Berkeley, California
Berkeley is a city on the east shore of San Francisco Bay in northern Alameda County, California. It is named after philosopher George Berkeley, it borders the cities of Oakland and Emeryville to the south and the city of Albany and the unincorporated community of Kensington to the north. Its eastern border with Contra Costa County follows the ridge of the Berkeley Hills; the 2010 census recorded a population of 112,580. Berkeley is home to the oldest campus in the University of California system, the University of California and the Lawrence Berkeley National Laboratory, managed and operated by the University, it has the Graduate Theological Union, one of the largest religious studies institutions in the world. Berkeley is considered one of the most liberal cities in the United States; the site of today's City of Berkeley was the territory of the Chochenyo/Huchiun band of the Ohlone people when the first Europeans arrived. Evidence of their existence in the area include pits in rock formations, which they used to grind acorns, a shellmound, now leveled and covered up, along the shoreline of San Francisco Bay at the mouth of Strawberry Creek.
Other artifacts were discovered in the 1950s in the downtown area during remodeling of a commercial building, near the upper course of the creek. The first people of European descent arrived with the De Anza Expedition in 1776. Today, this is noted by signage on Interstate 80, which runs along the San Francisco Bay shoreline of Berkeley; the De Anza Expedition led to establishment of the Spanish Presidio of San Francisco at the entrance to San Francisco Bay. Luis Peralta was among the soldiers at the Presidio. For his services to the King of Spain, he was granted a vast stretch of land on the east shore of San Francisco Bay for a ranch, including that portion that now comprises the City of Berkeley. Luis Peralta named his holding "Rancho San Antonio"; the primary activity of the ranch was raising cattle for meat and hides, but hunting and farming were pursued. Peralta gave portions of the ranch to each of his four sons. What is now Berkeley lies in the portion that went to Peralta's son Domingo, with a little in the portion that went to another son, Vicente.
No artifact survives of the Domingo or Vicente ranches, but their names survive in Berkeley street names. However, legal title to all land in the City of Berkeley remains based on the original Peralta land grant; the Peraltas' Rancho San Antonio continued after Alta California passed from Spanish to Mexican sovereignty after the Mexican War of Independence. However, the advent of U. S. sovereignty after the Mexican–American War, the Gold Rush, saw the Peraltas' lands encroached on by squatters and diminished by dubious legal proceedings. The lands of the brothers Domingo and Vicente were reduced to reservations close to their respective ranch homes; the rest of the land was parceled out to various American claimants. Politically, the area that became Berkeley was part of a vast Contra Costa County. On March 25, 1853, Alameda County was created from a division of Contra Costa County, as well as from a small portion of Santa Clara County; the area that became Berkeley was the northern part of the "Oakland Township" subdivision of Alameda County.
During this period, "Berkeley" was a mix of open land and ranches, with a small, though busy, wharf by the bay. In 1866, Oakland's private College of California looked for a new site, it settled on a location north of Oakland along the foot of the Contra Costa Range astride Strawberry Creek, at an elevation about 500 feet above the bay, commanding a view of the Bay Area and the Pacific Ocean through the Golden Gate. According to the Centennial Record of the University of California, "In 1866…at Founders' Rock, a group of College of California men watched two ships standing out to sea through the Golden Gate. One of them, Frederick Billings, thought of the lines of the Anglo-Irish Anglican Bishop George Berkeley,'westward the course of empire takes its way,' and suggested that the town and college site be named for the eighteenth-century Anglo-Irish philosopher." The philosopher's name is pronounced BARK-lee, but the city's name, to accommodate American English, is pronounced BERK-lee. The College of California's College Homestead Association planned to raise funds for the new campus by selling off adjacent parcels of land.
To this end, they laid out a plat and street grid that became the basis of Berkeley's modern street plan. Their plans fell far short of their desires, they began a collaboration with the State of California that culminated in 1868 with the creation of the public University of California; as construction began on the new site, more residences were constructed in the vicinity of the new campus. At the same time, a settlement of residences and various industries grew around the wharf area called "Ocean View". A horsecar ran from Temescal in Oakland to the university campus along; the first post office opened in 1872. By the 1870s, the Transcontinental Railroad reached its terminus in Oakland. In 1876, a branch line of the Central Pacific Railroad, the Berkeley Branch Railroad, was laid from a junction with the mainline called Shellmound into what is now downtown Berkeley; that same year, the mainline of the transcontinental railroad into Oakland was re-routed, putting the right-of-way along the bay shore through Ocean View.
