# History of Mathematics

## 3000 B.C.

ARISTOTLE-DEDUCTIVE LOGIC (340 B.C.E.) Aristotle wrote a book called "TOPICS" which started out with a discussion of deductive logic. The whole world reestablished this book starting with the Islamic translation on through time.

THALES, FOUNDER OF GREEK GEOMETRY (585 B.C.E.) The birth of Greek astronomy has been attributed to Thales of Miletus. Thales brought from Egypt a number of fundamental geometric principles. Thales, an Ionian (western border of Asia Minor) who was active near the start of the sixth century bc has been credited with a number of geometric theorems. 1. A Circle is bisected by its diameter. 2. Angles at the base of any isosceles triangle are equal. 3. If two straight lines intersect the opposite angles formed are equal. 4. If two triangles have two angles and one side respectively equal, the triangles are equal in all respects. Thales was also well known for forecasting the solar eclipse, so he was also considered a scientist.

SIEVE OF ERATOSTHENES (276-196 B.C.E.)

See how a list of primes are produced using Eratosthenes' method of "filtering".

GEMINUS (130-70 B.C.E.)

See what Geminus has to say about Euclids' Axioms and the proof he offers for the controversial Parallel Postulate.

PLATO'S ACADEMY(386 B.C.E) In 386 BC in Athen's Greece Plato's friends bought for him a local orchard in which he founded one of the world's first universities. It was destined to become the intellectual center of Greece for over nine hundred years. The academy was technically a religious fraternity. The students paid no fees but most came from rich families and were expected to donate. Women were also admitted to the student body as Plato was an ardent Feminist. The chief studies were mathematics and philosophy. Over the main entrance was the motto " Let no one without Geometry enter here" The main requirement for entrance was a passion for Geometry.

ARISTOTLE (340 B.C.E) Most of the major mathematical advances of the 4th century were made by those who studied at the academy. Their mathematical courses included arith- metic, theory of numbers, advanced geometry and astronomy. Plato and his aides taught by lecturing, by dialogue and by setting problems for the students to solve. One such problem was to find " The uniform and ordered movements of which the apparent motions of the planets can be accounted for". Their lectures were very technical with very abstract philosophical leanings. Students then, as always complained that their studies were not relevent enough for every day life. Many great scholars were tremendously influenced, including Aristotle whose notes and papers are still being studied today.

PLIMPTON 322 (1700 B.C.E.)

Plimptom 322 is an ancient Babylonian tablet on number theory. Each of its different rows correlate with various measurements and proportions of right triangles.

ZENO-PARADOXES OF MOTION (450 B.C.E.) This greek philosopher, Zeno, is duely noted for developing the paradox of infinity. His many paradoxes involve never ending motion of an object.

## 1-999

HYPATIA OF ALEXANDRIA (370-413 C.E.)

As one of the first documented female Mathematicians, Astronomers and Philosophers, find out how she spread her knowledge and how her life brutally ended.

ABU'L-HASAN IBN YUNUS (950-1009 C.E.)

Aside from his book with 81 chapters, this Astrologer produced many trigonometric tables designed for astronomical purposes.

MAYAN CALENDAR (200 C.E.) Among many cultural advances by the Maya included the development of mathematics and astronomy. The Maya used a mathematical system based on the number 20, insead of 10 as in the decimal system. Dots and dashes represented numbers, and a special symbol represented zero. Mathematicians consider the zero one of the world's great inventions. Maya priests developed a knowledge of astronomy by observing the positions of the sun, moon and stars. They made tables predicting eclipses and orbit of the planet Venus. The priests also used mathematics and astronomy to develop two kinds of calendars.One was a sacred almanac of 260 days. Each day was named with one of 20 day names and a number from 1 to 13. Each of the 20 day names had a god or goddess associated with it. The priests predicted good or bad luck by studying the combinations of gods or goddesses and numbers. The Maya also had a calendar of 365 days, based on the orbit of the earth around the sun.These days were divided into 18 months of 20 days each, plus 5 days at the end of the year. The Maya considered these last 5 days of the year to be extremely unlucky. During that period they fasted, made many sacrifices, and avoided unnecessary work.

