Compilation of Mathematicians and Their Contributions

I. classic Mathematicians Thales of Miletus Birthdate 624 B. C. Died 547-546 B. C. Nationality Greek Title Regarded as Father of Science Contri thoions * He is credit with the showtime exercise of deductive reasoning app impositiond to geometry. * uncovering that a circle isbisectedby its diameter, that the base angles of an isosceles tri posterioral be equal and thatvertical angles ar equal. * Accredited with set upation of the Ionian trail of maths that was a centre of learning and look. * Thales theorems de boundaryinationd in Geometry . The pairs of setback angles strivinged by dickens intersecting imbibes atomic reduce 18 equal. 2. The base angles of an isosceles triangle be equal. 3. The re center of attenti angiotensin-converting enzyme of the angles in a triangle is mavin hundred eighty. 4. An angle inscribed in a semicircle is a in effect(p) angle. Pythagoras Birthdate 569 B. C. Died 475 B. C. Nationality Greek Contributions * Pythagorean Theorem. In a ripe(p) angled triangle the squ atomic deem 18 of the hypoten engage is equal to the stub of the squ bes on the classify deuce sidiethylstilbesterol. lineage A proper(ip) triangle is a triangle that contains sensation right (90) angle.The longest side of a right triangle, c entirely told tolded the hypoten drug abuse, is the side reverse the right angle. The Pythagorean Theorem is of import in maths, physics, and astronomy and has practical applications in tireveying. * dogmatic a sophisticated numerology in which odd tots de observe male and rase womanish 1 is the generator of emergences and is the arrive of reason 2 is the subdue of opinion 3 is the itemise of harmony 4 is the enactment of justice and retribution (opinion squ ard) 5 is the event of marriage (union of the ? rst male and the ? st female rounds) 6 is the number of creation 10 is the holiest of all, and was the number of the universe, because 1+2+3+4 = 10. * Discovery of incommensurate prop ortions, what we would call today blind numbers. * Made the ? rst inroads into the branch of maths which would today be called Number system. * backcloth up a secret mystical society, kn suffer as the Pythagoreans that taught maths and Physics. Anaxagoras Birthdate 500 B. C. Died 428 B. C. Nationality Greek Contributions * He was the root to explain that the moon shines payable to reflected light from the lie. Theory of minute constituents of things and his emphasis on mechanised processes in the formation of order that paved the way for the atomic surmisal. * Advocated that matter is unruffled of unnumbered elements. * Introduced the smell of nous (Greek, mind or reason) into the philosophy of declines. The concept of nous (mind), an immeasurable and unchanging substance that enters into and controls all(prenominal) living object. He regarded material substance as an in impermanent plurality of imperishable primary elements, referring all generation and disappeara nce to mixture and separation, respectively.Euclid Birthdate c. 335 B. C. E. Died c. 270 B. C. E. Nationality Greek Title Father of Geometry Contributions * promulgated a admit called the Elements serving as the main schoolbookbook for teachingmathematics(e particular(a)lygeometry) from the time of its outcome until the recently 19th or proto(prenominal) 20th century. The Elements. w messinessness of the oldest surviving fragments of EuclidsElements, found atOxyrhynchus and dated to circa AD 100. * Wrote change by reversals on office,conic sections, k presentlyledge base-wide geometry,number assumptionandrigor. In addition to theElements, at least atomic number 23 works of Euclid establish survived to the present day. They follow the same logical mental synthesis asElements, with translations and be propositions. Those are the following 1. Data contains with the nature and implications of stipulation information in nonrepresentationalal tasks the subject matter i s final stagely associate to the world-class four books of theElements. 2. On Divisions of Figures, which survives only partial t unitaryly inArabictranslation, concerns the division of geometrical figures into devil or much than equal move or into parts in grantedratios.It is similar to a terzetto century AD work byHeron of Alexandria. 3. Catoptrics, which concerns the numeric opening of mirrors, oddly the images formed in trim and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor and E F Robertson who nameTheon of Alexandriaas a more likely condition. 4. Phaenomena, a treatise onspherical astronomy, survives in Greek it is quite similar toOn the Moving SpherebyAutolycus of Pitane, who flourished nearly 310 BC. * far-famed cardinal postulates of Euclid as menti whizzd in his book Elements . Point is that which has no part. 2. Line is a breadthless length. 3. The extremities of lines are specifys. 4. A straight line lies equally with respect to the points on itself. 5. One dis define draw a straight line from whatsoever point to any point. * TheElements as well include the following five common notions 1. Things that are equal to the same thing are in any case equal to cardinal another(prenominal) (Transitive property of equality). 2. If equals are added to equals, consequently the wholes are equal. 3. If equals are subtracted from equals, then the hold onders are equal. 4.Things that coincide with one another equal one another (Reflexive Property). 5. The whole is greater than the part. Plato Birthdate 424/423 B. C. Died 348/347 B. C. Nationality Greek Contributions * He helped to distinguish amidst lightanduse mathematicsby widening the gap between arithmetical, at present callednumber systemand logistic, now calledarithmetic. * make of the academyinAthens, the setoff-year institution of higher(prenominal) learning in the westbound solid ground. It provided a comprehensive curriculum, including such subjects as astronomy, biology, mathematics, political conjecture, and philosophy. Helped to lay the introductions of western philosophyandscience. * Platonic self-coloureds Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces confluence at each vertex. in that respect are exactly five solids which meet those criteria each is named according to its number of faces. * Polyhedron Vertices Edges FacesVertex configuration 1. tetrahedron4643. 3. 3 2. cube / hexahedron81264. 4. 4 3. octahedron61283. 3. 3. 3 4. dodecahedron2030125. 5. 5 5. icosahedron1230203. 3. 3. 3. 3 AristotleBirthdate 384 B. C. Died 322 BC (aged 61 or 62) Nationality Greek Contributions * Founded the Lyceum * His biggest piece to the athletic heavens of mathematics was his phylogenesis of the think of logic, which he termed uninflectedals, as the vertexr for mathematical study. He wrote extensively on this concept in his work anterior Analytics, which was create from Lyceum lecture notes some(prenominal) hundreds of years subsequently his death. * Aristotles Physics, which contains a discussion of the infinite that he believed existed in theory only, sparked much manage in later centuries.It is believed that Aristotle may have been the premier philosopher to draw the note of hand between actual and potential infinity. When considering 2 actual and potential infinity, Aristotle states this 1. A body is defined as that which is bounded by a surface, thitherfore there provokenot be an infinite body. 2. A Number, Numbers, by translation, is countable, so there is no number called infinity. 