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61-534: 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

122-563: 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

183-477: 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

244-518: 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

305-400: 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

366-487: 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

427-788: 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

488-420: 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

549-451: 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

610-645: Is buryed in the Chancell of Burstow Church". She also left instructions, and twenty five pounds, for the executor of her will to place "in the aforesaid Chancell of Burstow … A Marble stone or Monument, with an inscription in Latin, in memory of the late Reverend Mr. John Flamsteed". It seems no such monument was created, and almost 200 years later, a plaque was placed to mark his burial in the chancel. After his death, his papers and scientific instruments were taken by his widow. The papers were returned many years later, but

671-400: 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

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732-500: 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

793-617: 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

854-663: 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

915-653: 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

976-477: 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

1037-676: 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

1098-643: The Tower of London , Flamsteed had the opportunity to be taken by Titus to meet the King. He was subsequently admitted as an official Assistant to the Royal Commission and supplied observations in order to test St Pierre's proposal and to offer his own comments. The commission's conclusions were that, although St Pierre's proposal was not worth further consideration, the King should consider establishing an observatory and appointing an observer in order to better map

1159-478: 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

1220-586: 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

1281-639: The Master of Derby School, was delayed by some years of chronic ill health. During those years, Flamsteed gave his father some help in his business, and from his father learnt arithmetic and the use of fractions , developing a keen interest in mathematics and astronomy . In July 1662, he was fascinated by the thirteenth-century work of Johannes de Sacrobosco , De sphaera mundi , and on 12 September 1662 observed his first partial solar eclipse . Early in 1663, he read Thomas Fale 's Horologiographia: The Art of Dialling , which set off an interest in sundials . In

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1342-607: The Sun in large, closed elliptical orbits. Flamsteed later learned that Newton had gained access to his observations and data through Edmond Halley , his former assistant with whom he previously had a cordial relationship. As Astronomer Royal, Flamsteed spent some forty years observing and making meticulous records for his star catalogue, which would eventually triple the number of entries in Tycho Brahe 's sky atlas. Unwilling to risk his reputation by releasing unverified data, he kept

1403-554: The age of twenty-two. Flamsteed was greatly impressed (as Isaac Newton had been) by the work of Horrocks. In August 1665, at the age of nineteen and as a gift for his friend Litchford, Flamsteed wrote his first paper on astronomy, entitled Mathematical Essays , concerning the design, use and construction of an astronomer's quadrant , including tables for the latitude of Derby. In September 1670, Flamsteed visited Cambridge and entered his name as an undergraduate at Jesus College . While it seems he never took up full residence, he

1464-400: 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. John Flamsteed John Flamsteed FRS (19 August 1646 – 31 December 1719) was an English astronomer and the first Astronomer Royal . His main achievements were

1525-593: 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

1586-545: The distance to Mars and hence the astronomical unit . To this end, Flamsteed compared the apparent shift of Mars during the night with respect to other stars, this shift being superimposed on Mars' apparent night-to-night course among the stars. On 16 August 1680 Flamsteed catalogued a star, 3 Cassiopeiae , that later astronomers were unable to corroborate. Three hundred years later, the American astronomical historian William Ashworth suggested that what Flamsteed may have seen

1647-500: 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

1708-523: 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

1769-728: 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

1830-734: 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,

1891-500: 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

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1952-1060: 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 ,

2013-633: 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"

2074-506: The incomplete records under seal at Greenwich. In 1712, Isaac Newton , then President of the Royal Society , and Edmond Halley again obtained Flamsteed's data and published a pirated star catalogue. Flamsteed managed to gather three hundred of the four hundred printings and burned them. "If Sir I.N. would be sensible of it, I have done both him and Dr. Halley a great kindness," he wrote to his assistant Abraham Sharp . The data from

2135-640: The instruments disappeared. Flamsteed accurately calculated the solar eclipses of 1666 and 1668. He was responsible for several of the earliest recorded sightings of the planet Uranus , which he mistook for a star and catalogued as '34 Tauri'. The first of these was in December 1690, which remains the earliest known sighting of Uranus by an astronomer. In October 1672, when Mars was in opposition , Flamsteed used eyepieces with illuminated micrometer reticle carrying double cross-hairs, to measure Mars' diurnal parallax , thus allowing Flamsteed to estimate

