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60-523: Brattle was also a mathematician , astronomer , and an experienced traveler. Thomas Brattle was born on June 20, 1658, in Boston , Massachusetts Bay Colony , to Elizabeth Brattle née Tyng and Captain Thomas Brattle. He was the couple's second child, and the first son to survive past infancy. He had eight siblings, including William Brattle and Catherine Winthrop. Brattle's date of birth is often confused with

120-559: A compelling argument against the legal premises and procedures involved in the afflictions, accusations, and executions, with a particular focus on the invalidity of spectral evidence in proceedings. He argued that the procedures were so contrary to established practice and were dire in their consequences. Brattle's letter was designed to illustrate the wrongful convictions that the Court of Oyer and Terminer made during this time as they based their evidence on witchcraft from intangible evidence. He

180-471: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include

240-514: A letter to John Flamsteed , a mentor of his, stating that no one at Harvard could teach him mathematics so he took it upon himself to do so. Thomas and a group of other prominent colonists studied several comets that appeared in the late seventeenth century. He wrote several essays on these comets. Brattle later travelled abroad and then settled in Boston in 1693, where he pursued a short business career and gave several gifts to Harvard. That same year, he

300-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while

360-487: A mathematical algorithm in order to end smallpox . Although he failed, it can be seen that Brattle was heavily involved in education and scientific discovery. Brattle made more substantial contributions to science than any other American of the day. Brattle's mother was Elizabeth Brattle and his father Captain Thomas Brattle, who was one of Boston's wealthy maritime merchants. Brattle was an accomplished amateur mathematician and astronomer which eventually led him to becoming

420-766: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages

480-612: A wealthy merchant who made what was, at the time, the largest donation to Harvard in its history. Past residents include Pete Buttigieg , Al Jean , Horatio Alger Jr. , Alex Biega , David Halberstam , Christian Herter , Conan O'Brien , Sumner Redstone , Henry Hobson Richardson , Noah Welch , Cornel West , and Jeff Zucker . Another "Union" dormitory, named after Byron Hurlbut, a former Dean of Harvard College. Past notable residents include James Blake , Alice Crary , Roger W. Ferguson Jr. , Brian Greene , Amory Lovins , Roger Myerson , and Elizabeth Wurtzel . Lionel (built 1925)

540-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics

600-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics

660-454: Is a Muslim prayer space in the basement. Residents have included Jillian Dempsey , Alexander Fällström , Charles Lane , Eduardo Saverin , Esther Lofgren , Ben Mezrich , David Sacks , Mira Sorvino , and Paul Wylie . Opened in 1863, Grays became the college's first building with water taps in the basement. (Residents of other buildings in Harvard Yard had to haul water from pumps in

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720-674: Is located along the southern edge of the Yard, between Widener Library and Boylston Hall to the north, and Massachusetts Avenue to the south. It was constructed in 1931 as "part of President Lowell's plan to enclose the Yard from the traffic of Harvard Square." Past residents include Leonard Bernstein , Melissa Block , Benjamin C. Bradlee , Mark Danner , Jared Diamond , Bill Gates , Andre Gregory , Donald P. Hodel , Michael J. Kennedy , Ted Kennedy , Aga Khan IV , John Lithgow , Robert Lowell , Christopher Nowinski , Pat Toomey , David Vitter , Naomi Yang , and Randi Zuckerberg . To accommodate

780-508: Is located next to Johnston Gate . Designed by two Harvard Presidents, John Leverett and Benjamin Wadsworth , between 1718 and 1720 for the housing of sixty-four students, the building served various functions over the years, including a refuge for American soldiers during the Siege of Boston , and an observatory after Thomas Hollis ' donation of a twenty-four-foot telescope in 1722. Today, it houses

840-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing

900-474: Is the newest dormitory in Harvard Yard . Seen from the air, its seven buildings resemble a question mark. It is named after Ward M. Canaday, former president and major shareholder of Willys , manufacturer of Jeeps during World War II . Canaday's construction immediately followed the 1969 student takeover of University Hall , and certain features of its design were meant to confound student organizing. There

960-491: Is where Brattle met influential Puritan leader Cotton Mather . Although the two men agreed on many social and political ideologies later in life, they did not see eye to eye during their time at the Boston Latin School. It is documented that Thomas Brattle and other schoolmates enjoyed picking on Cotton Mather (to the point where he wrote to his father, Increase Mather , and requested to come home early). After his time at

