Congregational churches are Protestant churches in the Reformed tradition practicing congregationalist church governance, in which each congregation independently and autonomously runs its own affairs. Congregationalism, as defined by the Pew Research Center, is estimated to represent 0.5 per cent of the worldwide Protestant population. The report defines it narrowly, encompassing denominations in the United States and the United Kingdom, which can trace their history back to nonconforming Protestants, Separatists, English religious groups coming out of the English Civil War, other English dissenters not satisfied with the degree to which the Church of England had been reformed. Congregationalist tradition has a presence in the United States, the United Kingdom, Canada, South Africa, New Zealand, various island nations in the Pacific region, it has been introduced either by immigrant dissenter Protestants or by missionary organization such as the London Missionary Society. A number of evangelical Congregational churches are members of the World Evangelical Congregational Fellowship.
In the United Kingdom, many Congregational churches claim their descent from Protestant denominations formed on a theory of union published by the theologian and English separatist Robert Browne in 1582. Ideas of nonconforming Protestants during the Puritan Reformation of the Church of England laid foundation for these churches. In England, the early Congregationalists were called Separatists or Independents to distinguish them from the Calvinistic Presbyterians, whose churches embrace a polity based on the governance of elders. Congregationalists differed with the Reformed churches using episcopalian church governance, led by a bishop. Congregationalism in the United States traces its origins to the Puritans of New England, who wrote the Cambridge Platform of 1648 to describe the autonomy of the church and its association with others. Within the United States, the model of Congregational churches was carried by migrating settlers from New England into New York into the Old North West, further.
With their insistence on independent local bodies, they became important in many social reform movements, including abolitionism and women's suffrage. Modern Congregationalism in the United States is split into three bodies: the United Church of Christ, the National Association of Congregational Christian Churches and the Conservative Congregational Christian Conference, the most theologically conservative. Congregationalists believe their model of church governance fulfills the description of the early church and allows people the most direct relationship with God. Congregationalism is more identified as a movement than a single denomination, given its distinguishing commitment to the complete autonomy of the local congregation; the idea that each distinct congregation constitutes the visible Body of the church can, however, be traced to John Wycliffe and the Lollard movement, which followed Wycliffe's removal from teaching authority in the Roman Catholic Church. The early Congregationalists shared with Anabaptist theology the ideal of a pure church.
They believed the adult conversion experience was necessary for an individual to become a full member in the church, unlike other Reformed churches. As such, the Congregationalists were a reciprocal influence on the Baptists, they differed in counting the children of believers in some sense members of the church. On the other hand, the Baptists required each member followed by baptism. King Henry VIII made himself Supreme Head of the Church without allowing a change in doctrine or liturgy during his lifetime, he was not excommunicated but broke with Rome to legitimize his marriage to Anne Boleyn in 1533 after trying unsuccessfully to have his marriage with his wife, Catherine of Aragon annulled. Henry forced Parliament to approve the Act of Supremacy in 1534 which made him "the only supreme head on earth of the Church in England"; the title was changed to Supreme Governor of the Church of England in 1559. Still in effect; the Church of England ceased to be subject to the Church of Rome. However, it continued as before with the same episcopal ecclesiastical structure, Canon Law, Apostolic Succession.
It saw itself as the continuing Church in England without break. However its worship life was changed." The whole story of the English Reformation which produced the Church of England is a tale of retreat from the Protestant advance of 1550..." Pope Saint Pius V regretfully excommunicated Queen Elizabeth I. From the beginning of her reign a small but vocal party of radical Reformers Calvinists who represented less than 10% of the population pressed for the abolition of episcopacy - the 3-fold order of bishop priest and deacon - church music, the old canon law and liturgical and doctrinal practices they regarded as hangovers from Catholicism, they got nowhere. The persistence of the government's religious program and time had defeated them: England 80% Catholic in 1558 with a Catholic clergy evolved under Elizabeth. By 1600 the country was 20 % Catholic, 70 % Protestant C of 10 % Radicals; the great majority of Catholics had gone over to the Settlement as the Catholic-trained clergy ministered to them in the early years "with the vestments and movements of the old mass," Christopher Haigh, English Reformations p. 289, were replaced over four decades by new clergy weaned on the Prayer Book.
