Mathematicians Project Dany Gonzalez Joe Kennedy Joe Puchner Randy Spaulding Maria Agnesi (Italian, 1718-1799) •Was very religious, wanted to become a nun •Wrote a book on differential calculus •Also wrote Instituzioni analitiche ad uso della gioventù italiana, a book on systemic algebra •This book contains discussion about a cubic curve now know as the "witch of Agnesi“ •About this: “It took much skill and sagacity to reduce, as the author has done, to almost uniform methods these discoveries scattered among the works of modern mathematicians and often presented by methods very different from each other. Order, clarity and precision reign in all parts of this work. ... We regard it as the most complete and best made treatise.” •Pope Benedict XIV wrote to her, praising her for her advancements in mathematics in Italy •He appointed her to honorary reader at the University of Bologna. •She was a very religious and very scholarly woman, and she devoted her life to mathematics and religion Mohammed al-Khowarizmi (Arabic, c. 790-850) •First to use zero as a place holder •"Algorithm" derives from his name •Considered the first to write a book on algebra •Came up with six standard forms of equations: 1. Squares equal to roots. 2. Squares equal to numbers. 3. Roots equal to numbers. 4. Squares and roots equal to numbers; e.g. x2 + 10 x = 39 5. Squares and numbers equal to roots; e.g. x2 + 21 = 10 x 6. Roots and numbers equal to squares; e.g. 3 x + 4 = x2 •Wrote books on geography and astronomy •Considered one of the greatest mathematicians of all time: “Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus [another mathematician] because alKhwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers.” Charles Babbage (English, 1791-1871) •Originated the modern analytic computer •Educated at private schools in England, loved mathematics from an early age. •He is credited for providing the basic thinking behind modern computers: •“I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the table in a kind of dreamy mood, with a table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, Well, Babbage, what are you dreaming about?" to which I replied "I am thinking that all these tables" (pointing to the logarithms) "might be calculated by machinery.“” •He later published Reflections on the Decline of Science in England, which caused the formation of the British Association for the Advancement of Science. Bernoulli Family (Swiss, 1600s and 1700s) •They immigrated to Switzerland from the Netherlands to flee from Spanish oppression. •Accomplishments: •Daniel: Bernoulli’s Principle: Energy is conserved in a moving fluidthis can explain why an airplane can fly, and why a baseball pitcher can throw a curveball. •Jacob: First to use the term “integral” and was one of the first to use polar coordinates. •Johann: Studied reflection and refraction of light. •Johann II: Studied heat and light. •Johann III: Wrote numerous books on number theory, probability, and astronomy. “Nature always tends to act in the simplest way.” -Daniel Bernoulli Janos Bolyai (Hungarian, 1802-1860) •Was a genius from a very early age: “... when he was four he could distinguish certain geometrical figures, knew about the sine function, and could identify the best known constellations. By the time he was five [he] had learnt, practically by himself, to read. He was well above the average at learning languages and music. At the age of seven he took up playing the violin and made such good progress that he was soon playing difficult concert pieces.” •Wrote a complete treatise on non-Euclidean Geometry •Developed complex geometric numbers •Could speak nine languages and performed the violin in Vienna. •There is a crater on the moon named after him George Boole (English, 1815-1864) •Created Boolean Algebra (which many consider the foundation of computer science) •In Boolean algebra, he incorporated logic into mathematics •He also wrote books about differential equations and the calculus of finite differences •He also discovered general methods in probability •His work was highly recognized- he was given honorary degrees from the University of Dublin and the University of Oxford. •“I can speak confidently to the fact of his being not only well-versed in the highest branches of mathematics, but possessed of original power for their extension which gives him a very respectable rank among their English cultivators of this day.” •He died after he caught a cold when walking to teach a class in the rain Brahmagupta (Indian, 598-670) •The greatest Indian mathematician of the time •Understood number theory (“debt” is a negative number, “fortune” is a positive number): “A debt minus zero is a debt. A fortune minus zero is a fortune. Zero minus zero is a zero. A debt subtracted from zero is a fortune. A fortune subtracted from zero is a debt. The product of zero multiplied by a debt or fortune is zero. The product of zero multiplied by zero is zero. The product or quotient of two fortunes is one fortune. The product or quotient of two debts is one fortune. The product or quotient of a debt and a fortune is a debt. The product or quotient of a fortune and a debt is a debt.” •He also made significant advances in astronomy writing about the longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; and conjunctions of the planets. Rene Descartes (French, 1596-1650) •Came up with Cartesian Geometry (analytical geometry): •The basis is Cartesian coordinates (x,y) •This was the first ever link between Euclidean geometry and algebra. •It is the study of geometry using a