There was a strong prohibition movement in Berkel
Philip Glass
Philip Glass is an American composer. He is regarded as one of the most influential musicians of the late 20th century. Glass's work has been described as minimal music, having similar qualities to other "minimalist" composers such as La Monte Young, Steve Reich, Terry Riley. Glass describes himself as a composer of "music with repetitive structures", which he has helped evolve stylistically. Glass founded the Philip Glass Ensemble, he has written numerous operas and musical theatre works, twelve symphonies, eleven concertos, eight string quartets and various other chamber music, film scores. Three of his film scores have been nominated for Academy Awards. Glass was born in Baltimore, the son of Ida and Benjamin Charles Glass, his family were Jewish emigrants from Lithuania. His father owned his mother was a librarian. In his memoir, Glass recalls that at the end of World War II his mother aided Jewish Holocaust survivors, inviting recent arrivals to America to stay at their home until they could find a job and a place to live.
She developed a plan to help them develop skills so they could find work. His sister, would do similar work as an active member of the International Rescue Committee. Glass developed his appreciation of music from his father, discovering his father's side of the family had many musicians, his cousin Cevia was a classical pianist. He learned his family was related to Al Jolson. Glass's father received promotional copies of new recordings at his music store, he spent many hours listening to them, developing his taste in music. This openness to modern sounds affected Glass at an early age: My father was self-taught, but he ended up having a refined and rich knowledge of classical and contemporary music, he would come home and have dinner, sit in his armchair and listen to music until midnight. I caught on to this early, I would go and listen with him; the elder Glass promoted both new recordings and a wide selection of composers to his customers, sometimes convincing them to try something new by allowing them to return records they didn't like.
His store soon developed a reputation as Baltimore's leading source of modern music. Glass built a sizable record collection from the unsold records in his father's store, including modern classical music such as Hindemith, Bartók, Schoenberg and Western classical music including Beethoven's string quartets and Schubert's B♭ Piano Trio. Glass cites Schubert's work as a "big influence" growing up, he studied the flute as a child at the university-preparatory school of the Peabody Institute. At the age of 15, he entered an accelerated college program at the University of Chicago where he studied mathematics and philosophy. In Chicago he composed a twelve-tone string trio. In 1954 Glass traveled to Paris, where he encountered the films of Jean Cocteau, which made a lasting impression on him, he saw their work. His composition teachers included William Bergsma. Fellow students included Peter Schickele. In 1959, he was a winner in the BMI Foundation's BMI Student Composer Awards, an international prize for young composers.
In the summer of 1960, he studied with Darius Milhaud at the summer school of the Aspen Music Festival and composed a violin concerto for a fellow student, Dorothy Pixley-Rothschild. After leaving Juilliard in 1962, Glass moved to Pittsburgh and worked as a school-based composer-in-residence in the public school system, composing various choral and orchestral music. In 1964, Glass received a Fulbright Scholarship, his move away from modernist composers such as Boulez and Stockhausen was nuanced, rather than outright rejection: "That generation wanted disciples and as we didn't join up it was taken to mean that we hated the music, which wasn't true. We knew their music. How on earth can you reject Berio? Those early works of Stockhausen are still beautiful, but there was just no point in attempting to do their music better than they did and so we started somewhere else." He encountered revolutionary films of the French New Wave, such as those of Jean-Luc Godard and François Truffaut, which upended the rules set by an older generation of artists, Glass made friends with American visual artists and directors.
Together with Akalaitis, Glass in turn attended performances by theatre groups including Jean-Louis Barrault's Odéon theatre, The Living Theatre and the Berliner Ensemble in 1964 to 1965. These significant encounters resulted in a collaborati
Calvin C. Moore
Calvin C. Moore is an American mathematician who works in the theory of operator algebras and topological groups. Moore graduated from Harvard University with a bachelor's degree in 1958 and with a Ph. D. in 1960 under the supervision of George Mackey. In 1961 he became assistant professor at the University of California and professor in 1966. From 1977 to 1980, he was director of the Center for Applied mathematics. With Shiing-Shen Chern and Isadore Singer, he co-founded Mathematical Sciences Research Institute in 1982. From 1964 to 1965 he was at the Institute for Advanced Study at Princeton, he is a fellow of the American Academy of Sciences. From 1965 to 1967 he was a Sloan Fellow. From 1971 to 1979 he was a member of the Board of Trustees of the American Mathematical Society, whose fellow he is. Since 1977, he is co-editor of the Pacific Journal of Mathematics. From 1978 to 1979 he was a Miller research professor at Berkeley, he has written on a history of mathematics at Berkeley. His students include Bruce Blackadar.