3. Perceptible bodies exist both(prenominal)where, they have a place, so there cannot be an infinite body. But Aristotle says that we cannot say that the infinite does not exist for these reasons 1.If no infinite, magnitudes will not be cleavable into magnitudes, but magnitudes can be divisible into mag nitudes (potentially infinitely), thence an infinite in some sense exists. 2. If no infinite, number would not be infinite, but number is infinite (potentially), therefore infinity does exist in some sense. * He was the founder offormal logic, pioneered the study ofzoology, and left every prox scientist and philosopher in his debt through his contributions to the scientific mode. Erasthosthenes Birthdate 276 B. C. Died 194 B. C. Nationality Greek Contributions * Sieve of Eratosthenes Worked on primary numbers.He is remembered for his prime number sieve, the Sieve of Eratosthenes which, in modified form, is alleviate an meaning(a) tool innumber theoryresearch. Sieve of Eratosthenes- It does so by iteratively stoneing as composite (i. e. not prime) the multiples of each prime, starting with the multiples of 2. The multiples of a precondition prime are generated starting from that prime, as a taking over of numbers with the same difference, equal to that prime, between consecut ive numbers. This is the Sieves depict character from using trial division to sequentially test each view number for divisibility by each prime. Made a surprisingly undefiled measurement of the circumference of the Earth * He was the first person to use the word geography in Greek and he invented the discipline of geography as we understand it. * He invented a system oflatitudeandlongitude. * He was the first to calculate thetilt of the Earths axis( too with remarkable accuracy). * He may as well have accurately calculated thedistance from the earth to the sunand invented theleap day. * He to a fault created the firstmap of the worldincorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. Founder of scientificchronology. Favourite Mathematician Euclid paves the way for what we cognize today as euclidean Geometry that is considered as an indispensable for everyone and should be studied not only by stud ents but by everyone because of its vast applications and relevance to everyones daily life. It is Euclid who is gift with knowledge and therefore became the pillar of todays success in the field of geometry and mathematics as a whole. There were great mathematicians as there were numerous great mathematical knowledge that God wants us to know.In consideration however, there were some(prenominal) sagacious Greek mathematicians that had imparted their great contributions and therefore they deserve to be deemd. But since my task is to declare my favourite mathematician, Euclid deserves just to the highest degree of my kudos for laying down the foundation of geometry. II. Mathematicians in the Medieval Ages da Vinci of Pisa Birthdate 1170 Died 1250 Nationality Italian Contributions * Best know to the recente world for the spreading of the HindooArabic numeral system in Europe, primarily through the publication in 1202 of his Liber Abaci (Book of Calculation). Fibonacci introduc es the so-called Modus Indorum ( order of the Indians), today know as Arabic numerals. The book advocated numeration with the digits 09 and place value. The book showed the practical grandness of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. * He introduced us to the deflect we use in fractions, previous to this, the numerator has quotations around it. * The square settle down promissory note is withal a Fibonacci mode. He wrote following books that deals Mathematics teachings 1. Liber Abbaci (The Book of Calculation), 1202 (1228) 2. Practica Geometriae (The blueprint of Geometry), 1220 3. Liber Quadratorum (The Book of Square Numbers), 1225 * Fibonacci rank of numbers in which each number is the sum of the previous two numbers, starting with 0 and 1. This sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 The higher up in the sequence, the closer two consecutive Fibonacci numbers of the sequence divided by each other will shape up the gold ratio (approximately 1 1. 18 or 0. 618 1). Roger Bacon Birthdate 1214 Died 1294 Nationality English Contributions * Opus Majus contains manipulations of mathematics and optics, alchemy, and the positions and sizes of the celestial bodies. * Advocated the experimental method as the true foundation of scientific knowledge and who to a fault did some work in astronomy, chemistry, optics, and machine design. Nicole Oresme Birthdate 1323 Died July 11, 1382 Nationality french Contributions * He too certain a language of ratios, to relate urge on to force and resistance, and applied it to physical and cosmological questions. He made a careful study of musicology and employ his determinations to develop the use of irrational exponents. * archetypal to theorise that sound and light are a transfer of skill that does not displace matter. * His most principal(prenominal) contributions to mathematics are contained in Tractatus de configuratione qualitatum et motuum. * Developed the first use of military forces with waist-length exponents, calculation with irrational proportions. * He be the digression of the harmonic series, using the metre method button up taught in compaction classes today. Omar Khayyam Birhtdate 18 May 1048Died 4 December 1131 Nationality Arabian Contibutions * He realised solutions to boxlike compares using the intersection of conic sections with circles. * He is the author of one of the most important treatises on algebra written before new-fangled-day times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving tierce-dimensional comparisons by intersecting a hyperbola with a circle. * He contributed to a schedule reform. * Created important works on geometry, specifically on the theory of proportions. Omar Khayyams geometric solution to cubic equations. Binomial theorem and extraction of grow. * He may have been first to develop atomic number 91s Triangle, along with the essential Binomial Theorem which is sometimes called Al-Khayyams aspect (x+y)n = n ? xkyn-k / k (n-k). * Wrote a book entitled Explanations of the difficulties in the postulates in Euclids Elements The treatise of Khayyam can be considered as the first treatment of parallels axiom which is not based on petitio principii but on more transcendent postulate. Khayyam refutes the previous attempts by other Greek and Persian mathematicians to prove the proposition.In a sense he made the first attempt at faceting a non-Euclidean postulate as an alternative to the parallel postulate. Favorite Mathematician As distant as medieval times is concerned, people in this era were challenged with chaos, neighborly turmoil, economic issues, and numerous other disputes. Part of this era is tinted with so called Acheronian Ages that marked the history with unfavourable events. Therefore, mathematicians during this era-after they undergone the untold toils-were deserving individuals for gratitude and praises for they had supplemented the following generations with mathematical ideas that is very helpful and applicable.Leonardo Pisano or Leonardo Fibonacci caught my attention therefore he is my favourite mathematician in the medieval times. His desire to