coordinate plane and principles of algebra and analysis •Was also a very famous philosopher: •Driven to understand being and existence •Very famous quote: “Cogito Ergo Sum (I think therefore I am).” •Key thinker of the scientific revolution Leonhard Euler (Swiss, 1707-1783) Leonhard was born to a family of religion who's father was a pastor. He went to the Paris academy and that’s where he began working on his scholarly pieces. •Accomplishments•Published a book Mechanica in 1736 •Won the Grand Prize at Paris Academy •1759- took over the Berlin Academy •Chairman of physics in the Academy in St Petersburg •Director of geography at St. Petersburg Academy •Solved the problem of “the Bridges of Königsberg” •The problem was to find a path through the city that would cross each of 7 bridges once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time. •Euler proved that the problem has no solution. • "For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear." Pierre De Fermat (French, 1601-1665) Accomplishments•He received a degree in civil law in Toulouse and received a spot in parliament •Changed his name to Pierre de Fermat after receiving this recognition •Wrote Plane Roci • Most known for Fermat's Last Theorem- The first proof of this theorem was discovered in 1995! •New Account of Discoveries in the Science of Numbers •Fluent in four languages “I have found a very great number of exceedingly beautiful theorems.” Leonardo Pisano Fibbonaci (Italian, c. 1170-1250) Accomplishments •Liber abaci-Focused on forgotten math skills •Fibonacci's number sequences: 1,1, 2, 3, 5, 8, 13, 21… (sum of the previous two numbers) •Liber quadratorum-examining Pythagorean triples •Practica geometriae-Chapter 8 of Euclid's elemnts •Published over 6 math books in his career “... the serious and learned Master Leonardo Bigollo ....” Evariste Galois (French, 1811-1832) Accomplishments •Annales de mathématiques- book on continued fractions •the condition that an equation be soluble by radicalspaper written but teacher died before could be recognized for it •Galois theory-study of polynomial equations •Submitted papers before he died which got recognition later •Bulletin de Férussac- article written on Abel’s theory “This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research” Johann Carl Friedrich Gauss (German, 1777-1855) Accomplishments: •Disquisitiones Arithmeticae- book on the number theory •Wrote a dissertation on the fundamental theory of algebra •Director of a observatory in Gottingen •Theoria motus corporum coelestium in sectionibus conicis Solem ambientium- book on celestial bodies •Disquisitiones generales circa superficies curva- another book written on geography •Bestimmung der Genauigkeit der Beobachtungen – explained statistical estimators •Methodus nova integralium valores per approximationem inveniendi - book on approximate integration “To praise it would mean to praise myself .” Hypatia (Egyptian, c. 370-415) Accomplishments•Hypatia became head of the Platonist school at Alexandria •Taught philosophy of Neoplatonism •Focused mainly on Christian students to teach •Assisted her father in writing Almagest •She undertook original mathematical research •Synesius’ letters have been kept to admire the work of Hypatia “... by her eloquence and authority ... attained such influence that Christianity considered itself threatened ...” Johann Kepler (German, 1571-1630) Accomplishments•Best known for three principles of planetary motion •attend the University of Tbingen •“The More Reliable Bases of Astrology”rejected theory that stars guide human life •“The New Star in the Foot of the Serpent Bearer”-described the supernova that was witnessed by Kepler •Was able to explain how glasses work •Proposed the elliptical orbit, equality of areas, and the Harmonics of the World principles “I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses.” Felix Klein (German, 1849-1925) Accomplishments: •Attended University of Bonn •Über die Transformation der allgemeinen Gleichung des zweiten Grades zwischen LinienKoordinaten auf eine kanonische Form- written on line geometry •Appointed to professor at Erlangen •Klein wrote a major four volume classic on automorphic and elliptic modular functions •Klein was elected to the Royal Society •The London Mathematical Society awarded him their De Morgan Medal “Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.” Gottfried Leibniz (German, 1646-1716) •Philosopher and mathematician •Developed infinitesimal calculus (disputed with Newton as to who really discovered calculus) •Study of extremely small lengths and areas (i.e. the slopes of curves and the areas underneath them •discovered the mechanics (the Leibniz wheel) behind the first mechanical calculator, the arithmometer, patented by Thomas d’e Clomar nearly 150 years later •Refined the binary number system, the basis of all modern computers, nearly 250 years before its time •devised the Leibniz formula for pi •1 - 1/3 + 1/5 - 1/7 + 1/9 - ..... = π/4 “I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one.” Nikolai Lobachevsky (Russian, 17921856) •mathematician and geometer •founder of hyperbolic geometry (also called Lobachevskian geometry) •non-Euclidean geometry •does not follow Euclid’s parallel postulate •postulate states that with any given line and point not on that line, there is one line that goes through the point and does not intersect that line •based on geometry that is set on a saddleshaped plane (hyperbolic paraboloid) •the point used in Euclid’s parallel postulate has 2 lines that go through it while not intersecting