Galileo Galilei (1564-1642)
'Contributor' Names, with Birth and Death Dates
names in order by birth date
with brief notes on their contributions
Rene Descartes (1596-1650)
! Note !
The bottom part of this page is 'unfinished'.
Links were being added and tested in 2013-2017.
To be continued.
Biographical notes are to be added, and
mathematician names and dates may be added.
Links to start of mathematician birthdays below :
2000 BCE 1000 BCE 0 BCE 500
1000 1200 1400 1600
1700 1800 1900
This page presents a 'timeline' of the History of Mathematics --- containing mathematician names and their contributions --- along with their birth and death dates --- with 'external' links to more information on each mathematician.
We start from the oldest contributors at the top of the page to the more recent contributors at the bottom of the page.
The names are ordered according to their birth year (or an estimate thereof). This is to keep together the mathematicians who received their early training at about the same time (usually in their teens).
Hence they were likely to be contemporaries who would cooperate and/or compete with each other. And they were likely to be building on a common set of work and teaching --- in particular, the teaching and work of others born a decade or two before them.
I started this list (in 2011) based on a nice little book titled 'The Little Book of Mathematical Principles, Theories, and Things' by Dr. Bob Solomon --- published 2008 by Metro Books, New York.
That book traces many of the outstanding mathematical contributions throughout human history --- and provides birth and death dates, along with brief biographical notes, for many of the contributors to the body mathematical.
In June-July 2013, I added many names of contributors to mathematics based on the little, condensed book 'Classical Mathematics: A Concise History of Mathematics in the 17th and 18th Centuries', by Joseph Ehrenfried Hofmann. Published in 1959 by Philosophical Library Inc. Published again in 2003 by Barnes & Noble books.
For each of the mathematicians, I have added a web link for further information on the individual and his/her discoveries. Most of the links are to the Wikipedia web site. When Wikipedia does not have a page for the mathematician, I may provide a link to a 'home page' of the mathematician --- or a link to a web search on that mathematician's name.
If the list on this page does not satisfy, you may wish to try some of the lists of mathematicians at Wikipedia. In particular, here is a page for mathematicians by nationality, and here is a page for mathematicians by century.
This Should I become a mathematician? thread at physicsforums.com provides many interesting source books on mathematics and mathematicians.
For a compact, chronological list of mathematicians names and birth-death dates, see the list of David Joyce at Clark University. (Like most pages in userid directories at universities, this page is likely to go dead/missing within a decade. It was last updated in 1995.)
SEARCHING THIS PAGE :
If you are looking for some particular information, you can use the text search function of your web browser.
For example, if you are looking for information on 'polygons' --- or on specific polygons such as 'triangles', 'quadrilaterals', 'pentagons', or 'hexagons', enter a keyword such as 'polygon', 'triangle', 'tria', 'quad', 'pentagon', 'pent', 'hexagon', or 'hex' in the text search entry field of your web browser.
Some other keywords to try: 'perspective', 'projection', 'differential', 'infinit', 'surface', 'algebra', 'geometry', 'polyhedron', 'series', 'product', 'sum', ...
THE WONDERMENT OF IT ALL :
Mathematics offers many occasions for wonderment at the logical and geometric beauties of that subject matter --- and wonderment at some of the nobler accomplishments that are possible from the minds of humans.
The development of mathematical knowledge over the centuries is an amazing human achievement. It is one of the 'purer' pursuits of man.
Mathematics, like art, provides galleries of wondrous creations (or discoveries) --- galleries based on subjects such as 2D geometry, 3D geometry, number theory, complex numbers, quaternions (complex numbers on steroids), theory of solving equations and the related group theory, permutations and combinations, probability theory, graph theory, set theory, combinatorics, game theory, topology, computing/automata theory, code breaking and secure encoding, provability, paradoxes, etc. etc.
Enjoy the way mathematical history has unfolded!
START of TIMELINE :
Durer marking points for a perspective drawing of a lute
Throughout his lifetime, Maurolico made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy. He edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus. He also composed his own unique treatises on mathematics.
Niccolo Tartaglia (1500 to 1557) was an Italian mathematician, engineer (designing fortifications), a surveyor, and a bookkeeper from the then Republic of Venice. He provided an algebraic solution to cubic equations of the form x^3 + b x^2 = d. Tartaglia is also known for having given an expression (Tartaglia's formula) for the volume of a tetrahedron (including any irregular tetrahedra). This is a generalization of Heron's formula for the area of a triangle.