Frustrated at these leftovers from an earlier Ag
Robert Sedgewick (judge)
Robert Sedgewick was a Justice of the Supreme Court of Canada. Born in Aberdeen, Sedgewick's family immigrated to Nova Scotia while he was still an infant, he was educated at Dalhousie University in Halifax, graduating in 1867. He articled in Cornwall, Ontario, in the private practice of John Sandfield Macdonald, at that time both the Premier and the Attorney General of Ontario. Sedgewick was called to the bar in Ontario in 1872, in Nova Scotia in 1873 following his return to the province. Sedgewick established a private practice in Halifax, subsequently played an essential role in the establishment of the law school at Dalhousie in 1883. Beginning in the 1870s, Sedgewick became active in the Conservative Party of Canada; the connections thus established would serve him well, as his friend and former Halifax colleague John Sparrow David Thompson, who had become the federal Minister of Justice, appointed Sedgewick as Deputy Minister of Justice in February 1888. In this capacity, he played an important role in the establishment of the first national Criminal Code, enacted in 1892.
Thompson, who had by become the Prime Minister of Canada appointed Sedgewick to the Supreme Court of Canada on 18 February 1893, a position he was to hold until his death in 1906. He was a member of the North British Society. "Robert Sedgewick". Dictionary of Canadian Biography. University of Toronto Press. 1979–2016. Supreme Court of Canada Biography
Queen's Privy Council for Canada
The Queen's Privy Council for Canada, sometimes called Her Majesty's Privy Council for Canada or the Privy Council, is the full group of personal consultants to the monarch of Canada on state and constitutional affairs. Responsible government, requires the sovereign or her viceroy, the Governor General of Canada, to always follow only that advice tendered by the Cabinet: a committee within the Privy Council composed of elected Members of Parliament; those summoned to the QPC are appointed for life by the governor general as directed by the Prime Minister of Canada, meaning that the group is composed predominantly of former cabinet ministers, with some others having been inducted as an honorary gesture. Those in the council are accorded the use of an honorific style and post-nominal letters, as well as various signifiers of precedence; the government of Canada, formally referred to as Her Majesty's Government, is defined by the Canadian constitution as the sovereign acting on the advice of the Queen's Privy Council for Canada.
The group of people is described as "a Council to aid and advise in the Government of Canada, to be styled the Queen's Privy Council for Canada," though, by convention, the task of giving the sovereign and governor general advice on how to exercise the Royal Prerogative via Orders in Council rests with by the Cabinet—a committee of the Privy Council made up of other ministers of the Crown who are drawn from, responsible to, the House of Commons in the parliament. This body is distinct but entwined within the QPC, as the President of the Queen's Privy Council for Canada customarily serves as one of its members and cabinet ministers receive assistance in the performance of their duties from the Privy Council Office, headed by the Clerk of the Privy Council. While the Cabinet deals with the regular, day-to-day functions of the Crown-in-Council, occasions of wider national importance—such as the proclamation of a new Canadian sovereign following a demise of the Crown or conferring on royal marriages—will be attended to by more senior officials in the QPC, such as the prime minister, the Chief Justice of Canada, other senior statesmen.
The quorum for Privy Council meetings is four. The Constitution Act, 1867, outlines that persons are to be summoned and appointed for life to the Queen's Privy Council by the governor general, though convention dictates that this be done on the advice of the sitting prime minister; as its function is to provide the vehicle for advising the Crown, the members of the QPC are predominantly all living current and former ministers of the Crown. In addition, the chief justices of Canada and former governors general are appointed. From time to time, the leader of Her Majesty's Loyal Opposition and heads of other opposition parties will be appointed to the QPC, either as an honour or to facilitate the distribution of sensitive information under the Security of Information Act, it is required by law that those on the Security Intelligence Review Committee be made privy councillors, if they are not already. To date, only Prime Minister Paul Martin advised that Parliamentary Secretaries be admitted to the QPC.