spread out the Hindu-Arabic numerals in other countries thus signifies that he is a person of generosity, with his noble will, he deserves to be III. Mathematicians in the Renaissance Period Johann Muller Regiomontanus Birthdate 6 June 1436 Died 6 July 1476 Nationality German Contributions * He completed De Triangulis omnimodus. De Triangulis (On Triangles) was one of the first textbooks presenting the accepted state of trigonometry. His work on arithmetic and algebra, Algorithmus Demonstratus, was among the first containing symbolic algebra. * De triangu lis is in five books, the first of which gives the basic definitions quantity, ratio, equality, circles, arcs, chords, and the sine intent. * The crater Regiomontanus on the Moon is named after him. Scipione del Ferro Birthdate 6 February 1465 Died 5 November 1526 Nationality Italian Contributions * Was the first to enlighten the cubic equation. * Contributions to the rationalization of fractions with denominators containing sums of cube grow. Investigated geometry problems with a compass set at a fixed angle. Niccolo Fontana Tartaglia Birthdate 1499/1500 Died 13 December 1557 Nationality Italian Contributions He produce many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs his work was later validated by Galileos studies on move bodies. He also published a treatise on retrieving sunken charges. Cardano-Tartaglia p ractice. He makes solutions to cubic equations. Formula for solving all types of cubic equations, involving first real use of composite numbers (combinations of real and imaginary numbers). Tartaglias Triangle (earlier version of Pascals Triangle) A angulate cast of numbers in which each number is equal to the sum of the two numbers immediately above it. He gives an expression for the volume of a tetrahedron Girolamo Cardano Birthdate 24 September 1501 Died 21 September 1576 Nationality Italian Contributions * He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music. Was the first mathematician to make systematic use of numbers less than zero. * He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna. * Opus novum de proportionibus he introduced the binomial coefficients and the binomial theorem. * His book about games of chance, Liber de ludo aleae (Book on Games of Chance), written in 1526, but not publish ed until 1663, contains the first systematic treatment of prospect. * He studied hypocycloids, published in de proportionibus 1570. The generating circles of these hypocycloids were later named Cardano circles or cardanic ircles and were utilise for the construction of the first high-speed printing presses. * His book, Liber de ludo aleae (Book on Games of Chance), contains the first systematic treatment of probability. * Cardanos Ring Puzzle also cognise as Chinese Rings, still manufactured today and cogitate to the Tower of Hanoi puzzle. * He introduced binomial coefficients and the binomial theorem, and introduced and solved the geometric hypocyloid problem, as well as other geometric theorems (e. g. the theorem underlying the 21 spur wheel which converts pecker to reciprocal rectilinear motion).Binomial theorem-formula for multiplying two-part expression a mathematical formula use to calculate the value of a two-part mathematical expression that is squared, cubed, or broca ded to another power or exponent, e. g. (x+y)n, without explicitly multiplying the parts themselves. Lodovico Ferrari Birthdate February 2, 1522 Died October 5, 1565 Nationality Italian Contributions * Was publicly responsible for the solution of quartic equations. * Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published.As a result, mathematicians for the next several centuries tried to find a formula for the root of equations of degree five and higher. Favorite Mathematician Indeed, this period is supplemented with great mathematician as it moved on from the opprobrious Ages and undergone a rebirth. Enumerated mathematician were all astounding with their performances and contributions. But for me, Niccolo Fontana Tartaglia is my favourite mathematician not only because of his undisputed contributions but on the way he keep himself relieve scorn of conflicts bet ween him and other mathematicians in this period. IV. Mathematicians in the 16th degree centigradeFrancois Viete Birthdate 1540 Died 23 February 1603 Nationality cut Contributions * He substantial the first infinite-product formula for ?. * Vieta is most famous for his systematic use of decimal fraction distinction and variable letters, for which he is sometimes called the Father of Modern Algebra. (Used A,E,I,O,U for unknows and consonants for parameters. ) * Worked on geometry and trigonometry, and in number theory. * Introduced the polar triangle into spherical trigonometry, and say the multiple-angle formulas for sin (nq) and cos (nq) in terms of the powers of sin(q) and cos(q). * publish Francisci Viet? universalium inspectionum ad canonem mathematicum liber singularis a book of trigonometry, in abbreviated jurisprudenceen mathematicum, where there are many formulas on the sine and cosine. It is unusual in using decimal numbers. * In 1600, numbers potestatum ad exegesim resolutioner, a work that provided the means for extracting grow and solutions of equations of degree at most 6. trick Napier Birthdate 1550 Birthplace Merchiston Tower, Edinburgh Death 4 April 1617 Contributions * Responsible for advancing the notion of the decimal fraction by introducing the use of the decimal point. His suggestion that a simple point could be utilise to eparate whole number and fractional parts of a number concisely became accepted practice throughout Great Britain. * Invention of the Napiers Bone, a crude hand calculator which could be utilize for division and root extraction, as well as multiplication. * Written Works 1. A keep an eye onming(a) Discovery of the Whole Revelation of St. John. (1593) 2. A Description of the Wonderful Canon of Logarithms. (1614) Johannes Kepler Born December 27, 1571 Died November 15, 1630 (aged 58) Nationality German Title Founder of Modern Optics Contributions * He generalized Alhazens Billiard Problem, maturation the no tion of curvature. He was first to keep an eye on that the set of Platonic regular solids was incomplete if concave solids are admitted, and first to prove that there were only 13 Archimedean solids. * He prove theorems of solid geometry later discovered on the famous palimpsest of Archimedes. * He rediscovered the Fibonacci series, applied it to botany, and noted that the ratio of Fibonacci numbers converges to the Golden Mean. * He was a key early pioneer in conglutination, and embraced the concept of continuity (which others avoided due to Zenos paradoxes) his work was a direct inspiration for Cavalieri and others. He developed mensuration methods and anticipated Fermats theorem (df(x)/dx = 0 at percentage extrema). * Keplers Wine Barrel Problem, he utilise his cardinal concretion to deduce which barrel shape would be the best bargain. * Keplers Conjecture- is a mathematical conjecture about sphere packing in trio-dimensional Euclidean blank space. It says that no arra ngement of equally sized spheres plectrum space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements.Marin Mersenne Birthdate 8 September 1588 Died 1 September 1648 Nationality French Contributions * Mersenne primes. * Introduced several innovating concepts that can be considered as the priming coat of modern reflecting telescopes 1. Instead of using an eyepiece, Mersenne introduced the revolutionary idea of a entropy mirror that would reflect the light coming from the first mirror. This allows one to concentrate on the image behind the primary mirror in which a hole is drilled at the centre to unblock the rays. 2.Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirrors telescope designs. 3. Mersenne recognized also that he could proper the spherical aberration of the telescope by using nonspherical mirrors and that in the particular case of the afocal arra ngement he could do this correction by using two parabolic mirrors. * He also performed extensive experiments to narrow the acceleration of falling objects by comparing them with the swing of pendulums, reported in his Cogitata Physico-Mathematica in 1644.He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulums swings are not isochronous as Galileo thought, but that great swings take longer than small swings. Gerard Desargues Birthdate February 21, 1591 Died September 1661 Nationality French Contributions * Founder of the theory of conic sections. Desargues offered a unified approach to the several types of conics through projection and section. * Perspective Theorem that when two triangles are in perspective the meets of chalk uping sides are collinear. * Founder of projective geometry. Desarguess theorem The theorem states that if two triangles ABC and A? B? C? , situated in three -dimensional space, are related to each other in such a way that they can be enamorn perspectively from one point (i. e. , the lines AA? , BB? , and CC? all intersect in one point), then the points of intersection of corresponding sides all lie on one line provided that no two corresponding sides are * Desargues introduced the notions of the opposite ends of a straight line being regarded as coincident, parallel lines meeting at a point of infinity and regarding a straight line as circle whose center is at infinity. Desargues most important work Brouillon projet dune atteinte aux evenemens des rencontres d? une cone avec un plan (Proposed Draft for an set about on the results of taking plane sections of a cone) was printed in 1639. In it Desargues presented innovations in projective geometry applied to the theory of conic sections. Favorite Mathematician Mathematicians in this period has its own distinct, and unique knowledge in the field of mathematics.They carriaged the more i ntricate world of mathematics, this complex world of Mathematics had at times stirred their lives, ignite some conflicts between them, unfolded their flaws and weaknesses but at the end, they build harmonious world through the building blocky of their formulas and much has benefited from it, they indeed reflected the beauty of Mathematics. They were all thin mathematicians, and no doubt in it. But I admire John Napier for giving birth to Logarithms in the world of Mathematics. V. Mathematicians in the 17th Century Rene Descartes Birthdate 31 March 1596 Died 11 February 1650Nationality French Contributions * Accredited with the institution of ordinate geometry, the standard x,y co-ordinate system as the Cartesian plane. He developed the ordain system as a device to locate points on a plane. The coordinate system includes two perpendicular lines. These lines are called axes. The vertical axis is designated as y axis while the crosswise axis is designated as the x axis. The inte rsection point of the two axes is called the origin or point zero. The position of any point on the plane can be located by locating how far perpendicularly from each axis the point lays.The position of the point in the coordinate system is specified by its two coordinates x and y. This is written as (x,y). * He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. * Descartes was also one of the key figures in the Scientific Revolution and has been described as an example of genius. * He also pioneered the standard note of hand that uses superscripts to show the powers or exponents for example, the 4 used in x4 to indicate squaring of squaring. He invented the convention of representing un cognises in equations by x, y, and z, and knows by a, b, and c. * He was first to assign a primal place for algebra in our system of knowledge, and believed that algebra was a method to automa te or motorise reasoning, particularly about abstract, unknown quantities. * Rene Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). * He developed a rule for determining the number of autocratic and veto roots in an equation.The Rule of Descartes as it is known states An equation can have as many true positive roots as it contains changes of sign, from + to or from to + and as many false negative roots as the number of times two + signs or two signs are found in succession. Bonaventura Francesco Cavalieri Birthdate 1598 Died November 30, 1647 Nationality Italian Contributions * He is known for his work on the problems of optics and motion. * Work on the precursors of infinitesimal calculus. * Introduction of logarithms to Italy. First book was Lo Specchio Ustorio, overo, Trattato delle settioni coniche, or The Burning Mirror, or a Treatise on Conic Sections. In this b ook he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and confused combinations of these mirrors. * Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635).In this work, an landing field is considered as effected by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. * Cavalieris principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. * make tables of logarithms, emphasizing their practical use in the handle of astronomy and geography.Pierre de Fermat Birthdate 1601 or 1607/8 Died 1665 Jan 12 Nationality French Contributions * Early teachings that led to infinitesimal calculus, including his proficiency of adequality. * He is recognized for his discovery of an original method of determination the great and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and his research into number theory. * He made historied contributions to analytic geometry, probability, and optics. * He is best known for Fermats depart Theorem. Fermat was the first person known to have evaluated the inviolate of general power kick the buckets. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. * He invented a factorization methodFermats factorization methodas well as the proof technique of infinite descent, which he used to prove Fermats Last Theorem for the case n = 4. * Fermat developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on. With his gift for number relations and his ability to find proofs for many of his theorems, Fermat basically created the modern theory of numbers. Blaise Pascal Birthdate 19 June 1623 Died 19 August 1662 Nationality French Contributions * Pascals Wager * Famous contribution of Pascal was his Traite du triangle arithmetique (Treatise on the Arithmetical Triangle), commonly known today as Pascals triangle, which demonstrates many mathematical properties like binomial coefficients. Pascals Triangle At the age of 16, he formulated a basic theorem of projective geometry, known today as Pascals theorem. * Pascals law (a hydrostatics principle). * He invented the robotic calculator. He built 20 of these machines (called Pascals calculator and later Pascaline) in the following ten years. * Corresponded with Pierre de Fermat on probability theory, powerfully influencing the development of modern economics an d social science. * Pascals theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).Christiaan Huygens Birthdate April 14, 1629 Died July 8, 1695 Nationality Dutch Contributions * His work include early telescopic studies elucidating the nature of the rings of Saturn and the discovery of its moon Titan. * The invention of the pendulum clock. Spring driven pendulum clock, designed by Huygens. * Discovery of the centrifugal force, the laws for collision of bodies, for his region in the development of modern calculus and his original observations on sound perception. Wrote the first book on probability theory, De ratiociniis in ludo aleae (On Reasoning in Games of Chance). * He also designed more accurate clocks than were available at the time, suitable for sea navigation. * In 1673 he published his mathematical analysis of pendulums, Horologium Oscillatorium sive de motu pendu lorum, his greatest work on horology. Isaac typicality Birthdate 4 Jan 1643 Died 31 March 1727 Nationality English Contributions * He displace the foundations for differential and integral calculus.Calculus-branch of mathematics concerned with the study of such concepts as the rate of change of one variable quantity with respect to another, the gradient of a curve at a prescribed point, the computation of the level best and minimum values of functions, and the calculation of the area bounded by curves. Evolved from algebra, arithmetic, and geometry, it is the basis of that part of mathematics called analysis. * Produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Investigated the theory of light, explained gravity and hence the motion of the planets. * He is also famed for inventing Newtonian mechanics and explicating his famous three laws of motion. * The first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations * He discovered Newtons identities, Newtons method, classified cubic plane curves (polynomials of degree three in two variables) Newtons identities, also known as the NewtonGirard formulae, give relations between two types of regular polynomials, namely between power sums and elementary symmetric polynomials.Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots * Newtons method (also known as the NewtonRaphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. Gottfried Wilhelm Von Leibniz Birthdate July 1, 1646 Died November 14, 1716 Nationality GermanContributions * Leibniz invented a mechanical calculating machine which would multiply as well as add, the mechanics of which were still being used as late as 1940. * Developed the infinitesimal calculus. * He became one of the most productive inventors in the field of mechanical calculators. * He was the first to describe a pinwheel wind collector calculator in 16856 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. * He also keen the binary number system, which is at the foundation of virtually all digital fancyrs. Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denominate any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. * Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system. * He introduced several notations used to this day, for instance the integral sign ? representing an elongated S, from the Latin word summa and the d used for differentials, from the Latin word differentia.This cleverly suggestive notation for the calculus is probably his most enduring mathematical legacy. * He was the ? rst to use the notation f(x). * The notation used today in Calculus df/dx and ? f x dx are Leibniz notation. * He also did work in discrete mathematics and the foundations of logic. Favorite Mathematician Selecting favourite mathematician from these adept persons in mathematics is a laborious task, but as I read the contributions of these Mathematicians, I found Sir Isaac Newton to be the greatest mathematician of this period.He invented the useful but difficult subject in mathematics- the calculus. I found him cooperative with different mathematician to derive useful formulas despite the fact that he is bright enough. Open-mindedness towards others opi nion is what I discerned in him. VI. Mathematicians in the 18th Century Jacob Bernoulli Birthdate 6 January 1655 Died 16 August 1705 Nationality Swiss Contributions * Founded a school for mathematics and the sciences. * Best known for the work Ars Conjectandi (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. Jacob Bernoullis first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. * Introduction of the theorem known as the law of large numbers. * By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. * Published five treatises on infinite series between 1682 and 1704. * Bernoulli equation, y = p(x)y + q(x)yn. * Jacob Bernoullis paper of 1690 is important for the history of calculus, since the term integral appears for the first time with its integration meaning. observe a genera l method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola, the logarithmic verticillated and epicycloids around 1692. * Theory of permutations and combinations the so-called Bernoulli numbers, by which he derived the exponential series. * He was the first to think about the convergence of an infinite series and prove that the series is convergent. * He was also the first to propose continuously intensify interest, which led him to investigate Johan Bernoulli Birthdate 27 July 1667Died 1 January 1748 Nationality Swiss Contributions * He was a brilliant mathematician who made important discoveries in the field of calculus. * He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth. * Discovered fundamental principles of mechanics, and the laws of optics. * He discovered the Bernoulli series and made advances in theory of navigation and ship sailing. * Johann Bernoulli proposed the brachistochrone problem, which asks what shape a wire must be for a drop-off to slide from one end to the other in the shortest contingent time, as a challenge to other mathematicians in June 1696.For this, he is regarded as one of the founders of the calculus of variations. Daniel Bernoulli Birthdate 8 February 1700 Died 17 March 1782 Nationality Swiss Contributions * He is particularly remembered for his applications of mathematics to mechanics. * His pioneering work in probability and statistics. Nicolaus Bernoulli Birthdate February 6, 1695 Died July 31, 1726 Nationality Swiss Contributions Worked mostly on curves, differential equations, and probability. He also contributed to fluid dynamics. Abraham de Moivre Birthdate 26 May 1667 Died 27 November 1754 Nationality French Contributions Produced the second textbook on probability theory, The Doctrine of Chances a method of calculating the probabilities of events in play. * Pioneered the development of analytic geometry and the theory of probability. * Gives the first statement of the formula for the normal distribution curve, the first method of finding the probability of the occurrence of an mis fellow feeling of a given size when that error is expressed in terms of the variability of the distribution as a unit, and the first identification of the probable error calculation. Additionally, he applied these theories to gambling problems and actuarial tables. In 1733 he proposed the formula