Gerolamo Cardano (1501 to 1576) was an Italian Renaissance mathematician, physician, astrologer and gambler. He wrote more than 200 works on medicine, mathematics, physics, philosophy, religion, and music. His gambling led him to formulate elementary rules in probability, making him one of the founders of the field. He was a teacher of Lodovico Ferrari (see below).
Pedro Nunes (1502 to 1578) was a Portuguese mathematician, cosmographer, and professor. Nunes, considered to be one of the greatest mathematicians of his time, is best known for his contributions in the technical field of navigation, which was crucial to the Portuguese period of discoveries. He was the first to understand why a ship maintaining a steady course would not travel along a great circle, the shortest path between two points on Earth, but would instead follow a spiral course, called a loxodrome. The later invention of logarithms allowed Leibniz to establish algebraic equations for the loxodrome. In his 'Treaty defending the sea chart', Nunes argued that a nautical chart should have its parallels and meridians shown as straight lines. Yet he was unsure how to solve the problems that this caused: a situation that lasted until Mercator developed the projection bearing his name. The Mercator Projection is the system which is still used. Nunes also solved the problem of finding the day with the shortest twilight duration, for any given position, and its duration. This problem per se is not greatly important, yet it shows the geometric genius of Nunes as it was a problem which was independently tackled by Johann and Jakob Bernoulli more than a century later with less success. They could find a solution to the problem of the shortest day, but failed to determine its duration, possibly because they got lost in the details of differential calculus which, at that time, had only recently been developed. The achievement also shows that Nunes was a pioneer in solving maxima and minima problems, which became a common requirement only in the next century using differential calculus.
Gemma Frisius (1508 to 1555) was a physician, mathematician, cartographer, philosopher, and instrument maker. He created important globes, improved the mathematical instruments of his day and applied mathematics in new ways to surveying and navigation. In 1533, he described for the first time the method of triangulation still used today in surveying. Twenty years later, he was the first to describe how an accurate clock could be used to determine longitude. His students included Gerardus Mercator (who became his collaborator), Johannes Stadius, John Dee, Andreas Vesalius and Rembert Dodoens.
Gerhardus Mercator (1512 to 1594) was a 'Belgian/German' cartographer, philosopher and mathematician. He is best known for his work in cartography, in particular the world map of 1569 based on a new projection which represented sailing courses of constant bearing as straight lines. He was the first to use the term 'Atlas' for a collection of maps.
Georg Joachim Rhaeticus (1514 to 1576) was a mathematician, cartographer, navigational-instrument maker, medical practitioner, and teacher from the Austrian area. He is perhaps best known for his trigonometric tables and as Nicolaus Copernicus's sole pupil. He facilitated the publication of Copernicus's 'De revolutionibus orbium coelestium' ('On the Revolutions of the Heavenly Spheres'). Rheticus produced the first publication of six-function trigonometric tables (although the word trigonometry was not yet coined). A student, Valentin Otto, oversaw the hand computation of approximately 100,000 ratios to at least ten decimal places. When completed in 1596, the volume, 'Opus palatinum de triangulus', filled nearly 1,500 pages. Its tables were accurate enough to be used in astronomical computation into the early twentieth century.
Peter_Ramus (or Pierre de la Ramée) (1515 to 1572) was an influential French humanist, logician, and educational reformer. A Protestant convert, he was killed during the St. Bartholomew's Day Massacre. He was also known as a mathematician, a student of Johannes Sturm. He had students of his own. He corresponded with John Dee on mathematics, and at one point recommended to Elizabeth I that she appoint Dee to a university chair. His emphasis on technological applications and engineering mathematics was coupled to an appeal to nationalism (France was well behind Italy, and needed to catch up with Germany).
Lodovico Ferrari (1522 to 1565) was an Italian mathematician. 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. (Ferrari died of white arsenic poisoning, allegedly murdered by his greedy sister. Another interesting death.)
Abraham Ortelius (1527 to 1598) was a Flemish cartographer and geographer, generally recognized as the creator of the first modern atlas, the 'Theatrum Orbis Terrarum' ('Theatre of the World'). He is also believed to be the first person to imagine that the continents were joined together before drifting to their present positions.