2196-580: 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

2257-474: 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

2318-471: The pirated catalogue were used by the London cartographer John Senex to produce star charts in the 1720s before Flamsteed's own charts were ready. In 1725 Flamsteed's own version of Historia Coelestis Britannica was published posthumously, edited by his wife, Margaret Flamsteed . This contained Flamsteed's observations, and included a catalogue of 2,935 stars to much greater accuracy than any prior work. It

2379-671: The places of the fixed stars, so as to find out the so much desired Longitude of places for Perfecteing the Art of Navigation". In June 1675, another royal warrant provided for the founding of the Royal Greenwich Observatory , and Flamsteed laid the foundation stone on 10 August. In February 1676, he was admitted a Fellow of the Royal Society , and in July, he moved into the Observatory where he lived until 1684, when he

2440-497: The preparation of a 3,000-star catalogue, Catalogus Britannicus , and a star atlas called Atlas Coelestis , both published posthumously. He also made the first recorded observations of Uranus , although he mistakenly catalogued it as a star, and he laid the foundation stone for the Royal Greenwich Observatory . Flamsteed was born in Denby , Derbyshire , England, the only son of Stephen Flamsteed and his first wife, Mary Spadman. He

2501-531: 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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2562-484: 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

2623-412: 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

2684-403: 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

2745-558: The stars and the motions of the Moon in order to underpin the successful development of the lunar-distance method of finding longitude. On 4 March 1675 Flamsteed was appointed by royal warrant "The King's Astronomical Observator" – the first English Astronomer Royal , with an allowance of £100 a year. The warrant stated his task as "rectifieing the Tables of the motions of the Heavens, and

2806-570: The summer of 1663, he read Wingate's Canon , William Oughtred 's Canon , and Thomas Stirrup's Art of Dialling . At about the same time, he acquired Thomas Street 's Astronomia Carolina, or A New Theory of the Celestial Motions ( Caroline Tables ). He associated himself with local gentlemen interested in astronomy, including William Litchford, whose library included the work of the astrologer John Gadbury which included astronomical tables by Jeremiah Horrocks , who had died in 1641 at

2867-406: 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

2928-554: 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

2989-543: The year 1667 and not 1680, some historians feel that all Flamsteed may have done was incorrectly note the position of a star already known. In 1681 Flamsteed proposed that the two great comets observed in November and December 1680 were not separate bodies, but rather a single comet travelling first towards the Sun and then away from it. Although Isaac Newton first disagreed with Flamsteed, he later came to agree with him and theorized that comets, like planets, moved around

3050-943: 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

3111-489: Was "[e]levated to the priesthood [and] appointed rector" of the small village of Burstow , near Crawley in Surrey . He held that office, as well as that of Astronomer Royal, until his death. He is buried at Burstow, and the east window in the church was dedicated to him as a memorial. The will of Flamsteed's widow, Margaret, left instructions for her own remains to be deposited "in the same Grave in which Mr John Flamsteed

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3172-468: 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

3233-503: 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

3294-540: Was educated at the free school of Derby and at Derby School , in St Peter's Churchyard, Derby , near where his father carried on a malting business . At that time, most masters of the school were Puritans . Flamsteed had a solid knowledge of Latin , essential for reading the scientific literature of the day, and a love of history , leaving the school in May 1662. His progress to Jesus College, Cambridge , recommended by

3355-470: 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

3416-517: 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

3477-489: 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

3538-431: 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

3599-490: Was persuaded by his mistress, Louise de Kérouaille, Duchess of Portsmouth , to hear about a proposal to find longitude by the position of the Moon from an individual known as Le Sieur de St Pierre. Charles appointed a Royal Commission to examine the proposal in December 1674, consisting of Lord Brouncker , Seth Ward , Samuel Moreland , Christopher Wren , Silius Titus , John Pell and Robert Hooke . Having arrived in London on 2 February 1675, and staying with Jonas Moore at

3660-496: Was the most recent supernova in the galaxy's history, an event which would leave as its remnant the strongest radio source outside of the Solar System, known in the third Cambridge (3C) catalogue as 3C 461 and commonly called Cassiopeia A by astronomers. Because the position of "3 Cassiopeiae" does not precisely match that of Cassiopeia A, and because the expansion wave associated with the explosion has been worked backward to

3721-541: Was there for two months in 1674, and had the opportunity to hear Isaac Newton's Lucasian Lectures . Ordained a deacon, he was preparing to take up a living in Derbyshire when he was invited to London by his patron Jonas Moore , Surveyor-General of the Ordnance. Moore had recently made an offer to the Royal Society to pay for the establishment of an observatory. These plans were, however, preempted when Charles II

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