Appointees to the Queen's Privy Council must recite the requisite oath: I, do solemnly and sincerely swear that I shall be a true and faithful servant to Her Majesty Queen Elizabeth the Second, as a member of Her Majesty's Privy Council for Canada. I will in all things to be treated and resolved in Privy Council and declare my mind and my opinion. I shall keep secret all matters committed and revealed to me in this capacity, or that shall be secretly treated of in Council. In all things I shall do as a faithful and true servant ought to do for Her Majesty. Provincial premiers are not appointed to the QPC, but have been made members on special occasions, such as the centennial of Confederation in 1967 and the patriation of the constitution of Canada in 1982. On Canada Day in 1992, which marked the 125th anniversary of Canadian Confederation, Governor General Ramon Hnatyshyn appointed eighteen prominent Canadians to the Privy Council, including former Premier of Ontario David Peterson, retired hockey star Maurice Richard, businessman Conrad Black.
The use of Privy Council appointments as purely an honour was not employed again until 6 February 2006, when Harper advised the Governor General to appoint former Member of Parliament John Reynolds along with the new Cabinet. Harper, on 15 October 2007 advised Governor General Michaëlle Jean to appoint Jim Abbott. On occasion, non-Canadians have been appointed to the QPC; the first non-Canadian sworn of the council was Billy Hughes, Prime Minister of Australia, inducted on 18 February 1916 at the request of Robert Borden—to honour a visiting head of government, but so that Hughes could attend Cabinet meetings on wartime policy. Winston Churchill, Prime Minister of the United Kingdom, was inducted during a visit to Canada on 29 December 1941. Privy councillors are entitled to the style The Honourable or, for the prime minister, chief justice, or certain other emine
Order of St Michael and St George
The Most Distinguished Order of Saint Michael and Saint George is a British order of chivalry founded on 28 April 1818 by George, Prince Regent King George IV, while he was acting as regent for his father, King George III. It is named in honour of St Michael and St George; the Order of St Michael and St George was awarded to those holding commands or high position in the Mediterranean territories acquired in the Napoleonic Wars, was subsequently extended to holders of similar office or position in other territories of the British Empire. It is at present awarded to men and women who hold high office or who render extraordinary or important non-military service in a foreign country, can be conferred for important or loyal service in relation to foreign and Commonwealth affairs; the Order includes three classes, in descending order of seniority and rank: Knight Grand Cross or Dame Grand Cross Knight Commander or Dame Commander Companion It is used to honour individuals who have rendered important services in relation to Commonwealth or foreign nations.
People are appointed to the Order rather than awarded it. British Ambassadors to foreign nations are appointed as KCMGs or CMGs. For example, the former British Ambassador to the United States, Sir David Manning, was appointed a CMG when he worked for the British Foreign and Commonwealth Office, after his appointment as British Ambassador to the US, he was promoted to a Knight Commander, it is the traditional award for members of the FCO. The Order's motto is Auspicium melioris ævi, its patron saints, as the name suggests, are St. Michael the Archangel, St. George, patron saint of England. One of its primary symbols is that of St Michael subduing Satan in battle; the Order is the sixth-most senior in the British honours system, after The Most Noble Order of the Garter, The Most Ancient and Most Noble Order of the Thistle, The Most Illustrious Order of St Patrick, The Most Honourable Order of the Bath, The Most Exalted Order of the Star of India. The third of the aforementioned Orders—which relates to Ireland, no longer a part of the United Kingdom—still exists but is in disuse.
The last of the Orders on the list, related to India, has been in disuse since that country's independence in 1947. The Prince Regent founded the Order to commemorate the British amical protectorate over the Ionian Islands, which had come under British control in 1814 and had been granted their own constitution as the United States of the Ionian Islands in 1817, it was intended to reward "natives of the Ionian Islands and of the island of Malta and its dependencies, for such other subjects of His Majesty as may hold high and confidential situations in the Mediterranean". In 1864, the protectorate ended and the Ionian Islands became part of Greece. A revision of the basis of the Order in 1868, saw membership granted to those who "hold high and confidential offices within Her Majesty's colonial possessions, in reward for services rendered to the Crown in relation to the foreign affairs of the Empire". Accordingly, numerous Governors-General and Governors feature as recipients of awards in the order.