Rafael Bombelli (1530? to 1573) was an Italian mathematician. Born in Bologna, he is a central figure in the understanding of imaginary numbers (a name used later). Bombelli had the foresight to see that imaginary numbers were crucial and necessary to solving quartic and cubic equations. Bombelli explained arithmetic with complex numbers (a name used later). He was careful to point out that real parts add to real parts, and imaginary parts add to imaginary parts. Bombelli felt that none of the works on algebra by the leading mathematicians of his day provided a careful and thorough exposition of the subject. Instead of another convoluted treatise that only mathematicians could comprehend, Rafael decided to write a book on algebra that could be understood by anyone. His text would be self-contained and easily read by those without higher education. The book that he wrote in 1572, was entitled 'L'Algebra'. Another contribution: Bombelli used a method related to continued fractions to calculate square roots.
Cornelius Gemma (1535 to 1577?) was a physician, astronomer and astrologer, and the oldest son of cartographer and instrument-maker Gemma Frisius (see above). As an astronomer, Gemma is significant for his observations of a lunar eclipse in 1569 and of the 1572 supernova appearing in Cassiopeia. His predictions for 1561 provided detailed information on every lunar phase, and most planetary aspects and phases of fixed stars in relation to the sun, with a thoroughness that surpassed the predictions of his contemporaries. In his medical writings, in 1552, he published the first illustration of a human tapeworm. He remained committed to astrologic medicine, however, and believed that astral conjunctions generated disease. Gemma died around 1578 in an epidemic of the plague, to which a third of the population at Leuven also succumbed. He was only in his mid-forties.
Clavius (1538 to 1612) was a German Jesuit mathematician and astronomer who modified the proposal of the modern Gregorian calendar after the death of its primary author, Luigi Lilio. His math works included a 'Commentary on Euclid' (1574), 'Geometrica Practica' (1604), and 'Algebra' (1608). His mathematical works (in 5 volumes) are available online.
Francois Viete (Latin: Franciscus Vieta) (1540 to 1603) was a French mathematician whose work in algebraic equations was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He is also known for discovering the first infinite product in the history of mathematics --- a product which was is equal to pi.
Ludolf van Ceulen (1540 to 1610) was a German-Dutch mathematician who taught fencing and mathematics. Ludolph spent a major part of his life calculating the numerical value of the mathematical constant pi, using essentially the same methods as those employed by Archimedes some seventeen hundred years earlier. He published a 20-decimal value in 1596, later expanding this to 35 decimals.
Tycho Brahe (1546 to 1601) was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations. Tycho was well known in his lifetime as an astronomer and alchemist. He refuted the Aristotelian belief in an unchanging celestial realm. His precise measurements indicated that "new stars," (stellae novae, now known as supernovae) lacked the parallax expected in sub-lunar phenomena, and were therefore not "atmospheric" tailless comets as previously believed, but were above the atmosphere and moon. Using similar measurements he showed that comets were also not atmospheric phenomena, as previously thought. But he did not believe the earth could orbit the sun, because he could not detect any parallax effect in observing the stars. He was the last of the major naked eye astronomers, working without telescopes for his observations.
Tycho worked to combine the geo-centric Copernican system with the helio-centric Ptolemaic system into his own model of the universe. In his "geo-helio-centric" system, the sun, moon, and stars circle a central Earth, while the five planets orbit the Sun. Although Tycho's planetary model was discredited within the next 100 to 150 years, his astronomical observations were an essential contribution to the scientific revolution.
John Napier (1550 to 1617) was a Scottish landowner, mathematician, physicist, and astronomer. He used logarithms (exponents) to reduce multiplication and division to addition and subtraction. The process of multiplying two numbers:
Jobst Burgi (1552 to 1632) was a Swiss clockmaker, a maker of astronomical instruments, and a mathematician. Among his major inventions were the cross-beat escapement, and the remontoire, two mechanisms which improved the accuracy of mechanical clocks of the time by orders of magnitude. This allowed clocks to be used, for the first time, as scientific instruments, with enough accuracy to time the passing of stars (and other heavenly bodies) in the crosshairs of telescopes to start accurately charting stellar positions. Besides clocks, he also made mechanized celestial globes, and he made sextants for Kepler (see below). He invented logarithms independently of John Napier, since his method is distinct from Napier's. There is evidence that Bürgi arrived at his invention as early as 1588, six years before Napier began work on the same idea. By delaying the publication of his work to 1620, Bürgi lost his claim for priority in historic discovery. Bürgi was also a major contributor to prosthaphaeresis, a technique for computing products quickly using trigonometric identities, which predated logarithms.