for estimating a factorial as n = cnn+1/2e? n. * Published an article called Annuities upon Lives, in which he revealed the normal distribution of the mortality rate over a persons age. * De Moivres formula which he was able to prove for all positive integral values of n. * In 1722 he suggested it in the more well-known(a) form of de Moivres Formula Colin Maclaurin Birthdate February, 1698 Died 14 June 1746 Nationality Scottish Contributions * Maclaurin used Taylor series to think of maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions. Made world-shattering contributions to the gravitation attractiveness of ellipsoids. * Maclaurin discovered the EulerMaclaurin formula. He used it to sum powers of arithmetic progressions, derive Stirlings formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpsons rule as a special case. * Maclaurin contributed to the study of elliptic integrals, reducing many intractable integrals to problems of finding arcs for hyperbolas. * Maclaurin proved a rule for solving square linear systems in the cases of 2 and 3 unknowns, and discussed the case of 4 unknowns. around of his important works are Geometria Organica 1720 * De Linearum Geometricarum Proprietatibus 1720 * Treatise on Fluxions 1742 (763 pages in two volumes. The first systematic exposition of Newtons methods. ) * Treatise on Algebra 17 48 (two years after his death. ) * Account of Newtons Discoveries Incomplete upon his death and published in 1750 or 1748 (sources disagree) * Colin Maclaurin was the name used for the new Mathematics and Actuarial Mathematics and Statistics Building at Heriot-Watt University, Edinburgh. Lenard Euler Birthdate 15 April 1707 Died 18 September 1783 Nationality Swiss Contributions He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. * He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. * He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. * Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function 2 and was the first to write f(x) to denote the function f applied to the argument x. He als o introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Eulers number), the Greek letter ? for summations and the letter i to denote the imaginary unit. * The use of the Greek letter ? to denote the ratio of a circles circumference to its diameter was also popularized by Euler. * Well known in analysis for his frequent use and development of power series, the expression of functions as sums of infinitely many terms, such as * Euler introduced the use of the exponential function and logarithms in analytic proofs. He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms. * He also defined the exponential function for complex numbers, and discovered its relation to the trigonometric functions. * Elaborated the theory of higher transcenden tal functions by introducing the gamma function and introduced a new method for solving quartic equations. He also found a way to calculate integrals with complex intimidates, foreshadowing the development of modern complex analysis.He also invented the calculus of variations including its best-known result, the EulerLagrange equation. * Pioneered the use of analytic methods to solve number theory problems. * Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions and the analytic theory of continued fractions. For example, he proved the infinitude of primes using the divergence of the harmonic series, and he used analytic methods to gain some understanding of the way prime numbers are distributed. Eulers work in this area led to the development of the prime number theorem. He proved that the sum of the reciprocals of the primes diverges. In doing so, he discovered the connection between the Riemann zeta function and the prime numbers this is known as the Euler product formula for the Riemann zeta function. * He also invented the totient function ? (n) which is the number of positive integers less than or equal to the integer n that are coprime to n. * Euler also conjectured the law of quadratic reciprocity. The concept is regarded as a fundamental theorem of number theory, and his ideas paved the way for the work of Carl Friedrich Gauss. * Discovered the formula V ?E + F = 2 relating the number of vertices, edges, and faces of a convex polyhedron. * He made great strides in improving the numerical approximation of integrals, inventing what are now known as the Euler approximations. Jean Le Rond De Alembert Birthdate 16 November 1717 Died 29 October 1783 Nationality French Contributions * DAlemberts formula for obtaining solutions to the wave equation is named after him. * In 1743 he published his most famous work, Traite de dynamique, in which he developed his own laws of motion. * He created his ratio test, a test to see if a series converges. The DAlembert operator, which first arose in DAlemberts analysis of vibrating strings, plays an important role in modern theoretical physics. * He made several contributions to mathematics, including a suggestion for a theory of limits. * He was one of the first to appreciate the importance of functions, and defined the derivative of a function as the limit of a quotient of increments. Joseph Louise Lagrange Birthdate 25 January 1736 Died 10 April 1813 Nationality Italian French Contributions * Published the Mecanique Analytique which is considered to be his monumental work in the pure maths. His most prominent forge was his contribution to the the metric system and his addition of a decimal base. * Some refer to Lagrange as the founder of the Metric System. * He was responsible for developing the groundwork for an alternate method of writing Newtons Equations of Motion. This is referred to as Lagrangian Mechanics. * In 1772, he described the Langrangian points, the points in the plane of two objects in orbit around their common center of gravity at which the combined gravitational forces are zero, and where a third particle of negligible mass can remain at rest. He made significant contributions to all fields of analysis, number theory, and classical and celestial mechanics. * Was one of the creators of the calculus of variations, deriving the EulerLagrange equations for extrema of functionals. * He also extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. * Lagrange invented the method of solving differential equations known as variation of parameters, applied differential calculus to the theory of probabilities and attained notable work on the solution of equations. * He proved that every natural number is a sum of four squares. Several of his early papers also deal with questions of number theory. 1. Lagrange (17661769) was the first to prove that Pells equation has a no ntrivial solution in the integers for any non-square natural number n. 7 2. He proved the theorem, stated by Bachet without justification, that every positive integer is the sum of four squares, 1770. 3. He proved Wilsons theorem that n is a prime if and only if (n ? 1) + 1 is always a multiple of n, 1771. 4. His papers of 1773, 1775, and 1777 gave demonstrations of several results enunciated by Fermat, and not previously proved. 