01History of Mathematicians

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HISTORY OF MATHEMATICIAN


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BIOGRAPHYThough his exploits in the field of geometry,

science, and physics are widely famous, not

much is known about his personal life, as all

records have been lost. He was so much in

love with geometry and his inventions that

the last words he uttered were "Do not

disturb my circles."

He was killed in the Second Punic War by a

Roman soldier against the wishes of General

Marcellus. Plutarch writes that Archimedeswas contemplating a mathematical diagram

at the time of his death. His tomb was

engraved with the figure of a sphere andcylinder as per his wish.


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INVENTIONS

In the field of mathematics, Archimedes produced severaltheorems that became widely known throughout the world.He is credited with producing some of the principles ofcalculus long before Newton and Leibniz. He worked outways of squaring the circle and computing areas of severalcurved regions. His interest in mechanics is credited with

influencing his mathematical reasoning, which he used indevising new mathematical theorems. He proved that thesurface area and volume of a sphere are two-thirds that of itscircumscribing cylinder.

He is credited with the invention of Archimedes screw or screwpump, which is a device used to raise the level of water froma lower area to a higher elevation. He is known for theformulation of Archimedes' principle, a hydrostatic principlestating that an object in any liquid is buoyed by force equalto the weight of fluid it displaces. Legend has it that hediscovered the principle of buoyancy while taking bath and

following the discovery, he ran naked shouting "Eureka,Eureka," meaning I have found it.


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Using the method of exhaustion, he was able toaddress irrational numbers, such as square rootsand Pi. He showed how to calculate areas andtangents. His mastery of applied mathematics

reflects from his work on the Archimedes screw.

From his invention of war machines, such asparabolic mirrors, Archimedes claw and death rayand complex lever systems, shows that he playedan important role in guarding Syracuse against the

siege laid by Romans. Though he could not saveSyracuse from being captured by General MarcusClaudius Marcellus and his Roman forces in 212B.C., his war machines might have delayed thecapture. Archimedes himself was killed when thecity was captured by the Romans.

Undoubtedly, Archimedes was one of the mostbrilliant minds of all times. His contributions in thefield of geometry, science, and physics trulyreflect his genius. He wrote many treatises, butonly a few would survive the Middle Ages. Still his

work and fame live on.


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BACKGROUND

Charles Babbage was born in London, England December 26,

1791. Babbage suffered from many childhood illnesses,

which forced his family to send him to a clergy operated

school for special care.

Babbage had the advantage of a wealthy father that wished to

further his education. A stint at the Academy at Forty Hills

in Middlesex began the process and created the interest in

Mathematics. Babbage showed considerable talent inMathematics, but his disdain for the Classics meant that

more schooling and tutoring at home would be required

before Babbage would be ready for entry to Cambridge.

Babbage enjoyed reading many of the major works in

math and showed a solid understanding of what theories

and ideas had validity. As an undergraduate, Babbage

setup a society to critique the works of the Frenchmathematician, Lacroix, on the subject of differential and

integral calculus. Finding Lacroix's work a masterpiece and

showing the good sense to admit so, Babbage was asked to

setup a Analytical Society that was composed of

Cambridge undergraduates.


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CONTRIBUTIONS

Written Works:

A Comparative View of the Various Institutions for the

Assurance of Lives (1826)

Table of Logarithms of the Natural Numbers from 1 to 108,

000 (1827)

Reflections on the Decline of Science in England (1830)On the Economy of Machinery and Manufactures (1832)

Ninth Bridgewater Treatise (1837)

Passages from the Life of a Philosopher (1864)

Famous Quote:

"The whole of the developments and operations of analysis

are now capable of being executed by machinery. ... Assoon as an Analytical Engine exists, it will necessarily

guide the future course of science."

---Excerpt from the Life of a Philosopher


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Ren Descartes was born on March 31, 1596 in a village in Touraine,

France, which is now called La Haye-Descartes. His mother died shortly

after he was born (thirteen months). About 1606, Ren entered the

Jesuit college of La Fleche, in which a relative of his, Father Charlet, atheologian would watch out for him. Because of his delicate health,

Descartes was allowed to spend mornings in bed, meditating, reading,

and writing -a habit he maintained for most of his life.

He left La Fleche, because he was more confused about knowledge, and

he did not get his thirst for knowledge fulfilled. He then studied at theUniversity of Poitiers in 1615-16, earning a bachelor's degree and a

licentiate in law there.