Luca Valerio (1553 to 1618) was an Italian mathematician. He developed ways to find volumes and centers of gravity of solid bodies using the methods of Archimedes. He corresponded with Galileo Galilei and was a member of the Accademia dei Lincei.
Edward Wright (1558 to 1615) was an English mathematician and cartographer noted for his book 'Certaine Errors in Navigation' (1599), which for the first time explained the mathematical basis of the Mercator projection, and set out a reference table giving the linear scale multiplication factor as a function of latitude, calculated for each minute of arc up to a latitude of 75°. This was in fact a table of values of the integral of the secant function, and was the essential step needed to make practical both the making and the navigational use of Mercator charts. (Mercator had not explained his method.)
A skilled designer of mathematical instruments, Wright made models of an astrolabe and a pantograph, and a type of armillary sphere. In the 1610 edition of 'Certaine Errors', he described inventions such as the "sea-ring" that enabled mariners to determine the magnetic variation of the compass, the sun's altitude and the time of day in any place if the latitude was known; and a device for finding latitude when one was not on the meridian using the height of the pole star.
Wright translated John Napier's pioneering 1614 work which introduced the idea of logarithms from Latin into English. Wright's work influenced, among other persons, Dutch astronomer and mathematician Willebrord Snellius; Adriaan Metius, the geometer and astronomer from Holland; and the English mathematician Richard Norwood, who calculated the length of a degree on a great circle of the earth (367,196 feet ; 111,921 m) using a method proposed by Wright. John Collins, in "Navigation by the Mariners Plain Scale New Plain'd" (1659), stated that Mercator's chart ought "more properly to be called Wright's chart".
Thomas Harriot (1560 to 1621) was an English astronomer, mathematician, ethnographer, and translator. After his graduation from Oxford in 1580, Harriot was first hired by Sir Walter Raleigh as a mathematics tutor. He used his knowledge of astronomy/astrology to provide navigational expertise, help design Raleigh's ships, and serve as his accountant. Prior to his expedition to the Americas with Raleigh (to Roanoke Island, 1585), Harriot wrote a treatise on navigation. In addition, he made efforts to communicate with Manteo and Wanchese, two Native Americans who had been brought to England. Harriot deciphered a phonetic alphabet to transcribe their Carolina Algonquian language.
As a scientific adviser during the voyage, Harriot was asked by Raleigh to find the most efficient way to stack cannon balls on the deck of the ship. His ensuing theory about the close-packing of spheres shows a striking resemblance to atomism and modern atomic theory, which he was later accused of believing. His correspondence about optics with Johannes Kepler, in which he described some of his ideas on sphere-stacking, later influenced Kepler's conjecture on 'sphere-packing'.
Halley's Comet in 1607 turned Harriot's attention towards astronomy. In early 1609 he bought a "Dutch trunke" (telescope), invented in 1608, and his observations were amongst the first uses of a telescope for astronomy. Harriot is now credited as the first astronomer to draw an astronomical object after viewing it through a telescope. He drew a map of the Moon on July 26, 1609, preceding Galileo by several months. The observatory in the campus of the College of William and Mary (Williamsburg, Virginia) is named in Harriot's honour.
Harriot apparently died of a cancer that started on his lip. Harriot's accomplishments remain relatively obscure because he did not publish any of his results and also because many of his manuscripts have been lost. Those that survive are sheltered in the British Museum and in the archives of the Percy family at Petworth House (Sussex) and Alnwick Castle (Northumberland).
Thomas Fincke (1561 to 1646) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years. His lasting achievement is found in his book 'Geometria rotundi' (1583), in which he introduced the modern names of the trigonometric functions tangent and secant.
Adriaan_van_Roomen (1561 to 1615) was a Flemish mathematician. He met Kepler (see below), and discussed with François Viète two questions about equations and tangencies. He then spent some time in Italy, particularly with Clavius in Rome in 1585. After 1610 he tutored mathematics in Poland. He worked in algebra, trigonometry and geometry; and on the decimal expansion of pi.