With Claude Schochet, Global Analysis on Foliated Spaces, MSRI Publications, Springer Verlag 1988, 2nd ed. Cambridge University Press 2006. Homepage
Tom Stoppard
Sir Tom Stoppard is a Czech-born British playwright and screenwriter. He has written prolifically for TV, radio and stage, finding prominence with plays such as Arcadia, The Coast of Utopia, Every Good Boy Deserves Favour, Professional Foul, The Real Thing, The Invention of Love, Rosencrantz and Guildenstern Are Dead, he co-wrote the screenplays for Brazil, The Russia House, Shakespeare in Love, has received an Academy Award and four Tony Awards. His work covers the themes of human rights and political freedom delving into the deeper philosophical thematics of society. Stoppard has been a key playwright of the National Theatre and is one of the most internationally performed dramatists of his generation. In 2008, The Daily Telegraph ranked him number 11 in their list of the "100 most powerful people in British culture". Born in Czechoslovakia, Stoppard left as a child refugee, he settled with his family in Britain after the war, in 1946, having spent the three years prior in a boarding school in Darjeeling in the Indian Himalayas.
After being educated at schools in Nottingham and Yorkshire, Stoppard became a journalist, a drama critic and in 1960, a playwright. Stoppard was born Tomáš Straussler, in Zlín, a city dominated by the shoe manufacturing industry, in the Moravia region of Czechoslovakia, he is a physician employed by the Bata shoe company. His parents were members of a long-established community. Just before the German occupation of Czechoslovakia, the town's patron, Jan Antonín Baťa, transferred his Jewish employees physicians, to branches of his firm outside Europe. On 15 March 1939, the day the Nazis invaded Czechoslovakia, the Straussler family fled to Singapore, where Bata had a factory. Before the Japanese occupation of Singapore, his brother, their mother were sent on to Australia. Stoppard's father remained in Singapore as a British army volunteer, knowing that, as a physician, he would be needed in its defence. Stoppard was four years old. In the book Tom Stoppard in Conversation, Stoppard tells how his father died in Japanese captivity, a prisoner of war but has said that he subsequently discovered that Straussler was reported to have drowned on board a ship bombed by Japanese forces whilst trying to flee Singapore in 1942.
In 1941, when Tomas was five, the three were evacuated to India. The boys attended Mount Hermon School, an American multi-racial school, where Tomas became Tom and his brother Petr became Peter. In 1945, his mother, married British army major Kenneth Stoppard, who gave the boys his English surname and, in 1946, moved the family to England. Stoppard's stepfather believed that "to be born an Englishman was to have drawn first prize in the lottery of life" —a quote from Cecil Rhodes —telling his 9 year-old stepson: "Don't you realise that I made you British?" Setting up Stoppard's desire as a child to become "an honorary Englishman". "I often find I'm with people who forget I don't quite belong in the world we're in", he says. "I find I put a foot wrong—it could be pronunciation, an arcane bit of English history—and I'm there naked, as someone with a pass, a press ticket." This is reflected in his characters, he notes, who are "constantly being addressed by the wrong name, with jokes and false trails to do with the confusion of having two names".
Stoppard attended the Dolphin School in Nottinghamshire, completed his education at Pocklington School in East Riding, which he hated. Stoppard left school at seventeen and began work as a journalist for the Western Daily Press in Bristol, never receiving a university education. Years he came to regret not going to university, but at the time he loved his work as a journalist and felt passionately about his career, he worked at the paper from 1954 until 1958, when the Bristol Evening World offered Stoppard the position of feature writer, humor columnist, secondary drama critic, which took Stoppard into the world of theater. At the Bristol Old Vic—at the time a well-regarded regional repertory company—Stoppard formed friendships with director John Boorman and actor Peter O'Toole early in their careers. In Bristol, he became known more for his strained attempts at humor and unstylish clothes than for his writing. Stoppard wrote short radio plays in 1953–54 and by 1960 he had completed his first stage play, A Walk on the Water, re-titled Enter a Free Man.