In 1965 the order was opened to women, with Evelyn Bark becoming the first female CMG in 1967. The British Sovereign appoints all other members of the Order; the next-most senior member is the Grand Master. The office was filled by the Lord High Commissioner of the Ionian Islands. Grand Masters include: 1818–1825: Sir Thomas Maitland 1825–1850: Prince Adolphus, Duke of Cambridge 1850–1904: Prince George, Duke of Cambridge 1904–1910: George, Prince of Wales 1910–1917: None 1917–1936: Edward, Prince of Wales 1936–1957: Alexander Cambridge, 1st Earl of Athlone 1957–1959: Edward Wood, 1st Earl of Halifax 1959–1967: Harold Alexander, 1st Earl Alexander of Tunis 1967–present: Prince Edward, Duke of KentThe Order included 15 Knights Grand Cross, 20 Knights Commanders, 25 Companions but has since been expanded and the current limits on membership are 125, 375, 1,750 respectively. Members of the Royal Family who are appointed to the Order do not count towards the limit, nor do foreign members appointed as "honorary members".
The Order has six officers. The Order's King of Arms is not a member of the College of Arms, like many other heraldic officers; the Usher of the Order is known as the Lady Usher of the Blue Rod. Blue Rod does not, unlike the usher of the Order of the Garter, perform any duties related to the House of Lords. Prelate – The Rt. Rev. David Urquhart Chancellor – Rt Hon. Lord Robertson of Port Ellen Secretary – Sir Simon McDonald Registrar – Sir David Manning King of Arms – Sir Jeremy Greenstock Lady Usher of the Blue Rod – Dame DeAnne Julius Members of the Order wear elaborate regalia on important occasions, which vary by rank: The mantle, worn only by Knights and Dames Grand Cross, is made of Saxon blue satin lined with crimson silk. On the left side is a representation of the star; the mantle is bound with two large tassels. The collar, worn only by Knights and Dames Grand Cross, is made of gold, it consists of depictions of crowned lions, Maltese Crosses, the cyphers "SM" and "SG", all alternately.
In the centre are two winged lions, each holding a book and seven arrows. At less important occasions, simpler insignia are used: The star is an insignia used only by Knights and Dames Grand Cross and Knights and Dames Commanders, it is worn pinned to the left breast. The Knight and
The Honourable Society of Gray's Inn known as Gray's Inn, is one of the four Inns of Court in London. To be called to the bar and practise as a barrister in England and Wales, a person must belong to one of these Inns. Located at the intersection of High Holborn and Gray's Inn Road in Central London, the Inn is both a professional body and a provider of office accommodation for many barristers, it is ruled by a governing council called "Pension", made up of the Masters of the Bench, led by the Treasurer, elected to serve a one-year term. The Inn is known for its gardens, or Walks, which have existed since at least 1597. Gray's Inn does not claim a specific foundation date. Law clerks and their apprentices have been established on the present site since at least 1370, with records dating from 1381. During the 15th and 16th centuries, the Inn grew with great prestige, reaching its pinnacle during the reign of Elizabeth I; the Inn was home to many important barristers and politicians, most notably Francis Bacon, counted Elizabeth herself as a patron.
Thanks to the efforts of prominent members such as William Cecil and Gilbert Gerard, Gray's Inn became the largest of the four by number, with over 200 barristers recorded as members. During this period, the Inn became noted for the masques and revels that it threw, William Shakespeare is believed to have first performed The Comedy of Errors there; the Inn continued to prosper during the reign of James I and the beginning of that of Charles I, when over 100 students per year were recorded as joining. The outbreak of the First English Civil War in 1642 during the reign of Charles I disrupted the systems of legal education and governance at the Inns of Court, shutting down all calls to the Bar and new admissions, Gray's Inn never recovered. Fortunes continued to decline after the English Restoration, which saw the end of the traditional method of legal education. Although now more prosperous, Gray's Inn is today the smallest of the Inns of Court. Gray's Inn and the other three Inns of Court remain the only bodies allowed to call a barrister to the Bar, allowing him or her to practise in England and Wales.