DIOPHANTUS OF ALEXANDRIA(250 C.E.) 250 BC Number Theory, Algebra Diophantus worked during the middle of the 3rd century, is best known for his Arithmetica, a work on the theory of numbers. The Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution) and interminate equations. The method for solving these equations is now known as Diophantine analysis. Diophantus was always satisfied with a rational solution and did not require a whole number. He did not deal in negative solutions and one solution was all he required. Most of the Arithmetica problems lead to quadratic equations. He also introduced an algebraic symbolism that used an abbreviation for the unknown.

BEDE'S LIFE (673-735 C.E.)

See what Bede had done in his life and how he influenced others.

KHOWARIZMI COINS TERM ALGEBRA (810 C.E.) Sometime around A.D. 830, Muhammad ibn Musa al-Khwarizmi composed the earliest known Arabic treatment of algebra. As a scholar at the HOUSE OF WISDOM, which began in Baghdad as the library of Harun al-Rashid with other noted colleagues. They were known as the sons of Moses. Al-Khowarizmi was well known for his famous writing called "al-Kitab al-mukhtasar fi hisab al-jabrwa'l-muqabala or The compendious book on calculation by completion and balancing. This writing was conceived as an elementary textbook of practical mathematics and began with the discussion of the algebra of first and second degree equations and moved on in its final two parts to the business of practical applications. Also in his famous writing he distinguished and solved six types of algebraic equations including quadratic, square roots , etc. The HOUSE OF WISDOM functioned as the center of study and research in the Islamic world of the ninth century.

DIOPHANTUS (250 C.E.) An Alexandrian Greek , he wrote many manuscripts, but only six of the thirteen books of Arithmetica have survived. The manuscripts that were saved dealt primarily with Polygonal Numbers, Number Theory, and some forms of algebra. Below is a well known puzzle regarding Diophantus: "God granted him to be a boy for the sixth part of his life, and adding a twelfth part to this, He clothed his cheeks with down; He lit him the light of wedlock after a seventh part, and five years after his marriage He granted him a son. Alas! late-born wretched child; after attaining the measure of half his father's life, chill Fate took him. After consoling his grief by this science of numbers for four years he ended his life. THE SOLUTION IS THAT DIOPHANTUS MARRIED AT AGE 33,HAD A SON WHEN HE WAS 37, AND DIED WHEN HE WAS 84.

HERON-GEOMETRTY (75 C.E.)

Heron of Alexandria is somewhat of a "hero" in the world of geometry and mechanics. His interest in these subjects lead him to introducing the concept of minimal path.

PTOLEMY-TRIGONOMETRY (150 C.E.)

Ptolemy spent most of his life in Alexandria where he became one of the most influential astronomers and geographers of his time. He set forth for consideration geocentric theory that prevailed up into the 17th century C.E. All his work lead into trigonometry where he used chords rather than sin and cos.

## 1000-1499

DURER (1471-1528 C.E.) See how he tells you about his magic square. He also talks about his shell curves.

ULUGH BEG (1393-1449 C.E.) He was primarily an astronomer and he build an observatory. He compiled tables of sins and tans at 1 degree intervals. His work was correct to at lease 8 decimal places.

LEONARDO FIBONACCI (Approx. 1170-1228 C.E.)

See how to generate a list of Fibonacci numbers.

NICOLAUS COPERNICUS (1473-1543 C.E.) A Polish astronomer,he is known as the founder of modern astronomy. In his famous writing De revolutionibus, he relates evidence proving that the earth is not the centre of the universe, and that it revolves around the sun.

THE CODE OF QUIPU (900-1532 C.E.)

See what one of the most ancient methods of codification is. Find out how you can learn to be a quipumaker.

SCIPIONE DAL FERRO (1465-1526 C.E.)

See how this Italian mathematician solved a cubic equation using x^3+mx=n.

ROGER BACON'S PLACE IN THE HISTORY OF ALCHEMY (1267 C.E.) He was a 13th century natural philosopher and chemist. He was extremely important to the development of modern science. He is always mentioned in general histories of alchemy and chemistry.

THOMAS BRADWARDINE (1325 C.E.) Bradwardine studied at Merton College Oxford, in 1337 he was made chancellor at St Paul's Cathedral. He studied bodies in uniform motion and ratios of speed in the treatise.