Henry Briggs (1561 to 1630) was an English mathematician notable for changing the original logarithms invented by John Napier into common (base 10) logarithms. He published Napier's logarithms as simplified tables and helped them gain acceptance among the scientific and academic communities.
Bartholomaeus Pitiscus (1561 to 1613) was a 16th-century German trigonometrist, astronomer and theologian who first coined the word Trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619). Pitiscus edited 'Thesaurus mathematicus' (1613) in which he improved the trigonometric tables of Georg Joachim Rheticus.
Galileo Galilei (1564 to 1642) was an Italian physicist, mathematician, and astronomer. He provided rules for how a body falls under gravity. For example: If a body is dropped from rest, the distance it falls varies with the square of the time. Other discoveries by Galileo :
Also Galileo was a leading supporter of Copernicus's Sun-centered system --- which led to his spending his last years under house arrest due to the influence of the Catholic Church.
Johannes Kepler (1571 to 1630) was a German mathematician, astronomer and astrologer. Using copious data on planetary movements, he provided three laws about the motion of planets. The first and most revolutionary: Planets travel in ellipses rather than circles. Isaac Newton was later able to deduce the 3 Kepler laws based on his laws of motion and of gravity.
Also, Kepler showed that the square, triangle and hexagon are the only regular polygons that can be used to cover a plane without leaving any gaps. This is known as a 'tesselation' or 'tiling' of the plane.
William Oughtred (1574 to 1660) was an English mathematician. After John Napier invented logarithms, and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, it was Oughtred who first used two such scales sliding by one another to perform direct multiplication and division; and he is credited as the inventor of the slide rule in 1622. Gunter required the use of a pair of dividers, to lay off distances on his rule; Oughtred made the step of sliding two rules past each other to achieve the same ends. Oughtred also introduced the "×" symbol for multiplication as well as the abbreviations "sin" and "cos" for the sine and cosine functions.
Oughtred published 'Clavis Mathematicae' (The Key to Mathematics) in 1631. It became a classic, reprinted in several editions, and used by Wallis and Isaac Newton (see below) amongst others. It was not ambitious in scope, but aimed to represent current knowledge of algebra concisely. It argued for a less verbose style of mathematics, with a greater dependence on symbols.
Mathurin Jousse (ca. 1575? to 1645) was a French inventor and a technician in iron works. He was also said to be an "engineer and architect of the town of de La Flèche". It is said that he carried out several repair/construction jobs of, large and small, for the town and the Jesuit college there, such as repair of the large clock on the Saint-Thomas bell tower. Jousse was curious about science and techniques. He possessed scientific instruments, some he made himself, and a rich library in which there were many books of arithmetic, geometry and astronomy. His treatise "Secret d'architecture", entirely devoted to stereotomy, appeared in La Flèche in 1642. It is said that he knew Francois Derand (see below), a student at the Jesuit college in La Fleche who also wrote a text on stereotomy.
Johann Faulhaber (1580 to 1635) was a German mathematician. Born in Ulm, Faulhaber trained as a weaver and later took the role of a surveyor of the city of Ulm. He collaborated with Johannes Kepler and Ludolph van Ceulen (see above). Besides his work on the fortifications of cities (notably Basel and Frankfurt), Faulhaber built water wheels in his home town and geometrical instruments for the military. Faulhaber supervised the first publication of Henry Briggs's logarithms in Germany. Faulhaber's major math contribution involved calculating the sums of powers of integers. Jacob Bernoulli makes references to Faulhaber in his 'Ars Conjectandi'. Faulhaber made a major impression on Descartes and influenced his thinking. In 1631, Faulhaber published 'Academia Algebra'.
Edmund Gunter (1580 to 1626) was an English mathematician, of Welsh descent. In 1619, Gunter was appointed professor of astronomy in Gresham College, London. This post he held till his death. In 1620, he published his 'Canon triangulorum'. With Gunter's name are associated several useful inventions, descriptions of which are given in his treatises on the Sector, Cross-staff, Bow, Quadrant and other instruments. In 1624, Gunter published a collection of his mathematical works. It was entitled 'The description and use of sector, the cross-staffe, and other instruments for such as are studious of mathematical practise'. It was a manual not for cloistered university fellows but for sailors and surveyors in real world. It was written, and published, in English not Latin.