5.His Recherches dArithmetique of 1775 developed a general theory of binary quadratic forms to handle the general problem of when an integer is representable by the form. Gaspard Monge Birthdate May 9, 1746 Died July 28, 1818 Nationality French Contributions * artificer of descriptive geometry, the mathematical basis on which technical drawing is based. * Published the following books in mathematics 1. The Art of Manufacturing Cannon (1793)3 2. Geometrie descriptive. Lecons donnees aux ecoles normales (Descriptive Geometry) a recording of Monges lectures. (1799) Pierre Simon Laplace Birthdate 23 March 1749Died 5 March 1827 Nationality French Contributions * theorise Laplaces equation, and pioneered the Laplace transform which appears in many branches of mathematical physics. * Laplacian differential operator, widely used in mathematics, is also named after him. * He restated and developed the nebular hypothesis of the origin of the solar system * Was one of the first scientists to postulate the cosmos of black holes and the notion of gravitational collapse. * Laplace made the non-trivial extension of the result to three dimensions to yield a more general set of functions, the spherical harmonics or Laplace coefficients. Issued his Theorie analytique des probabilites in which he move down many fundamental results in statistics. * Laplaces most important work was his Celestial Mechanics published in 5 volumes between 1798-1827. In it he sought-after(a) to give a complete mathematical description of the solar system. * In Inductive probability, Laplace set out a mathematical system of inducive reasoning based on probability, which we would today recognise as Bayesian. He begins the text with a series of principles of probability, the first six being 1.Probability is the ratio of the favored events to the total possible events. 2. The first principle assumes equal probabilities for all events. When this is not true, we must first determine the probabilities of each event. Then, the probability is the sum of the probabilities of all possible favored events. 3. For independent events, the probability of the occurrence of all is the probability of each multiplied together. 4. For events not independent, the probability of event B following event A (or event A causing B) is the probability of A multiplied by the probability that A and B both occur. 5.The probability that A will occur, given that B has occurred, is the probability of A and B occurring divided by the probability of B. 6. Three corollaries are given f or the sixth principle, which amount to Bayesian probability. Where event Ai ? A1, A2, An exhausts the list of possible causes for event B, Pr(B) = Pr(A1, A2, An). Then * Amongst the other discoveries of Laplace in pure and applied mathematics are 1. Discussion, contemporaneously with Alexandre-Theophile Vandermonde, of the general theory of determinants, (1772) 2. Proof that every equation of an even degree must have at least one real quadratic factor 3.Solution of the linear partial differential equation of the second order 4. He was the first to consider the difficult problems multiform in equations of mixed differences, and to prove that the solution of an equation in finite differences of the first degree and the second order might always be obtained in the form of a continued fraction and 5. In his theory of probabilities 6. Evaluation of several common definite integrals and 7. General proof of the Lagrange turnaround time theorem. Adrian Marie Legendere Birthdate 18 Sept ember 1752 Died 10 January 1833 Nationality French Contributions Well-known and important concepts such as the Legendre polynomials. * He developed the least squares method, which has broad application in linear regression, signal processing, statistics, and curve fitting this was published in 1806. * He made substantial contributions to statistics, number theory, abstract algebra, and mathematical analysis. * In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss in connection to this, the Legendre symbol is named after him. * He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. Best known as the author of Elements de geometrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. * He introduced what are now known as Legendre functions, solutions to Legendres differential equation, used to determine, via power series, the attraction of an e llipsoid at any exterior point. * Published books 1. Elements de geometrie, textbook 1794 2. Essai sur la Theorie des Nombres 1798 3. Nouvelles Methodes pour la Determination des Orbites des Cometes, 1806 4. Exercices de Calcul Integral, book in three volumes 1811, 1817, and 1819 5.Traite des Fonctions Elliptiques, book in three volumes 1825, 1826, and 1830 Simon Dennis Poison Birthdate 21 June 1781 Died 25 April 1840 Nationality French Contributions * He published two memoirs, one on Etienne Bezouts method of elimination, the other on the number of integrals of a finite difference equation. * Poissons well-known correction of Laplaces second order partial differential equation for potential today named after him Poissons equation or the potential theory equation, was first published in the Bulletin de la societe philomatique (1813). Poissons equation for the divergence of the gradient of a scalar field, ? in 3-dimensional space Charles Babbage Birthdate 26 December 1791 Death 18 Oc tober 1871 Nationality English Contributions * Mechanical design who originated the concept of a programmable computing machine. * Credited with inventing the first mechanical computer that in conclusion led to more complex designs. * He invented the Difference Engine that could compute simple calculations, like multiplication or addition, but its most important trait was its ability create tables of the results of up to seven-degree polynomial functions. Invented the Analytical Engine, and it was the first machine ever designed with the idea of programming a computer that could understand commands and could be programmed much like a modern-day computer. * He produced a Table of logarithms of the natural numbers from 1 to 108000 which was a standard reference from 1827 through the end of the century. Favorite Mathematician Noticeably, Leonard Euler made a mark in the field of Mathematics as he contributed several concepts and formulas that encompasses many areas of Mathematics-Ge ometry, Calculus, Trigonometry and etc.He deserves to be praised for doing such great things in Mathematics, indeed, his work laid foundation to make the lives of the following generation sublime, ergo, He is my favourite mathematician. VII. Mathematicians in the 19th Century Carl Friedrich Gauss Birthdate 30 April 1777 Died 23 February 1855 Nationality German Contributions * He became the first to prove the quadratic reciprocity law. * Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae (Latin, Arithmetical Investigations), which, among things, introduced the symbol ? or congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon (17-sided polygon) can be constructed with straightedge and compass. * He developed a method of measuring the horizontal fanaticism of the magnetised field which was in use well into the second fractional of the 20th century, and worked out the mathematical theory for separating the inner and outer (magnetospheric) sources of Earths magnetic field.Agustin Cauchy Birthdate 21 August 1789 Died 23 May 1857 Nationality French Contributions * His most notable research was in the theory of residues, the question of convergence, differential equations, theory of functions, the legitimate use of imaginary numbers, operations with