He noted that the work owed much to Robert Bolt's Flowering Cherry and Arthur Miller's Death of a Salesman. Within a week after sending A Walk on the Water to an agent, Stoppard received his version of the "Hollywood-style telegrams that change struggling young artists' lives." His first play was optioned, staged in Hamburg broadcast on British Independent Television in 1963. From September 1962 until April 1963, Stoppard worked in London as a drama critic for Scene magazine, writing reviews and interviews both under his name and the pseudonym William Boot. In 1964, a Ford Foundation grant enabled Stoppard to spend 5 months writing in a Berlin mansion, emerging with a one-act play titled Rosencrantz and Guildenstern Meet King Lear, which evolved into his Tony-winning play Rosencrantz and Guildenstern Are Dead. In the following years, Stoppard produced several works for radio and the theatre, including "M" is for Moon Among Other Things, A Separate Peace and If You're Glad I'll Be Frank. On 11 April 1967 – following acclaim at the 1966 Edinburgh Festival – the opening of Rosencrantz and Guildenstern Are Dead in a National Theatre producti
David Eisenbud
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California and was Director of the Mathematical Sciences Research Institute from 1997 to 2007, he was reappointed to this office in 2013, his term has been extended until July 31, 2022. Eisenbud is the son of mathematical physicist Leonard Eisenbud and collaborator of renowned physicist Eugene Wigner. Eisenbud received his Ph. D. in 1970 from the University of Chicago, where he was a student of Saunders Mac Lane and, James Christopher Robson. He taught at Brandeis University from 1970 to 1997, during which time he had visiting positions at Harvard University, Institut des Hautes Études Scientifiques, University of Bonn, Centre national de la recherche scientifique, he joined the staff at MSRI in 1997, took a position at Berkeley at the same time. From 2003 to 2005 Eisenbud was President of the American Mathematical Society. Eisenbud's mathematical interests include commutative and non-commutative algebra, algebraic geometry and computational methods in these fields.
He has written over 150 books with over 60 co-authors. Notable contributions include the theory of matrix factorizations for maximal Cohen–Macaulay modules over hypersurface rings, the Eisenbud–Goto conjecture on degrees of generators of syzygy modules, the Buchsbaum–Eisenbud criterion for exactness of a complex, he proposed the Eisenbud–Evans conjecture, settled by the Indian mathematician Neithalath Mohan Kumar. He has had 31 doctoral students, including Craig Huneke, Mircea Mustaţă, Irena Peeva, Gregory G. Smith. Eisenbud's hobbies are music, he has appeared in Brady Haran's Numberphile web series. Eisenbud was elected Fellow of the American Academy of Arts and Sciences in 2006, he was awarded the Leroy P. Steele Prize in 2010. In 2012 he became a fellow of the American Mathematical Society. Eisenbud, David. Three-dimensional link theory and invariants of plane curve singularities. Annals of Mathematical Studies. 110. Princeton, N. J.: Princeton U. Press. Vii+171. ISBN 978-0-691-08381-0. Eisenbud, David.
Commutative algebra with a view toward algebraic geometry. Graduate Texts in Mathematics. 150. New York: Springer-Verlag. Xvi+785. ISBN 0-387-94268-8. MR 1322960. Eisenbud, David; the geometry of schemes. Graduate Texts in Mathematics. 197. Berlin. X+294. ISBN 978-0-387-98638-8. MR 1730819. Eisenbud, David; the geometry of syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics. 229. New York: Springer-Verlag. Xvi+243. ISBN 0-387-22215-4. David Eisenbud, Joseph Harris. 3264 and All That: A Second Course in Algebraic Geometry. Cambridge University Press. ISBN 978-1107602724. Eisenbud, David. "Progress in the theory of complex algebraic curves". Bull. Amer. Math. Soc.. 21: 205–232. Doi:10.1090/s0273-0979-1989-15807-2. MR 1011763. Eisenbud, David. "Cayley-Bacharach theorems and conjectures". Bull. Amer. Math. Soc.. 33: 295–324. Doi:10.1090/s0273-0979-96-00666-0. MR 1376653. Eisenbud–Levine–Khimshiashvili signature formula O'Connor, John J.. David Eisenbud at the Mathematics Genealogy Project Eisenbud's biographical page at MSRI
Alan Alda
Alan Alda is an American actor, screenwriter and author. A six-time Emmy Award and Golden Globe Award winner, he played Hawkeye Pierce in the war television series M*A*S*H, he has appeared on television programs such as Scientific American Frontiers, The West Wing, 30 Rock, in films such as Same Time, Next Year and Crimes and Misdemeanors. He experienced success as a director with 1981's The Four Seasons. In 2004, Alda was nominated for the Academy Award for Best Supporting Actor in The Aviator. Alda was born Alphonso Joseph D'Abruzzo on January 1936 in the Bronx, New York City. Alda spent his childhood with his parents travelling around the United States in support of his father's job as a performer in burlesque theatres, his father Robert Alda was an actor and singer, his mother Joan Browne was a homemaker and former beauty-pageant winner. His father was of Italian descent and his mother was of Irish ancestry, his adopted surname, "Alda", is a portmanteau of D'Abruzzo. When Alda was seven years old, he contracted polio.