1020-484: The American Revolution . Past residents include Charles Francis Adams Sr. , John Quincy Adams , Horatio Alger Jr. , Jim Cramer , Ralph Waldo Emerson , Edward Everett , Boisfeuillet Jones Jr. , Joseph P. Kennedy Sr. , Wendell Phillips , Henry David Thoreau , George Santayana , Charles Sumner , John Updike , and William Weld . Holworthy Hall was built in 1812 and was named after Sir Matthew Holworthy,

1080-608: The Boston Latin School , Brattle attended Harvard University and received an AB in mathematics and science. In 1676, Brattle graduated from Harvard College with an A.B.. Brattle developed marked skill in mathematics and science. Brattle was interested in many areas including mathematics, architecture, and astronomy. Brattle gained most of his education on his own due to the bad leadership at Harvard in his undergraduate years. He used whatever books that were available and studied with John Foster and Dr. William Avery. Brattle wrote

1140-637: The Congregational church . This sparked an intense dispute between Brattle and famous Puritan minister, Cotton Mather . Rather than being similar to the Puritans, his church was more like the Church of England. He was eulogized by the Reverend Benjamin Colman as "worth Christian philosopher, who was also the glory of his country in respect to his excelling knowledge of mathematics". Brattle participated in

1200-576: The House system . South of Harvard Yard on Holyoke Street, Apley Court has the most spacious rooms among the freshman dorms; accommodations include marble bathrooms. Formerly part of Adams House , it is the only one of the Gold Coast apartment buildings – luxurious private apartments built south of the Yard in the late 1890s – to now be a freshman dormitory. Notable residents have included T. S. Eliot . Completed in 1974, Canaday Hall

1260-634: The Pythagorean school , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c.  AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of

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1320-469: The Salem Witch Trials as one of the observers and commentators. Later, he was one of personages who became more open about their criticisms of the trials. Along with Robert Calef and Thomas Maule , he was particularly critical of the procedures adopted. On October 8, 1692, Brattle wrote a letter to an unnamed English clergyman containing his sentiments. The letter was circulated widely in Boston at

1380-656: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of

1440-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of

1500-578: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became

1560-595: The Union Dormitories, Pennypacker is named for Henry Pennypacker, a former president of Harvard's admissions committee. The studios of radio station WHRB (95.3 FM) are in the basement. Past residents include Kristin Goss , Hendrik Hertzberg , Nicholas Kristof , Bjorn Poonen , Peter Sagal , Andrew Tobias , Chris Wallace , and Fernando Zobel de Ayala . Stoughton Hall (built 1805) is Harvard's second building to be named Stoughton Hall. Designed by Charles Bulfinch , it

1620-533: The Yard.) Nicknamed "The Harvard Hilton", it is considered the most luxurious dormitory in the Yard. Past residents include Jeff Bingaman , Rosa Brooks , Charles Joseph Bonaparte , Michael Cohrs , Jeremy Doner , Ryan Fitzpatrick , Langdon Gilkey , Charles Grier Sellers , Swinburne Hale , Julie Hilden , Marcial Lichauco , Norman Mailer , Malia Obama , Natalie Portman , Joseph Ransohoff , Frank Rich , Mo Rocca , Joshua Sharfstein , Don Sweeney , John Weidman , and Michael Weishan . Located just outside

1680-429: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Stoughton Hall This is a list of dormitories at Harvard College . Only freshmen live in these dormitories, which are located in and around Harvard Yard . Sophomores, juniors and seniors live in

1740-588: The college, and was an unofficial professor of astronomy and mathematics. When Brattle died, he left the New World with a new rational approach towards thought. Brattle is also credited as being the first person to import an organ to the colonies. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of

1800-554: The confines of Harvard Yard, Greenough is part of a group of dormitories outside the Yard called the "Union Dormitories". Past notable residents include Elliott Abrams , Bill Kristol , Wallace Shawn , Laurence Tribe , Kyriakos Mitsotakis , and Colin Jost . Built in 1763 by Thomas Dawes and named for Thomas Hollis and his family, Hollis is one of the oldest buildings at Harvard (after only Massachusetts Hall (1720) and Holden Chapel (1744)), and housed George Washington's troops during