HISTORY OF MIDDLE EASTERN MATHEMATICS (800-1449 C.E.)

An exellent lift of Arabic mathematicians, information of Greek Astronomy, Greek mathematics, and Ptolemy's Geography can be found in this source.

DURER'S FAMOUS PORTRAITS AND HIS BIOGRAPHY (1471-1528 C.E.)

Albrecht Durer was the most famous artist Germany in the sixteen century. Durer stressed geometry and measurement as the keys to understanding the art and wood craft work. He also created Durer's Melancolia contains magic square. This web site will link you to the record of the brilliant colorful portrait and life of Durer.

NICOLE ORESME-COORDINATES, FRACTIONAL COORDINATES (1360 C.E.)

Nicole Oresme studied theology in the Universeity of Paris. Later he was a chaplain and financial advisor to King Charles V. Oresme invented coordinate geometry and was the first to use fractional exponents in his work.

REGIOMONTANUS-TRIGONOMETRY (1436-1476 C.E.)

Johan regiomontanus was well known for his work in many fields of science including astronomy and mathematics. In astronomy he specialized optical enhancement instruments. In mathematics he focused mainly on algebra and trigonometry. He made important contributions to trigonometry and astronomy. In 1472 he made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years later.

## 1500-1600

LEONARDO DA VINCI (1505C.E.)

Leonardo da Vinci was an Italian painter, draftman, sculptor, architect, and engineer. This WELCOME TO THE MUSEUM will lead you to the main gallery which includes Oil Painting, Engineering and Futuristic Designs, Drawings and Sketches, and Life and Times of Leonardo da Vinci.

RENE DESCARTES(1596-1650 C.E.) He was a rationalist philosopher and mathematician. See a short biographyon him during his life.

RAFAEL BOMBELLI (1526-1572 C.E.)

Bombelli helped engineer the reclamation of the marshes of the Val di Chiana, which helped springboard his writing of the books titled ALGEBRA (I-V).

TARTAGLIA (1545 C.E.) Tartaglia was famed for his algebraic solution of cubic equations which was published in Cardan's Ars Magna. He wrote in 1537 on the application of mathematics to artillery fire. He described new ballistic methods and instruments including the first firing tables.

CHRISTOPHER CLAVIUS (1583 CE) Clavius was called the Euclid of the 16th century. His most important achievement related to the reform of the calendar under Gregory XIII.

GEMMA FRISIUS (1508-1555 C.E.) See what he has accomplished in his life. He supported himself by publishing his books.

CARDANO-CUBIC AND QUADRATIC EQUATIONS (1550 C.E.)

Girolamo Cardano's work Ars Magna was the first Latin treatise about algebra exclusively. In his work, Cardano became highly influential to the discovery of the solutions and understanding of the cubic and quadratic equations.

CLAVIUS-ASTRONOMY AND CALENDARS (1537-1612 C.E.)

Christopher Clavius did a great deal of his most significant work at about 45 years of age. He was able to use algebraic logic in order to coordinate the Julian calender with the Gregorian calender with respect to leap years. He was also the first ever use the decimal point.

## 1600-1700

SIR ISAAC NEWTON (1642-1727 C.E.) Here is a portrait of Sir Isaac Newton and a brief description of him. Then look at the first 26 years of his life.

GIOVANNI CEVA (1678 C.E.) Ceva used the properties of the center of gravity of a system of points to obtain the relations of the segments. Much of his mathematical work had to do with hydraulics.

NEWTON'S "PRINCIPIA" (1687 C.E.)

See the principle agruments of "Principia" that was written by Sir Isaac Newton. There is a little more about his book two of "Principia"

WILLIAM OUGHTRED (1574-1660 C.E.) Mr. Oughtred is best known for his invention of an early form of the slide rule. He also invented many new symbols.

CHRISTOPHER WREN (1632-1723 C.E.)

He was into a little bit of everything. He formulated a graphical method of representing comets and eclipses.

COLIN MACLAURIN (1698-1746 C.E.)

Maclaurin studied higher plane curves and developed the Maclaurin power series.

JOHN WALLIS (1616-1703 C.E.)

As an influential mathematician before Newton, Wallis contributed to the advancement of Calculus. He evaluated integrals and also accepted negative and complex roots when solving polynomial expressions.