Willebrord Snellius van Roijen 'Snell' (1581 to 1626) was a Dutch astronomer and mathematician. In the west, especially the English speaking countries, his name has been attached to the law of refraction of light for several centuries, but it is now known that this law was first discovered by Ibn Sahl in 984. The same law was also investigated by Ptolemy and in the Middle Ages by Witelo, but due to lack of adequate mathematical instruments (trigonometric functions) their results were saved as tables, not functions. In 1615, he planned and carried into practice a new method of finding the radius of the earth, by determining the distance of one point on its surface from the parallel of latitude of another, by means of triangulation. His work 'Eratosthenes Batavus' ("The Dutch Eratosthenes"), published in 1617, describes the method. Snellius also produced a new method for calculating pi --- the first such improvement since ancient times.
Artus de Lionne (1583 to 1663)
Gregoire de Saint-Vincent (1584 to 1667) was a Flemish Jesuit and
mathematician. Saint-Vincent discovered that the area under a rectangular
hyperbola ( i.e. a curve given by xy = k ) is the same over [a,b] as
over [c,d] when a/b = c/d. This discovery was fundamental for
the development of the theory of logarithms and an eventual recognition
of the natural logarithm (whose series representation was discovered by
Nicholas Mercator (not to be confused with Gerardus Mercator the cartographer),
but was only later recognized as a log of base e).
The stated property allows one to define a function A(x) which is the
area under said curve from 1 to x, which has the property that
A(xy) = A(x)+A(y). Since this functional property characterizes
logarithms, it has become mathematical fashion to call such a
function A(x) a logarithm. In particular when we choose the rectangular
hyperbola xy = 1, one recovers the natural logarithm.
To a large extent, recognition of de Saint-Vincent's achievement in
quadrature of the hyperbola is due to his student and co-worker
Alphonse Antonio de Sarasa, with
Marin Mersenne (see below) acting as catalyst.
It was in attempting to
'square the circle' that Saint-Vincent made
Isaac Beeckman (1588 to 1637) was a Dutch philosopher and scientist.
Rejecting Aristotle, Beeckman developed the concept that matter is
composed of atoms. In 1618, he became a teacher and friend of René Descartes.
He convinced Descartes to devote his studies to a mathematical approach to
nature. When Descartes returned to the Dutch Republic in the autumn of
1628, Beeckman also introduced him to many of Galileo's ideas. In his time,
Beeckman was considered to be one of the most educated men in Europe.
For example, he had deeply impressed Mersenne, despite their opposing
Marin Mersenne (1588 to 1648), a French priest, conjectured that all
numbers of the form 2^n - 1, where n is prime, are prime. It turns out that
2^11 - 1 is 23 x 89, and hence not prime. If it were true, we would have a
simple formula for finding infinitely many primes.
For n = 2,3,5,7, the Mersenne numbers are 3, 7, 31, 127 --- all prime.
Note that Euclid (ca. 325-265 B.C.) showed that there are infinitely many
primes, but he did not find a rule for generating a succession of them.
Thomas Hobbes (1588 to 1679) was an English philosopher, best known
today for his work on political philosophy. His mathematics contributions
are not very significant, but he got into a long dispute with John Wallis,
who was second only to Isaac Newton as the leading English mathematician
of their age.
Richard Norwood (1590 to 1665) was an English mathematician, diver,
and surveyor. In 1616, he was sent to survey the islands of Bermuda
(also known as the Somers Isles). He was (around 1630 to 1640) a teacher
of mathematics in London. Between 1633 and 1635, he personally measured,
partly by chain and partly by pacing, the distance between London and
York, making corrections for all the windings of the way, as well as for
the ascents and descents. He also, from observations of the sun's altitude,
computed the difference of latitude of the two places, and so calculated
the length of a degree of the meridian. His result was some 600 yards
too great; but it was the nearest approximation that had then been made
in England. (See Edward Wright above.) Isaac Newton noted Norwood's work
in his 'Principia Mathematica'. Norwood is credited with founding Bermuda's
oldest school, Warwick Academy, in 1662. He died at Bermuda in 1675,
aged about eighty-five, and was buried there. He has been called
"Bermuda's outstanding genius of the seventeenth century" (in spite of
some alleged collusion with the governor during the 1616 survey) --- probably
by Bermudans eager for a noted Bermudan.
Francois Derand (ca. 1590 to 1644) was a French Jesuit architect.