1860-500: The earliest known mathematicians was Thales of Miletus ( c.  624  – c.  546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c.  582  – c.  507 BC ) established

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1920-511: The eighteenth century when it was headed by Sir Isaac Newton . Sir Isaac Newton was so impressed with Brattle's work that he planned to procure his papers on astronomy and math after Brattle's death in order to benefit the Royal Society. In an attempt to obtain them, Newton tried to make his brother, William Brattle, a member of the Society, however William declined. In 1711, Brattle attempted to use

1980-708: The first concrete fragmentation of a previously united New England Congregational Community. Outside of his involvement in the Salem witch trials, Brattle and his younger brother William provided new radical ideas that the Puritan Church did not agree with. Brattle preached some of these more liberal ideas in the church he founded, the Brattle Street Church, which led to an argument with Puritan minister Cotton Mather . Also, both Thomas and William improved Harvard College. Thomas donated money many times, served as treasurer of

2040-715: The first-born son of the Brattle family (also named Thomas Brattle) – who was born on, and died on, September 5, 1657. As a child, Brattle was exposed to radical forms of the Puritan faith, primarily through his father's participation in the controversial founding of the Third (South) Church, which advocated for ecclesiastical reforms. The church's membership included many notable members such as Samuel Sewall , Samuel Adams , and Benjamin Franklin . At one point in time, Thomas' father, Captain Brattle,

2100-494: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of

2160-992: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,

2220-629: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"

2280-569: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at

2340-470: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to

2400-494: The offices of Harvard's president, with a handful of freshmen living on the uppermost floor. Five of the United States' Founding Fathers lived here: John Adams , John Hancock , Samuel Adams , Elbridge Gerry , and James Otis Jr. Other residents have included Zabdiel Adams , John Harbison , Alan Jay Lerner , John Redcliffe-Maud , Elliot Richardson , Jared Sparks , Jones Very , and Edward Wigglesworth . Matthews Hall

2460-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in

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2520-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate

2580-412: The remaining witchcraft cases and no one else was found guilty thereafter. Although Brattle's letter was written after 20 people were already wrongfully convicted, his powerful letter helped shape the future of Salem. As a result of the reaction toward theological, political, and cultural transformations that affected the whole of New England in the later half of the 17th century, the Brattle Street Church

2640-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced

2700-495: The sinking of the RMS Titanic . Notable residents include Darren Aronofsky , Phil Bredesen , William S. Burroughs , Peter Chiarelli , Seth Goldman , Joseph Lelyveld , Soledad O'Brien , Tom Ridge , John Roberts , David Souter , Caspar Weinberger , Tim Wirth , and Mark Zuckerberg . Thayer was built in 1870 and originally offered housing to students who had trouble affording the ever-increasing prices of housing outside

2760-457: The time, and it continues to be studied for its reasoned attack on the witchcraft trials in Salem. The "highly literate" and "satirical tone" of the letter was seen as writing beyond its time, leading Perry Miller to call it a "milestone in American literature." Brattle denounced the persecution of suspected witches, and his letter revealed a "chink in the armor" of Puritan ideology. Brattle presents

2820-505: The university. Past notable residents include James Agee , Bill Ackman , Conrad Aiken , Steve Ballmer , Virgilio Barco Isakson , Andy Borowitz , Hamzah bin al Hussein , E. E. Cummings , Roy J. Glauber , Walter Isaacson , Ji Chaozhu , Perri Klass , Bernard Francis Law , John F. Manning , Crown Princess Masako , Jonathan Mostow , Gabe Newell , Arthur Schlesinger Jr. , Edward Seaga , Jonathan Taylor Thomas , James Tobin , Stephanie Wilson , and Owen Wister . Built in 1870, Weld

2880-603: The unofficial professor of mathematics and astronomy at Harvard. There he taught and trained students in return for their assistance in his research. His work was directly influenced by the ideas of Robert Boyle and John Flamsteed , which he communicated to his students. In addition to being a professor, he became the treasurer of Harvard College. Circumstantial evidence indicates that he designed Stoughton Hall at Harvard and his own Brattle Street Meeting House. Brattle lived in London from 1682 to 1689 in order to study science. There he