GIRARD DESARGUES (1640 C.E.) Desargues was a founder of projective geometry. His work centered on the theory of conic sections and perspective. He also wrote on the cutting of stones for use in buildings and sundials.

FOLIUM OF DESCARTES (1638 C.E)

Rene Descartes was a French philosopher who directed the way to Cartesian geometry by being the first to apply algebra to geometry. In his work, Descartes investigated different curves one of which is called the Folium of Descartes; take a look.

Pascal invented the first mechanical adding machine. He also configured an arithmetical triangle, nowadays called Pascal's Trangle, which produces coefficients of the expansion of a binomial. He is best known in mathematics for his work on probability that he did with another mathematician named Fermat.

## 1700-1800

FRANKLIN SQUARE (1750 C.E.)

See some of his squares he has done and some history on them.

KARL GAUSS (1777-1855 C.E.)

He was a German Scientist and Mathematician who was sometimes called the "prince of mathematics."

GEORGES LOUIS LECLERC COMTE de BUFFON (1707-1788 C.E.) See how he used a probability experiment which he carried out calculating pi. Also his needle experiment caused much discussion and discovery about probability.

PIERRE SIMON LAPLACE (Born 28/3/1740) See how Laplace's Equation was solved. Laplace proved the stability of the solar system. He wrote his first mathematics paper at the age of 16 at Caen University.

JOSEPH LA GRANGE (1736-1813 C.E.)

First introduced the method of Lagrange Multipliers.

GIOVANNI SACCHERI (1733 C.E.) His two most important books were the "Logic Demonstration" an explanation of logic and the Euclides. Much of his logical and mathematical reasoning has become part of mathematical logic and non-Euclidean geometry.

MARIA GAETANA AGNESI (1748 C.E.) Maria was an Italian woman of remarkable intellectual gifts and attainments.She wrote an excellent treatise on conic sections and the first treating of the analysis of finite quantities; the second the analysis of infintesimals.

JOHANN HEINRICH LAMBERT (1728-1777 C.E.)

Johann Heinrich Lambert came from a poor family and had to support himself to achieve his goal as mathematician. He developed Demoivre's theorem on trigonometry and non-Euclidean geometry. Find out more from this web site on the biography of mathematicians and scientists of the seventeenth centuries.

GAUSS' LEMNISCATE CONSTANT (1799 C.E.)

This web site illustrates Gauss's observation on the massive field of elliptic modular functions and the lemniscate constant. It also links to Inverse Symbolic Calculator web page and The Mathcad PLUS 6.0 for further illustration.

BROOK TAYLOR-SERIES, GEOMETRY, CALCULUS OF FINITE DISTANCES (1715 C.E.)

Brook Taylor wasn't the first to look for polynomial approximations of trancendental functions, but his published work in 1715 C.E. was one of the first comprehensive works on the topic.

ALEXIS CLAIRAUT-SOLID ANALYTIC GEOMETRY (1713-1765 C.E.)

Clairaut work on all tpes of mathematics. He took part in verifying Newton's theoretical proof that the Earth is oblate spheroid and that the earh was flat at the north and south poles. He studied the Three Body Problem and did a great deal of research into Calculus.

## 1800-1900

CANTOR, GEORG (1845-1918 C.E.)

Georg Cantor was one of the most assailed mathematicians in history. He developed the modern theory on infinite sets. Despite the irony of spending his later year in mental institution, Georg Cantor was recognized for his lifetime echievement by the Royal Society of London and was made a member of to other Societies for Mathematics and Sciences. This web site will link you to related information on Cantor: Karl Weierstrass, Zeno of Elea, Cantor function, Cantor set, Cantor-Bernstein theorem, Zeno's paradoxes.

EVARISTE GALOIS (1811-1832 C.E.)

He was a french Mathematician who develpoed new techniques to study equations called group theory.

SONYA KOVALEVSKAYA (1850-1891 C.E.)

Sonya was a great mathematician, a writer, and advocate of women's rights in the 19th century.

CHARLOTTE ANGAS SCOTT (1858-1931)

She was one of England's first women to obtain a doctorate in mathematics.