the separate line •had the Lobachevsky Prize for superior mathematicians named after himself. •“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.” Marin Mersenne (French, 1588-1648) •Theologian, philosopher, mathematician, and music theorist •Studied Mersenne primes, where positive integers one less than a power of two, in which the power must be prime, yield another prime number •47 Mersenne primes are known •formula helped in finding the largest known prime number •12,978,189 digits long •Helpful for determining strength of computer’s computing capability by programming the computer to find a Mersenne prime •Was the first to determine the speed of sound in air by measuring the return of an echo. His final product was in error by only 10% •“[Animals] do not so much act as be put into action, and that objects make an impression on their senses such that it is necessary for them to follow it just as it is necessary for the wheels of a clock to follow the weights and the spring that pulls them.” John Napier (Scottish, 1550-1617) "Seeing there is nothing that is so troublesome to mathematical practice.... than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are... subject to many slippery errors, I began therefore to consider [how] I might remove those hindrances." •mathematician, physicist, astronomer, and astrologer •Devised the widely used mathematics of logarithms •Used to simplify calculations •Logb(xy)=logb(x) + logb(y) •log(1000) = 3 = 103 •Logarithms have many applications •The shell of the sea creature nautilus displays a logarithmic spiral •Measurements and charts in logarithmic scales •Psychology: relationship between stimulus and sensation •Probability and statistics •Chemistry: entropy •Music: intervals •Aside from mathematics •Believed the world would end in 1688 or 1700 Sir Isaac Newton (English, 1643-1727) •physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian •Devised the widely known concept of gravity and the three laws of motion •gravity is the natural phenomenon by which physical bodies attract wiht a force proportional to their mass •Laws of Motion 1.If a body is at rest it remains at rest or if it is in motion it moves with uniform velocity until it is acted on by a resultant force. 2.Force is equal to mass times acceleration 3.For every action, there is an equal and opposite reaction •Created the first practical reflecting telescope •Combination of curved mirrors that reflect light and form an image •Allows viewing of very large diameter objectives •Worked with Leibniz in the development of calculus - the study of change •Differential calculus - study of rates at which quantities change •Integral Calculus - the determination, properties, and application of integrals •Praised as one of the most influential people in human history • “This most beautiful system [The Universe] could only proceed from the dominion of an intelligent and powerful Being.” Blaise Pascal (French, 1623-1662) •mathematician, physicist, writer, and Catholic philosopher •Was a child prodigy •Devised Pascal’s Triangle •a triangular array of numbers in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row •Has useful applications in binomial expansions and combinations •Worked extensively in the fields of hydrodynamics and hydrostatics, mainly in the development of the principles of hydraulic fluids •Invented the hydraulic press and the syringe •The SI unit of pressure, the pascal, is named after Blaise Pascal for his contributions to the science behind pressure •“All human evil comes from a single cause, man's inability to sit still in a room.” •Srinivasa Ramanujan (Indian, 1887-1920) •mathematician •Devised Ramanujan primes •prime numbers that satisfy Ramanujan’s equation for counting primes •Found the Hardy-Ramanujan number 1729 •the smallest number expressable as the sum of two cubes in two different ways •Devised the Ramanujan theta function •“An equation for me has no meaning unless it expresses a thought of God.” Bernhard Riemann (German, 1826-1866) •Mathematician •developed ideas concerning the geometry of space •has a large effect on modern physics •created Riemannian geometry •geometry in an area that is not necessarily flat, but infinitely close to flat •introduced the Riemann zeta function •developed theories of higher dimensions •“If only I had the theorems! Then I should find the proofs easily enough.” Thales of Miletus -Born in about 624 BC in Asia Minor, now Turkey. -Recognized as the first Greek philosopher. -Taught Anaximander, a famous philosopher. -First Natural Philosopher in the Milesian School. -He rejected mythological explanations of things, and therefore is sometimes called the “father of science.” -Correctly predicted the eclipse of the sun in 585 BC. -died in around 547 BC in Asia Minor. “Nothing is more active than thought, for it travels over the universe, and nothing is stronger than necessity for all must submit to it.” John Von Neumann -Born in December 28 1903 in Budapest, Hungary. -Taught in both the United States and Europe. -Was one of the 6 original math professors in Princeton, one of the others being Albert Einstein. -Was the co-editor of the Annals of Mathematics and Compositio Mathematica. -Awarded the Bocher Prize from the American Mathematical Society. -Many regard him as the greatest modern mathematician because of his contributions to functional analysis, quantum mechanics, continuous geometry, economics, game theory, hydrodynamics, statistics, and computer science. -Died in February 8 1957 in Washington DC. “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.” Andrew