections by a plane: the circle, the ellipse, the hyperbola, and the parabola. Apollonius discovered and named the latter two curves. In Conies, he gives a thorough treatment of the theory of these curves and related matters, developing a total of 387 propositions. Apollonius also demonstrated applications of the geometry of conic sections and curves to various mathematical problems. His work led to the separation of geometry into the two divisions of solid geometry and plane geometry.

In addition to Conies, Apollonius wrote at least eleven books, some in more than one volume. Of these, only one—Cutting Off a Ratio (also known as On Proportional Section)—survives in an Arabic translation. The others are known only by mention or discussion by other Greek mathematicians and authors.

In addition to his work in pure mathematics, Apollonius analyzed the properties of light and its reflection by curved mirrors, and he invented a sundial based on a conic section. Of particular importance was his application of geometry to astronomy. His use of elliptical orbits with eccentric and epicylic motion to explain the complex movement of planets, including their retrograde motion, was accepted until the time of Copernicus (1473-1543).

The work of Apollonius had an extensive effect on the subsequent development of mathematics and is still relevant today. Later mathematicians influenced by Apollonius's work include Rene Descartes (1596-1650) in the development of Cartesian mathematical science; Johannes Kepler (1571-1630) in his proposal of elliptical orbits for the planets; and Isaac Newton (1642-1727), who used conic sections in understanding the force of gravity.

ARCHIMEDES

Greek Mathematician and Inventor (287 B.C.E.-212 b.c.e.)

Archimedes was the greatest mathematician of the ancient world and one of the greatest mathematicians of all time. He was born in the Greek city of Syracuse on the island of Sicily. As a young man, Archimedes studied with successors of Euclid at Alexandria, Egypt. He returned to Syracuse after his studies and spent the rest of his life there. Archimedes is famous for his practical applications of mathematics. During his time in Egypt, Archimedes invented a device now known as the Archimedean screw. This device is still employed in many parts of the world to pump water for irrigation A short time later, he invented the double pulley, which was used by merchants to haul boats out of water. Archimedes also expanded the principles of the common lever. 

In his lifetime, Archimedes was best known for his war machines. Some commentaries describe his huge catapults that could hurl enormous rocks great distances. Another of Archimedes' war machines could snatch ships out of the water and crush them. Archimedes also studied the center of gravity, or the balancing point of geometric shapes; the specific gravity of geometric solids; and what traditionally became known as Archimedes' Principle, used to determine the weight of a body immersed in a liquid. Some of Archimedes' other discoveries include determining that the value of ____ is between ___ and ___, showing that the surface of a sphere is four times the area of its great circle, and finding that the volume of a sphere is two-thirds the volume of its circumscribed (bounding) cylinder. In making these discoveries, Archimedes used integration, an early form of calculus. Some historians claim that if Archimedes had had access to modern mathematics notation, he could have invented the calculus nearly 2,000 years earlier than Sir Isaac Newton.

CHARLES BABBAGE

British Mathematician and Inventor (1791-1871)

Charles Babbage was born in England in 1791. He lived during the Industrial Revolution, and his scientific, technological, and political endeavors contributed significantly to its effects. Babbage was the son of a wealthy banker and attended Cambridge University. A brilliant man, he was elected to membership in the Royal Society before receiving his master's degree in 1817. He was appointed to the Lucasian Chair of Mathematics at Cambridge in 1828, a position also held by such great scientists as Sir Isaac Newton and today's Stephen Hawking. As an authentic Newtonian, Babbage advocated the reduction of all things to numerical terms and believed that they could then be understood and controlled. He was particularly attracted to the use of statistics. Babbage is often regarded as the "father of computing." In 1823, with financial support from the British government, he began work on what he called the Difference Engine, a steam-powered machine that would calculate mathematical tables correct to twenty decimal places. He built prototypes that produced tables of logarithms correct to eight decimal places but was never successful in constructing a full-size version. Instead, in 1833, Babbage became interested in designing and building an Analytical Engine. This device was to be a mechanical apparatus that could perform any mathematical calculation. It would be controlled by a "program" of instructions that the machine would read from punched paper cards. Although his Analytical Engine has never been constructed, Babbage's basic design was the foundation of modern digital computers. Babbage was active in a variety of areas. Fascinated with rail travel, he performed research on railroad safety and efficiency, invented the cowcatcher, and promoted a standard gauge for train tracks. He established the modern postal system in Britain by developing uniform postal rates. His production of the first dependable actuarial tables of statistical life expectancies helped found the modern insurance industry. Babbage invented, among many other devices, the dynamometer, better lights for lighthouses, and a speedometer. His ideas contributed to the growth of the machine tool industry. He also developed mathematical approaches to deciphering codes.

Concerned about the level of interest in science, Babbage published Reflections on the Decline of Science in England in 1830. He also helped create the British Association for the Advancement of Science, the Analytical Society, the Statistical Society, and the Royal Astronomical Society.

Babbage's book On the Economy of Machinery and Manufactures (1832) established the scientific study of manufacturing, known as operations research. It made an important contribution to political and social economic theory by regarding manufacturing as the primary component of economics. Quoted by Karl Marx in Das Kapital, its ideas were important in Marxist economic theory. His other writings included Ninth Bridgewater Treatise (1837), in which he attempted to harmonize his scientific and religious beliefs. Although he was, for many years, a popular member of London society, he became ill-natured and unpopular in his old age. The honorary title of baron was offered to him, but he insisted instead on a life peerage— having all the privileges of a hereditary baron, including a seat in the House of Lords. It was never granted. He died in London in 1871.