2940-938: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in

3000-461: Was appointed as the Harvard College treasurer and he served in that position for twenty years until his death. During his time as treasurer, the finances of the college grew exponentially. Brattle was a member of the intellectually elite Royal Society . The Royal Society was a new group of scientific thinkers that practiced a more intense and rational thought process. This group grew much larger in

3060-632: Was built by Thomas Dawes . The original Stoughton Hall was built in 1700 and funded by Massachusetts Lieutenant Governor William Stoughton , who also presided over the Salem witch trials . Past residents include Francis Parkman , Philippe de Montebello , Trip Hawkins , Jeremy Lin , Eric Maskin , Mehmet Oz , Nathan Pusey , Sydney Schanberg , and Edmund Ware Sinnott . Straus was built in 1926 by three brothers in memory of their parents, Isidor and Ida Straus , New York department store entrepreneurs who owned both Macy's and Abraham & Straus and died in

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3120-496: Was careful to not critique the "Salem Gentlemen", which he referred to as the judges and ministers, but rather focused on critiquing the methods they used. After Governor Phips read Brattle's letter, he ordered that the courts could no longer use intangible evidence as a source to convict individuals of witchcraft. Phips dissolved the court entirely within the same month. Six months later, the Superior Court of Massachusetts took over

3180-599: Was designed by Peabody & Stearns and built from 1871–1872. Past notable residents include Philip Warren Anderson , Danny Biega , Matt Birk , Matt Damon , John Dos Passos , Maura Healey , Barney Frank , William Randolph Hearst , Mark Penn , Daniel Quillen , Robert Rubin , Chuck Schumer , Lloyd Shapley , Maurice Wertheim , and Elizabeth Wurtzel . Past residents include Timothy Crouse , Al Franken , Al Gore , Edward Gorey , Tommy Lee Jones , Arthur Kopit , Charles Murray , Thomas Oliphant , Meredith Salenger , Tanya Selvaratnam , and Bob Somerby . Part of

3240-470: Was formed as a result of radical development in the evolution of colonial congregationalism - bringing reason and religion together in a new church. The Congregational Church was broadly catholic, but used conservative principles of congregationalism (that just liberty and privilege should be allowed to all, while imposing nothing upon an individual). Although it did not make any radical changes from contemporary theological consensus - its foundation did represent

3300-521: Was given by Harvard President A. Lawrence Lowell as a memorial to Lionel de Jersey Harvard , the first relative of John Harvard to attend Harvard, and who was killed in World War I. Past residents include Peter Benchley , Lou Dobbs , Kevin Kallaugher , Grover Norquist , Endicott Peabody , and Erich Segal . The oldest surviving building at Harvard and the country's oldest dormitory, Massachusetts Hall

3360-508: Was involved in both scientific communities which can "help us understand a good deal about the progress of scientific expertise in colonial New England," since he was able to communicate information to both communities. Among his accomplishments, he was also a member of Royal Society , and Ancient and Honorable Artillery Company of Massachusetts. Brattle was also the principal founder of the Brattle Street Church , which broke away from

3420-485: Was named the wealthiest man in the colony. After the death of his father, Thomas was appointed administrator of the estate on April 12, 1683, leaving him with a large sum of money and a healthy plot of land. Before attending Harvard University in 1676, he attended the Boston Latin School . This school was open to all boys regardless of class, and served to educate and prepare the young men for university. The Boston Latin School

3480-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support

3540-462: Was popular during the same period. Past residents include Robert Bacon , Ben Bernanke , Michael Crichton , Christopher Durang , Daniel Ellsberg , Douglas J. Feith , Fred Grandy , Lionel de Jersey Harvard , Rashida Jones , John F. Kennedy , Douglas Kenney , Michael Kinsley , Neil H. McElroy , Neil deGrasse Tyson , Patrick Harlan and Scott Weinger . The second largest of the freshman dormitories, and actually three buildings, Wigglesworth

3600-521: Was the second of two important additions to the Harvard campus designed by Ware & Van Brunt (the first being Memorial Hall ). It was a gift of William Fletcher Weld , in memory of his brother Stephen Minot Weld , and represented a new trend toward picturesque silhouettes that became important in American domestic architecture of the later nineteenth century, as can be seen in the Queen Anne style which

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