Although the Inn was a disciplinary and teaching body, these functions are now shared between the four Inns, with the Bar Standards Board acting as a disciplinary body and the Inns of Court and Bar Educational Trust providing education. The Inn remains a collegiate self-governing, unincorporated association of its members, providing within its precincts library, dining and office accommodation, along with a chapel. Members of the Bar from other Inns may use these facilities to some extent. During the 12th and early 13th centuries, the law was taught in the City of London by the clergy. Two events happened which ended the Church's role in legal education: firstly, a papal bull that prohibited the clergy from teaching the common law, rather than canon law; the common law began to be practiced and taught by laymen instead of clerics, these lawyers migrated to the hamlet of Holborn, just outside the City and near to the law courts at Westminster Hall. The early records of all four Inns of Court have been lost, it is not known when each was founded.
The records of Gray's Inn itself are lost until 1569, the precise date of founding cannot therefore be verified. Lincoln's Inn has the earliest surviving records. Gray's Inn dates from at least 1370, takes its name from Baron Grey of Wilton, as the Inn was Wilton's family townhouse within the Manor of Portpoole. A lease was taken for various parts of the inn by practising lawyers as both residential and working accommodation, their apprentices were housed with them. From this the tradition of dining in "commons" by using the inn's main hall, followed as the most convenient arrangement for the members. Outside records from 1437 show that Gray's Inn was occupied by socii, or members of a society, at that date. In 1456 Reginald de Gray, the owner of the Manor itself, sold the land to a group including Thomas Bryan. A few months the other members signed deeds of release, granting the property to Thomas Bryan. Bryan acted as either a feoffee or an owner representing the governing body of the Inn but in 1493 he transferred the ownership by charter to a group including Sir Robert Brudenell and Thomas Wodeward, reverting the ownership of the Inn back to the Gray family.
In 1506 the Inn was sold by the Gray family to Hugh Denys and a group of his feoffees including Roger Lupton. This was not a purchase on behalf of the society and after a five-year delay, it was transferred under the will of Denys in 1516 to the Carthusian House of Jesus of Bethlehem, which remained the Society's landlord until 1539, when the Second Act of Dissolution led to the Dissolution of the Monasteries and passed ownership of the Inn to the Crown. During the reign of Elizabeth I, Gray's Inn rose in prominence, that period is considered the "golden age" of the Inn, with Elizabeth serving as the Patron Lady; this can be traced to the actions of Nicholas Bacon, William Cecil and Gilbert Gerard, all prominent members of the Inn and confidantes of Elizabeth. Cecil and Bacon in particular took pains to find the most promising young men and get them to join the Inn. In 1574 it was the largest of all the
Osgoode Hall Law School
Osgoode Hall Law School shortened to Osgoode, is the law school of York University in Toronto, Canada. The school was founded by the Law Society of Upper Canada, named for William Osgoode, an Oxford University graduate and barrister of Lincoln's Inn, the first to serve as the Chief Justice of Upper Canada; the school signed an agreement of affiliation with York University in 1965 following a decision by the provincial government requiring all law schools to be affiliated with a university. It was located at Osgoode Hall in downtown Toronto, which houses the headquarters of the Law Society, relocated to York University's Keele Campus in 1969; the law school is home to the Law Commission of the Osgoode Hall Law Journal. Osgoode hosts Professional Development Programs which are located in downtown Toronto at 1 Dundas St. near the original Osgoode Hall building. A variety of LL. M. and Ph. D. degrees in law are available. Its alumni include three Canadian Prime Ministers and ten Justices of the Supreme Court of Canada, four of whom were Chief Justices.
The current dean of the law school is Mary Condon. QS world university rankings 2018 places Osgoode Hall Law School in the bracket of 51st to 100th top law schools in the world. Maclean's magazine has ranked Osgoode second amongst Canadian law schools in 2011, 2012 and 2013. In the 2008 rankings published by Canadian Lawyer Magazine, Osgoode was ranked first in Canada, was awarded high marks for the quality of its professors, flexible curriculum, the diversity and relevance of course offerings. For its first eight decades, Osgoode Hall Law School was located at Osgoode Hall at the corner of Queen Street and University Avenue; the structures at Queen and University are still known as Osgoode Hall. They remain the headquarters of the Law Society of Upper Canada and house the Court of Appeal for Ontario; the law school is located on the Keele Campus of York University, in the Toronto suburb of North York. In May 2007, Dean Monahan announced plans for an extensive renovation and extension of Osgoode Hall Law School involving a renovation of the existing building, the addition of an additional wing.