determinants, the theory of equations, the theory of probability, and the applications of mathematics to physics. * His publications introduced new standards of rigor in calculus from which grew the modern field of analysis.In Cours danalyse de lEcole Polytechnique (1821), by developing the concepts of limits and continuity, he provided the foundation for calculus essentially as it is today. * He introduced the epsilon-delta definition for lim its (epsilon for error and delta for difference). * He transformed the theory of complex functions by discovering integral theorems and introducing the calculus of residues. * Cauchy founded the modern theory of elasticity by applying the notion of pressure on a plane, and assuming that this pressure was no longer perpendicular to the plane upon which it acts in an elastic body.In this way, he introduced the concept of stress into the theory of elasticity. * He also examined the possible deformations of an elastic body and introduced the notion of strain. * One of the most prolific mathematicians of all time, he produced 789 mathematics papers, including 500 after the age of fifty. * He had sixteen concepts and theorems named for him, including the Cauchy integral theorem, the Cauchy-Schwartz inequality, Cauchy sequence and Cauchy-Riemann equations. He defined continuity in terms of infinitesimals and gave several important theorems in complex analysis and initiated the study of per mutation groups in abstract algebra. * He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner. * He was the first to define complex numbers as pairs of real numbers. * Most famous for his single-handed development of complex function theory.The first pivotal theorem proved by Cauchy, now known as Cauchys integral theorem, was the following where f(z) is a complex-valued function holomorphic on and within the non-self-intersecting closed curve C (contour) lying in the complex plane. * He was the first to prove Taylors theorem rigorously. * His greatest contributions to mathematical science are enveloped in the rigorous methods which he introduced these are mainly embodied in his three great treatises 1. Cours danalyse de lEcole royale polytechnique (1821) 2. Le Calcul infinitesimal (1823) 3.Lecons sur les applications de calcul infinitesimal La geometrie (18261828) Nicolai Ivanovich Lobachevsky Birthdate December 1, 1792 Died Feb ruary 24, 1856 Nationality Russian Contributions * Lobachevskys great contribution to the development of modern mathematics begins with the fifth postulate (sometimes referred to as axiom XI) in Euclids Elements. A modern version of this postulate reads Through a point lying outback(a) a given line only one line can be drawn parallel to the given line. * Lobachevskys geometry found application in the theory of complex numbers, the theory of vectors, and the theory of relativity. Lobachevskiis deductions produced a geometry, which he called imaginary, that was internally consistent and harmonious yet different from the traditional one of Euclid. In 1826, he presented the paper Brief Exposition of the Principles of Geometry with Vigorous Proofs of the Theorem of Parallels. He refined his imaginary geometry in subsequent works, dating from 1835 to 1855, the last being Pangeometry. * He was well respected in the work he developed with the theory of infinite series especially trigonome tric series, integral calculus, and probability. In 1834 he found a method for approximating the roots of an algebraic equation. * Lobachevsky also gave the definition of a function as a correspondence between two sets of real numbers. Johann Peter Gustav Le Jeune Dirichlet Birthdate 13 February 1805 Died 5 May 1859 Nationality German Contributions * German mathematician with deep contributions to number theory (including creating the field of analytic number theory) and to the theory of Fourier series and other topics in mathematical analysis. * He is credited with being one of the first mathematicians to give the modern formal definition of a function. Published important contributions to the biquadratic reciprocity law. * In 1837 he published Dirichlets theorem on arithmetic progressions, using mathematical analysis concepts to tackle an algebraic problem and thus creating the branch of analytic number theory. * He introduced the Dirichlet characters and L-functions. * In a coupl e of papers in 1838 and 1839 he proved the first class number formula, for quadratic forms. * Based on his research of the structure of the unit group of quadratic fields, he proved the Dirichlet unit theorem, a fundamental result in algebraic number theory. He first used the pigeonhole principle, a basic counting argument, in the proof of a theorem in diophantine approximation, later named after him Dirichlets approximation theorem. * In 1826, Dirichlet proved that in any arithmetic progression with first term coprime to the difference there are infinitely many primes. * Developed significant theorems in the areas of elliptic functions and applied analytic techniques to mathematical theory that resulted in the fundamental development of number theory. * His lectures on the equilibrium of systems and potential theory led to what is known as the Dirichlet problem.It involves finding solutions to differential equations for a given set of values of the boundary points of the region on which the equations are defined. The problem is also known as the first boundary-value problem of potential theorem. Evariste Galois Birthdate 25 October 1811 Death 31 May 1832 Nationality French Contributions * His work laid the foundations for Galois Theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. * He was the first to use the word group (French groupe) as a technical term in mathematics to represent a group of permutations. Galois published three papers, one of which laid the foundations for Galois Theory. The second one was about the numerical resolution of equations (root finding in modern terminology). The third was an important one in number theory, in which the concept of a finite field was first articulated. * Galois mathematical contributions were published in full in 1843 when Liouville reviewed his manuscript and declared it sound. It was at last published in the OctoberNovember 1846 issue of the Journal de Mathem atiques Pures et Appliquees. 16 The most famous contribution of this manuscript was a novel proof that there is no quintic formula that is, that fifth and higher degree equations are not generally solvable by radicals. * He also introduced the concept of a finite field (also known as a Galois field in his honor), in essentially the same form as it is understood today. * One of the founders of the branch of algebra known as group theory. He developed the concept that is today known as a normal subgroup. * Galois most significant contribution to mathematics by far is his development of Galois Theory.He realized that the algebraic solution to a polynomial equation is related to the structure of a group of permutations associated with the roots of the polynomial, the Galois group of the polynomial. He found that an equation could be solved in radicals if one can find a series of subgroups of its Galois group, each one normal in its successor with abelian quotient, or its Galois group i s solvable. This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois orig