BANNEKER, BENJAMIN

American Mathematician and Astronomer (1731-1806)

Benjamin Banneker is best known for his work in mathematics and astronomy. According to W. Douglas Brown, Banneker was "the first American Negro to challenge the world by the independent power of his intellect." A native of Baltimore County, Maryland, Benjamin Banneker was born on November 9, 1731, and spent most of his life on his father's farm located in what is now Ellicott City, Maryland. Although his father had been a slave, his mother was born free to a white English woman who came to America as an indentured servant and married a native African. Banneker's family had sufficient means to afford schooling. The school was only open in the winter, and the pupils included a few whites and two or three black children. There Benjamin learned to read and do arithmetic to "double fractions." When he became old enough to help on his father's farm, he continued to teach himself. In his early life, Benjamin constructed a wooden clock that was a reliable timepiece for over 20 years. It was the first striking clock of its kind made completely in America. Benjamin quickly became known as the smartest mathematician for miles around. In 1791, Banneker was nominated by Secretary of State Thomas Jefferson and appointed by President George Washington to the commission to survey federal land for a national capital in Washington, D.C. He had an important role in the layout and design of the city, though his name does not appear on any contemporary documents. Banneker devoted himself to the study of astronomy. In 1792, he produced his first almanac in which he recorded solar and lunar eclipses, tide tables, and positions of the Sun, Moon, and planets for each day of the year. The renowned work was given to Thomas Jefferson along with a letter from Banneker pleading for the rights of slaves held in the colonies. Jefferson sent the almanac to M. de Condorcet, secretary of the Academy of Sciences at Paris, praising the work. Thereafter, Banneker published yearly almanacs until his health declined in 1804. Benjamin Banneker died on October 9, 1806.  On the day of his funeral, fire consumed his house, which destroyed his laboratory.

CARROLL, LEWIS

British Mathematician, Writer, and Photographer (1832-1898)

Lewis Carroll is the pen name of Charles Lutwidge Dodgson, who was born in Darebury, England, in 1832 and died in Guildford, England, in 1898. He taught mathematics at Christ Church College of Oxford University for most of his life and wrote a number of mathematics texts. His fame, however, rests in being the author of children's stories and poems, including Alice's Adventures in Wonderland A865) and Through the Looking Glass (1872). Dodgson's father was an Anglican minister who had excelled in mathematics at Christ Church College. As a child, Dodgson invented games and stories to entertain his ten brothers and sisters. He attended Richmond School and Rugby School before entering Christ Church College in 1851. He did particularly well in mathematics and classics and, after graduating in 1854 with first honors in mathematics, immediately became an instructor in mathematics at Christ Church, remaining in that position until 1881. Dodgson was the author of a number of mathematics articles and books, including Notes on the First Two Books of Euclid (1860); Euclid and His Modern Rivals (1879); A Syllabus of Plane Algebraic Geometry (1860); Curiosa Mathematica. Part I (1888) and Part II (1894); and Symbolic Logic, Part I (1896) and Part II (unpublished until 1977).

Dodgson, or Carroll, is best remembered for the children's books that resulted from his efforts to entertain the children of the Dean of Christ Church, Henry George Liddell. One of Liddell's daughters, Alice, is immortalized as the heroine of one of the most popular children's books ever to be written.

EINSTEIN, ALBERT

American Physicist and Mathematician (1879-1955)

Albert Einstein is perhaps the best-known scientist who ever lived. His contributions include the special and general theories of relativity, the assertion of the equivalence of mass and energy, and the quantum explanation of the behavior of electromagnetic radiation, including light. Einstein was born in Ulm, Germany, in 1879 and died in Princeton, New Jersey, in 1955. Einstein showed little academic ability before entering the Federal Polytechnic Academy in Zurich, Switzerland, in 1896, where he studied both mathematics and physics. After graduating in 1900, he briefly taught school and then took a position in the patent office. During this time, he wrote articles on theoretical physics in his spare time.

Einstein's ability to apply advanced mathematics in the solution of complex physical problems led to the publication of a group of momentous papers in 1905. A doctorate from the University of Zurich and world fame soon followed. The subjects of the 1905 publications included special relativity, the equivalence of matter and energy, and the quantum nature of radiation. These revolutionary publications, in combination with the general theory of relativity, which he published in 1915, and the development of quantum mechanics, to which he made significant contributions, transformed science and again demonstrated the indispensability of mathematics in the scientific endeavor.  The atomic age, the space age, and the electronic age owe much to Einstein's contributions to physics, changing human civilization more dramatically in the twentieth century than in previous centuries combined.

GERMAIN, SOPHIE

French Mathematician (1776-1831)

Sophie Germain is remembered for her work in the theory of numbers and in mathematical physics. Germain was born in Paris to a father who was a wealthy silk merchant. She educated herself by studying books in her father's library, including the works of Sir Isaac Newton and the writings of mathematician Leonhard Euler. When the Ecole Polytechnique opened in 1794, even though women were not allowed to attend as regular students, Germain obtained lecture notes for courses and submitted papers using the pseudonym M. LeBlanc.

One of the instructors, noted scientist Joseph-Louis Lagrange, became her mentor. In 1804 Germain began to correspond with German mathematician Carl Friedrich Gauss, sending him discoveries she made in number theory. Among these was a limited proof of Fermat's Last Theorem, her best known contribution to mathematics. This theorem was finally proved in 1994 using her approach. Germain also corresponded with mathematician Adrien Marie Legendre, who used her suggestions in one of his publications.

In mathematical physics, Germain is known for her work in acoustics and elasticity. She won a prize from the French Academy of Sciences in 1816 for the development of mathematical models for the vibration of elastic surfaces. Subsequently, she was invited to attend sessions of the Academy of Sciences and the Institut de France, but because she was a woman, she could never join either group.

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