The building was designed by architect Jack Diamond with the construction of the renovated building beginning in the summer of 2009. The project had been majorly funded by a $2.5 million gift by Ignat Kaneff, the building has been renamed in his honor. The law school is referred to by York as its faculty of law. Osgoode's Professional Development offices and classrooms are based at 1 Dundas Street West in Downtown Toronto, overlooking Yonge-Dundas Square; the Legal & Literary Society, Osgoode Hall Law School's official student society, coordinates student activities both on and off campus. The organization funds over fifty student clubs, as well as the student newspaper, Obiter Dicta. John Robert Cartwright, former Chief Justice Peter Cory, former Puisne Judge and former Chancellor of York University Sir Lyman Duff, former Chief Justice Frank Joseph Hughes, former Puisne Judge Wilfred Judson, former Puisne Judge Andromache Karakatsanis, current Puisne Judge Patrick Kerwin, former Chief Justice Bora Laskin, former Chief Justice Malcolm Rowe, current Puisne Judge Wishart Spence, former Puisne Judge John Arnup, Moderator for United Church of Canada, Justice at Ontario Court of Appeal George Ethelbert Carter Kim Carter, Chief Military Judge of the Canadian Forces Marcel Crête, jurist and Chief Justice of Quebec Bud Cullen, Judge at Federal Court of Canada Charles Dubin, former Chief Justice of Ontario Daniel Dumais, Emeritus Lawyer distinction from Barreau du Quebec, Puisne Judge of Superior Court of Quebec Asher Grunis, President of the Supreme Court of Israel Sydney Harris, activist lawyer and judge, President of the Canadian Jewish Congress Bill Hastings, Chief Censor of New Zealand, District Court Judge of New Zealand Russell G. Juriansz, first South Asian appointed to Ontario Court of Appeal Harry S. Laforme, Justice at Ontario Court of Appeal Patrick LeSage, Chief Justice of Ontario Superior Court of Justice Malcolm Archibald Macdonald, Chief Justice of British Columbia Mark MacGuigan, Attorney General of Canada, Justice of the Federal Court of Appeal Goldwyn Arthur Martin, QC, Justice at Ontario Court of Appeal Roy McMurtry, Chief Justice of Ontario, Attorney General of Ontario, Canadian High Commissioner to the United Kingdom James Chalmers McRuer, Ontario Court of Appeal, Chief Justice at High Court of Justice of Ontario Charles Terrence Murphy, Judge at Ontario Superior Court, President of North Atlantic Assembly Dennis O'Connor, Associate Chief Justice of Ontario James O'Reilly, Federal Court Judge Coulter Osborne, Associate Chief Justice of Ontario John Richard, NAFTA Adjudicator, Chief Justice of the Federal Court of Appeal Charles Stuart, Justice of the Supreme Court of Alberta Michael Tulloch, Justice at the Ontario Court of Appeal Karen M. Weiler, past Judge Court Martial Appeal Court of Canada, Justice at Ontario Court of Appeal Sharon A. Williams, Judge ad litem at the International Criminal Tribunal for the Former Yugoslavia Warren Winkler, Chief Justice of Ontario Willy Mutunga, former Chief Justice of Kenya Sir John A. Macdonald William Lyon Mackenzie King Arthur Meighen Bill Davis, 18th Premier of Ontario George Drew, 14th Premier of Ontario Ernie Eves, 23rd Premier of Ontario Howard Ferguson, 9th Premier of Ontario Leslie Frost, 16th Premier of Ontario William Howard Hearst, 7th Premier of Ontario Rachel Notley, 17th Premier of Alberta John Robarts, 17th Premier of Ontario John Black Aird, former Lieutenant Governor of Ontario, Canadian Senator and founding partner of Aird & Berlis LLP Lincoln Alexander, 24
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