Wiles -Born in April 11 1953 in Cambridge, England. -Spent most of his life trying to prove the Shimura-Taniyama conjecture, knowing it would prove Fermat’s last theorem. -Spent 2 years in Oxford as a Royal Society Research member. -Eventually proved Fermat's theorem and was awarded the Shaw Prize for Mathematical Sciences in 2005. -Got an asteroid named after him, asteroid 9999 Wiles. -Named Sir Andrew Wiles later in his life. “I realized that anything to do with Fermat's Last Theorem generates too much interest.” Zeno of Elea -Born in about 490 BC in Elea, now southern Italy. -not much known about Zeno. -studied with Parmenides in Elea. -it is said that he visited Socrates and Parmenides met with Zeno in Athens. -argued that something without magnitude cannot exist. -Often got in arguments with Plato and Aristotle. -He posed paradoxes to challenge mathematical views of the time. -Died in 425 BC in Elea. "My writing is an answer to the partisans of the many... with a view to showing that the hypothesis of the many, if examined in sufficient detail, leads to even more absurd results that the hypothesis of the One." Archimedes -Born in 287 BC in Sicily. -invented the device known as Archimedes screw in Egypt. -Wrote many books about geometry. -wrote a book One Plane Equilibriums, Sphere and Cylinder, On Spirals and so on. -Approximated pi extremely accurately -while pursuing many things, Archimedes always said that his biggest interest was mathematics. -helped build many machines according to King Herod. -Claimed he could move the world with a simple lever. -died in 212 BC in Sicily. “Give me a place to stand, and I will move the world” Euclid -born in about 325 BC. -considered the most important early mathematician. -Most famous for his book The Elements, which describes geometry. -His book The Elements consisted of 13 books. -His book begins with definitions and 5 postulates. -So influential that most of his students wrote books about him. -died in about 265 BC in Alexandria, Egypt. “The laws of nature are but the mathematical thoughts of God.” Pythagoras -Born in about 569 BC in Samos, Ionia. -described as the first pure mathematician. -the 2 people that had a big influence on him were Thales and Anaximander. -not much known about his childhood or actual work. -famous for the Pythagorean theorem. -discovered irrationals. -first to be able to construct the first 3 solids but not the last 2. -taught that the earth was a sphere and was at the center of the universe. -died in about 475 BC. “The oldest, shortest words - "yes" and "no" - are those which require the most thought.” Jean Le Rond d'Alembert -born in November 17 in Paris, France. -had to take care of himself for most of his life because his father died when he was 9. -helped improve Newtons definition of force. -Studied laws and dynamics of motions and fluids -Went from the Paris Academy to the Berlin Academy because of disagreements with classmates. -was wanted as the President of the Berlin Academy but declined. -died in October 29 1783 in Paris. “The imagination in a mathematician who creates makes no less difference than in a poet who invents…. Of all the great men of antiquity, Archimedes may be the one who most deserves to be placed beside Homer.” QUIZ! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Who came up with a theorem that wasn’t proved until over 300 years after his death? Who proved the above theorem? Which mathematician wanted to become a nun? Which mathematician used paradoxes as proofs? Which mathematician studied laws and dynamics of motions and fluids? Which mathematician came up with the theorem that states “a² + b² = c²”? This mathematician has a branch of math named after him: _______ean Geometry. This German mathematician wrote about celestial bodies and statistical estimators. This mathematician was Egyptian. The _______ Theory is a study on polynomial equations. This mathematician wrote a whole treatise on non-Euclidean Geometry. Which modern mathematician contributed to functional analysis, quantum mechanics, continuous geometry, economics, game theory, hydrodynamics, statistics, and computer science? Which mathematician came up with a series where the next number is the sum of the previous two? This mathematician wrote a major four volume classic on automorphic and elliptic modular functions. This mathematician came up with three laws about planetary motion. This mathematician and philosopher is also known as the “father of science.” QUIZ! 17. 18. 19. 20. 21. 22. 23. 24. This mathematician solved “the Bridges of Konigsberg.” These two mathematicians are disputed as being the inventors of calculus. This mathematician is considered the father of computer science. This mathematician is considered the father of the analytical computer. This Indian mathematician understood positive and negative number theory. This Arabic mathematician was the first to use zero as a placeholder. This mathematical family fled from the Netherlands to avoid Spanish oppression. This mathematician was also a philosopher, known for the quote, “I think, therefore I am.” 25. This mathematician founded hyperbolic geometry. 26. This mathematician was the first to calculate the speed of sound. 27. This mathematician invented logarithms. 28. This mathematician has a unit of pressure named after him. 29. This mathematician discovered Ramanujan primes. 30. This mathematician created geometry in an area that is not necessarily flat, but infinitely close to flat. 31. This Greek mathematician approximated pi extremely accurately.