At the age of twenty-two he left Paris and join the army of Prince Maurice

of Nassau. In the next year he was transferred to the army of

Maximailian. Duke ofB

avaria.B

ut in the night of November 10, 1619,he had a series of three dreams, that he interpreted as a message from

God tell him to devote his life to the rational quest for certain truth.

After ending his voluntary military service he went back to Paris.


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The social life in Paris was too distracting, so he moved to Holland in

1628. He lived in Holland until 1649. During this time, he avoided

reading any scholastic texts.

He wrote a couple of works in Holland, but when he heard of the

Inquisition condemning Galileo to death for his thoughts, as well as,

other thinkers, he decided to suppress his works.

In late 1604, Descartes' daughter, though he was never married, and father

died.

Descartes' philosophy became famous during the last decade of his life.

Descartes was later accused of heresy at the University of Leyden and

wrote a letter of self-defense to its trustees in 1647. He feared that he

might be arrested and killed, like Galileo, but that never happened.

In around 1648, Queen Christina of Sweden invited him to come to her

court to instruct her in philosophy. Despite his cautious reluctance,Descartes accepted her invitation. She sent an admiral with a warship

to carry him to Sweden, and Descartes left for Stockholm in September

of 1649. This was the costliest mistake of his life.


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German mathematician who is sometimes called the "prince ofmathematics." He was a prodigious child, at the age of threeinforming his father of an arithmetical error in a complicatedpayroll calculation and stating the correct answer. In school,when his teacher gave the problem of summing the integers

from 1 to 100 (an arithmetic series ) to his students to keepthem busy, Gauss immediately wrote down the correctanswer 5050 on his slate. At age 19, Gauss demonstrated amethod for constructing a heptadecagon using onlya straightedge and compass which had eluded the Greeks.(The explicit construction of the heptadecagon wasaccomplished around 1800 by Erchinger.) Gauss also showedthat only regular polygons of a certain number of sides

could be in that manner (a heptagon, for example, couldnot be constructed.) Gauss proved the fundamental theoremof algebra, which states that every polynomial has a rootof the form a+bi. In fact, he gave four different proofs, thefirst of which appeared in his dissertation. In 1801, he provedthe fundamental theorem of arithmetic, which states thatevery natural number can be represented asthe product ofprimes in only one way. At age 24, Gauss

published one of the most brilliant achievements inmathematics, Disquisitiones Arithmeticae (1801). In it, Gausssystematized the study ofnumber theory (properties ofthe integers ). Gauss proved that every number is the sum ofat most threetriangular numbers and developedthe algebra ofcongruences.


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n 1801, Gauss developed the method ofleast squares fitting, 10 yearsbeforeLegendre, but did not publish it. The method enabled him to calculatethe orbit of the asteroid Ceres, which had been discovered byPiazzi from

only three observations. However, after his independentdiscovery,Legendre accused Gauss of plagiarism. Gauss published hismonumental treatise on celestial mechanics Theoria Motus in 1806. He becameinterested in the compass through surveying and developed the magnetometerand, withWilhelm Weber measured the intensity of magnetic forces.WithWeber, he also built the first successful telegraph. Gauss is reported to

have said "There have been only three epoch-makingmathematicians:Archimedes, Newton and Eisenstein" (Boyer 1968, p. 553). Mosthistorians are puzzled by the inclusion of Eisenstein in the same class as theother two. There is also a story that in 1807 he was interrupted in the middle ofa problem and told that his wife was dying. He is purported to have said, "Tellher to wait a moment 'til I'm through" (Asimov 1972, p. 280). Gauss arrived atimportant results on the parallel postulate, but failed to publish them. Creditfor the discovery ofnon-Euclidean geometry therefore went toJanosBolyai andLobachevsky. However, he did publish his seminal workon differential geometry in Disquisitiones circa superticiescurvas. The Gaussian curvature (or "second" curvature) is named for him. Healso discovered the Cauchy integral theorem