In 1643, he published "L'architecture des voûtes", a treatise on
stereotomy (cutting and assembling blocks into complex structures)
that is considered his masterwork.
Girard Desargues (1591 to 1661) was a French mathematician and engineer,
and is considered one of the founders of projective geometry.
Desargues' theorem and the
Desargues graph are named in his honor.
Gregoire de Saint-Vincent (1584 to 1667) was a Flemish Jesuit and mathematician. Saint-Vincent discovered that the area under a rectangular hyperbola ( i.e. a curve given by xy = k ) is the same over [a,b] as over [c,d] when a/b = c/d. This discovery was fundamental for the development of the theory of logarithms and an eventual recognition of the natural logarithm (whose series representation was discovered by Nicholas Mercator (not to be confused with Gerardus Mercator the cartographer), but was only later recognized as a log of base e). The stated property allows one to define a function A(x) which is the area under said curve from 1 to x, which has the property that A(xy) = A(x)+A(y). Since this functional property characterizes logarithms, it has become mathematical fashion to call such a function A(x) a logarithm. In particular when we choose the rectangular hyperbola xy = 1, one recovers the natural logarithm. To a large extent, recognition of de Saint-Vincent's achievement in quadrature of the hyperbola is due to his student and co-worker Alphonse Antonio de Sarasa, with Marin Mersenne (see below) acting as catalyst. It was in attempting to 'square the circle' that Saint-Vincent made these discoveries.
Isaac Beeckman (1588 to 1637) was a Dutch philosopher and scientist. Rejecting Aristotle, Beeckman developed the concept that matter is composed of atoms. In 1618, he became a teacher and friend of René Descartes. He convinced Descartes to devote his studies to a mathematical approach to nature. When Descartes returned to the Dutch Republic in the autumn of 1628, Beeckman also introduced him to many of Galileo's ideas. In his time, Beeckman was considered to be one of the most educated men in Europe. For example, he had deeply impressed Mersenne, despite their opposing religious views.
Marin Mersenne (1588 to 1648), a French priest, conjectured that all numbers of the form 2^n - 1, where n is prime, are prime. It turns out that 2^11 - 1 is 23 x 89, and hence not prime. If it were true, we would have a simple formula for finding infinitely many primes.
For n = 2,3,5,7, the Mersenne numbers are 3, 7, 31, 127 --- all prime.
Note that Euclid (ca. 325-265 B.C.) showed that there are infinitely many primes, but he did not find a rule for generating a succession of them.
Thomas Hobbes (1588 to 1679) was an English philosopher, best known today for his work on political philosophy. His mathematics contributions are not very significant, but he got into a long dispute with John Wallis, who was second only to Isaac Newton as the leading English mathematician of their age.
Richard Norwood (1590 to 1665) was an English mathematician, diver, and surveyor. In 1616, he was sent to survey the islands of Bermuda (also known as the Somers Isles). He was (around 1630 to 1640) a teacher of mathematics in London. Between 1633 and 1635, he personally measured, partly by chain and partly by pacing, the distance between London and York, making corrections for all the windings of the way, as well as for the ascents and descents. He also, from observations of the sun's altitude, computed the difference of latitude of the two places, and so calculated the length of a degree of the meridian. His result was some 600 yards too great; but it was the nearest approximation that had then been made in England. (See Edward Wright above.) Isaac Newton noted Norwood's work in his 'Principia Mathematica'. Norwood is credited with founding Bermuda's oldest school, Warwick Academy, in 1662. He died at Bermuda in 1675, aged about eighty-five, and was buried there. He has been called "Bermuda's outstanding genius of the seventeenth century" (in spite of some alleged collusion with the governor during the 1616 survey) --- probably by Bermudans eager for a noted Bermudan.
Francois Derand (ca. 1590 to 1644) was a French Jesuit architect. In 1643, he published "L'architecture des voûtes", a treatise on stereotomy (cutting and assembling blocks into complex structures) that is considered his masterwork.
Girard Desargues (1591 to 1661) was a French mathematician and engineer, and is considered one of the founders of projective geometry. Desargues' theorem and the Desargues graph are named in his honor.
Cycloid generated by a fixed point on a rolling circle.
Generation of a 'roulette' curve.
Generation of a (repeating, periodic) 'epicycloid' curve.
THE LINKS BELOW ARE 'UNDER CONSTRUCTION'.
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Page created 2011 Dec 11.