GUISEPPE PEANO (1858-1932 C.E.) He was one of the pioneers in mathematical logic and axiomatization of mathematics. See Peano's Axiome.

ABEL NIELS (1802-1829 C.E.)

He proved that it is not possible to solve a general fifth degree (or higher) polynomial equation by using a radical.

AUGUSTUS DE MORGAN (1806-1871 C.E.)

He was the first to define and name "Mathematical Induction." Symbolic logic has converses and contradictions in his De Morgans Laws.

EMMY NOETHER (1882-1935 C.E.)

Living through the Nazi era, she was an exceptional Jewish mathematician. She mainly studied abstract algebra; rings, groups and fields.

SRINIVASA RAMANUJAN (1887-1920 C.E.)

He was a natural genius and is considered a great mathematician. He came up with 40000 new original theorums recorded with his original research in two large notebooks. These encompass analytical theory of numbers, elliptic functions, continued fractions, and infinite series.

HENRI BROCARD (1873 CE) Henri Brocard was a French army officer who studied meteoroly but is best remembered for his work on the triangle. The Brocard points of a triangle ABC are O, O' where OAB, OBC and OCA and the angles O'BA, O'CB and O'AC are equal. Angle OAB is called the Brocard angle and satisfies cot OAB = Cot A + Cot B + Cot C.

BABBAGE-ANALYSIS (1812 C.E.)

Charles Babbage remarkebly thought up the principle for the anlytical engine which turns out to be the concept used behind the design of modern computers. Due to lack of funds from the English goverment he was never able to build his own analytical computer.

SYLVESTER-MATRICES (1879 C.E.)

James Sylvester was able to accomplish a great deal within the development of matrices. He is also the man that coined the term "discriminant" as the word to be used for equations of higher order than cubic.

## 1900-

GIUSEPPE PEANO (1890 C.E.) Peano was the founder of symbolic logic and his interests centered on the foundations of mathematics and on the development of a formal logical language. He produced an axiomatic definition of the natural number system and showed how the real number system can be derived from these postulates.

R.BUCKMINSTER FULLER (1895-1983 C.E.)

R.Buckminster Fuller,Jr. was born in Milton, Massachusetts, on July 12, 1895. Fuller introduced ground-breaking ideas in the of architecture, design, art, engineering, education, cartography and mathematics. Among his most notable inventions and discoveries are synergetic geometry, geodesic structures and tensegrity structures. There are magnificient pictures and more informations in this web site.

EINSTEIN, ALBERT (1879-1955 C.E.)

A life and times about Albert Einstein who was one of the greatest physicists of all time. This web site will also link you to the biography of German leaders: Hitler, Goering, and Goebbels. Albert Einstein established the special theory of relativity, created the theory of brownian motion, and founded the photon theory of light.

FLORENCE NIGHTINGALE DAVID (1909-1993 C.E.)

Florence fought for her rights after she was turned down on a job because she was a woman. When she inquired about the reason she didn't get the position, they told her even though she was the most qualified for the position she was a woman.

JOHN GEORGE KEMENY (1926-1992 C.E.) See his history and how he and Thomas Kurtz developed BASIC.

EMMY NOETHER (1930 C.E.) Emmy Noether is best known for her contributions to abstract algebra, in particular her study of chain conditions on ideals of rings. From 1927 on Noether collaborated with Helmut Hasse and Richard Brauer in work on non-commutative algebras. She also did important work in the theory of invariants, which led to formulations for several concepts of Einstein's general theory of relativity.

KURT GODEL (1931 C.E.) Kurt Godel together with Bertrand Russell is the most important name in logic and in the found-ations and philosohy of mathematics of this century.

HILBERT-23 FAMOUS PROBLEMS (1900 C.E.)

Since Euclid, David Hilbert up to this point had the most productivity with geometry. He came up with 21 new and viable axioms to add to the works of Euclidean geometry. In relation to these axioms, Hilbert published Grundlagen der Geometrie in 1900. This work went on to be heralded as his 23 famous Paris problems.

NOW INTRODUCING THE GRAPHING CALCULATOR (1990 C.E.)

The graphing calculator has brought a great deal into the class room and the work place. Just another tool to make our lives easier and more accurate. If used properly the graphing calculator can save time and increase production.