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G. W. Leibniz was one of the most important thinkers of his time. Hiscontributions to such diverse fields as philosophy, linguistics, and history areundeniable. And yet although he became acquainted quite late in his life with themathematical achieveme nts of his generation, it will always be his innovations inthis field that put him to the forefront of the enlightened thinkers of his era.These achievements are especially remarkable considering that Leibniz often

treated the subject as a corollary to his studies in other fields, notably logic,

philosophy, and even law. It was precisely for this reason that Leibniz had somuch success in the field, in that he was unhampered by much of the dogma thatmight have hindered its progress. Leibniz viewed the subject through his ownlens, interpreting the mathematical issues differently from his colleagues. Perhapsit was the distance from which he viewed the field that allowed Leibniz to besuch an innovator in the rapidly changing subject. He gathered and pr ocessed asmuch contem-porary mathematics as possible, reassessed it, and through his

innovative system of notation, repackaged it as a superior product. It wasLeibniz's algebraic symbolism that freed the subject from much of its rigid verbalstructure, allowing it to develop at an even faster rate. Leibniz's modernmathematical notation probably represents his greatest single contribution tomathematics. G.W. Leibniz is generally considered, along with Isaac Newton, as acofounder of the differential and integral Calculus.

INTRODUCTION


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Mathematicians had developed algebraic methods for finding areas and volumes of a great variety

geometric figures. This marks one of the greatest developments in m athematics since the Greeks be

using limits to approximate areas and then find the value of p. It was Cavalieri (1598-1647) who fir

introduced the concept of "indivisible magnitudes" in his Geometry of Indivisibles to study areas un

curves of the form:

y = xn (n(1)

At roughly the same time Descartes published his La Giomitrie, in which he showed, somewhat obs

how to use Viite's algebra to describe curves and obtain an algebraic analysis of geometric problems

319-331] The work of these two mathematici ans would have an especially great influence on the

development of Leibniz's new calculus. [4, X]


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Newton, Sir Isaac (1642-1727), Englishnatural philosopher, generally regardedas the most original and influentialtheorist in the history of science. Inaddition to his invention of theinfinitesimal calculus and a new theoryof light and color, Newtontransformed the structure of physicalscience with his three laws of motion

and the law of universal gravitation. Asthe keystone of the scientificrevolution of the 17th century,Newton's work combined thecontributions of Copernicus, Kepler,Galileo, Descartes, and others into a

new and powerful synthesis. Threecenturies later the resulting structure- classical mechanics - continues to bea useful but no less elegant monumentto his genius.


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Life & Character - Isaac Newton was born prematurely on Christmas day

1642 (4 January 1643, New Style) in Woolsthorpe, a hamlet near

Grantham in Lincolnshire. The posthumous son of an illiterate yeoman

(also named Isaac), the fatherless infant was small enough at birth to fit'into a quartpot.' When he was barely three years old Newton's

mother, Hanna (Ayscough), placed her first born with his grandmother

in order to remarry and raise a second family with Barnabas Smith, a

wealthy rector from nearby North Witham. Much has been made of

Newton's posthumous birth, his prolonged separation from his mother,and his unrivaled hatred of his stepfather. Until Hanna returned to

Woolsthorpe in 1653 after the death of her second husband, Newton

was denied his mother's attention, a possible clue to his complex

character. Newton's childhood was anything but happy, and

throughout his life he verged on emotional collapse, occasionally

falling into violent and vindictive attacks against friend and foe alike.


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Mathematics - The origin of Newton's interest in mathematics can be traced to his

undergraduate days at Cambridge. Here Newton became acquainted with a number of

contemporary works, including an edition of Descartes Gomtrie, John Wallis' Arithmetica

infinitorum, and other works by prominent mathematicians. But between 1664 and his return

to Cambridge after the plague, Newton made fundamental contributions to analytic

geometry, algebra, and calculus. Specifically, he discovered the binomial theorem, newmethods for expansion of infinite series, and his 'direct and inverse method of fluxions.' As the

term implies, fluxional calculus is a method for treating changing or flowing quantities. Hence,

a 'fluxion' represents the rate of change of a 'fluent'--a continuously changing or flowing

quantity, such as distance, area, or length. In essence, fluxions were the first words in a new

language of physics.

Scientific Achievements


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Pythagoras of Samos was an Ionian

(Greek) philosopher and founder of the

religious movement called

Pythagoreanism. He is often revered as

a great mathematician, mystic andscientist; however some have

questioned the scope of his

contributions to mathematics or natural

philosophy. We do know that

Pythagoras and his students believed

that everything was related tomathematics and that numbers were

the ultimate reality and, throughmathematics, everything could be

predicted and measured in rhythmic

patterns or cycles. The Pythagoreans

were musicians as well asmathematicians. Pythagoras wanted to

improve the music of his day, which hebelieved was not harmonious enough

and was too hectic.

01History of Mathematicians

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