To combat the disease, his parents administered a painful treatment regimen developed by Sister Elizabeth Kenny, consisting of applying hot woollen blankets to his limbs and stretching his muscles. Alda attended Archbishop Stepinac High School in New York. In 1956, he received his Bachelor of Arts degree in English from Fordham University in the Bronx, where he was a student staff member of its FM radio station, WFUV. Alda's half-brother, Antony Alda, born that year became an actor. During Alda's junior year, he studied in Paris, acted in a play in Rome, performed with his father on television in Amsterdam. In college, he was a member of the ROTC, after graduation, he served for a year at Fort Benning, six months in the United States Army Reserve on a tour of duty in Korea. Alda began his career in the 1950s, as a member of the Compass Players, an improvisational, comedy revue directed by Paul Sills, he joined the acting company at the Cleveland Play House during the 1958-59 season as part of a grant from the Ford Foundation, appearing in productions such as To Dorothy A Son, Heaven Come Wednesday and Job.
In the November 1964 world premiere at the ANTA Playhouse of the stage version of The Owl and The Pussycat, he played Felix the "Owl" opposite the "Pussycat", played by actress/singer Diana Sands. He continued to play Felix the "Owl" for the 1964-65 Broadway season. In 1966, he starred in the musical The Apple Tree on Broadway starring Barbara Harris. Alda says. Alda was part of the cast, along with David Frost, Henry Morgan and Buck Henry, of the American television version of That Was The Week That Was, which ran as a series from January 10, 1964 to May 1965, he made his Hollywood acting debut as a supporting player in Gone are the Days! – a film version of the Broadway play Purlie Victorious, which co-starred Ruby Dee and her husband, Ossie Davis. Other film roles followed, such as his portrayal of author and actor George Plimpton in the film Paper Lion, as well as The Extraordinary Seaman, the occult-murder-suspense thriller The Mephisto Waltz, with actresses Jacqueline Bisset and Barbara Parkins.
During this time, Alda appeared as a panelist on the 1968 revival of What's My Line?. He appeared as a panelist on I've Got a Secret during its 1972 syndication revival. In early 1972, Alda auditioned for and was selected to play the role of Hawkeye Pierce in the TV adaptation of the 1970 film MASH, he was nominated for 21 Emmy Awards, won five. He took part in writing 19 episodes, including the 1983 2½-hour series finale Goodbye and Amen, the 32nd episode he directed, it remains the single most-watched episode of any American broadcast network television series. Alda was the only series regular to appear in all 251 episodes. Alda commuted from Los Angeles to his home in New Jersey every weekend for 11 years while starring in M*A*S*H, his wife and daughters lived in New Jersey and he did not want to move his family to Los Angeles because he did not know how long the show would last. Alda's father, Robert Alda, half-brother Antony Alda appeared together in an episode of M*A*S*H, "Lend a Hand", during season eight.
Robert had appeared in "The Consultant" in season three. During the first five seasons of the series, the tone of M*A*S*H was that of a traditional "service comedy", in the vein of shows such as McHale's Navy. However, as the original writers left the series, Alda gained increasing control, by the final seasons had become a producer and creative consultant. Under his watch, M*A*S*H retained its comedic foundation, but assumed a somewhat more serious tone addressing political issues; as a result, the 11 years of M*A*S*H are split into two eras: the Larry Gelbart/Gene Reynolds "comedy" years, the Alan Alda "dramatic" years. Alda disagreed with this assessment. In a 2016 interview he stated, "I don't like to write political messages. I don't like plays. I do not think I am responsible for that."For the first three seasons and his co-stars Wayne Rogers and McLean Stevenson worked well together, but tensions increased as Alda's role grew in popularity. Rogers and Stevenson both left the show at the end of the third season.
At the beginning of the fourth season and the producers decided to find a replacement actor to play the sur
Mathematics
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to