Life History of MATHEMATICIANS OF Egypt and England

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Contents

WHAT IS A MATHAMETICS ? HISTORY OF MATHEMATICS. MATHEMATICIANS OF ENGLAND. Life History of MATHEMATICIANS

OF ENGLAND. MATHEMATICIANS OF EGYPT. Life History of MATHEMATICIANS OF EGYPT.

WHAT IS A MATHEMATHICS ?ANS Mathematics is the abstract science of

numbers, quantity and space. Mathematics is the body of knowledge centered on such concepts as quantity, structure, space and change, and also the academic discipline that studies them.

HISTORY OF MATHEMATHICS• This section is on the history of mathematicians. For a history of mathematics in

general, see History of mathematics.• In 1938 in the United States, mathematicians were desired as teachers,

calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians.

• One of 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' Theorem.

• The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".

MATHEMATICIANS of ENGLAND

NAME Famous mathematician of ENGLAND1) John Laden2) John Coach Adams3) George Boole

HISTORY OF JOHN LANDEN (MATHEMATICIAN OF ENGLAND)

• Life• He was born at Peakirk, near Peterborough in

Northamptonshire, on 28 January 1719. He was brought up to the business of a surveyor, and acted as land agent to Earl Fitzwilliam, from 1762 to 1788. Cultivating mathematics during his leisure hours, he became a contributor to the Ladies' Diary in 1744, published Mathematical Lucubrations in 1755, and from 1754 onwards communicated to the Royal Society valuable investigations on points connected with the fluxionary calculus.

WORK OF JOHN LANDEN

WORKS• The Ladies' Diary, various communications (1744-1760)• papers in the Phil. Trans. (1754, 1760, 1768, 1771, 1775,

1777, 1785)• Mathematical Lucubrations (1755)• A Discourse concerning the Residual Analysis (1758)• The Residual Analysis, book i. (1764)• Animadversions on Dr Stewarts Method of computing the

Sun's Distance from the Earth (1771)• Mathematical Memoirs (1780, 1789

JOHN COACH ADAMS• Born 5 June 1819

Laneast, Launceston, Cornwall, United Kingdom Died 21 January 1892 (aged 72)Cambridge ObservatoryCambridgeshire, England Nationality British Fields MathematicsAstronomy Institutions University of St. AndrewsUniversity of Cambridge Academic advisors John Hymers Notable awards Smith's Prize (1843)Copley Medal (1848)Gold Medal of the Royal Astronomical Society (1866}

•

GEORGE BOOLE• Born 2 November 1815

Lincoln, Lincolnshire, England Died 8 December 1864 (aged 49)Ballintemple, County Cork, Ireland Nationality British Religion Unitarian Era 19th-century philosophy Region Western Philosophy School Mathematical foundations of computing

• Main interests• Mathematics, Logic, Philosophy of mathematics • Notable ideas• Boolean algebra•

EARLY LIFE OF GEROGE BOOLE • Early life• Boole was born in Lincolnshire, England. His father, John Boole

(1779–1848), was a tradesman in Lincoln and gave him lessons. He had a primary school education, but little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. At age 16 Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster at Heigham's School. He taught briefly in Liverpool.

• Boole participated in the local Mechanics Institute, the Lincoln Mechanics' Institution, which was founded in 1833.Edward Bromhead, who knew John Boole through the institution, helped George Boole with mathematics books and he was given the calculus text of Sylvestre François Lacroix by the Rev. George Stevens Dickson of St Swithin's Lincoln. Without a teacher, it took him many years to master calculus.

HONOURS AND AWARDS

• Boole was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857. He received honorary degrees of LL.D. from the University of Dublin and Oxford University.

ALBERT EDWARD INGHAM

MAIN DEATAILSALBERT EDWARD INGHAM WAS BORN ON 3 APRIL 1900.HE WAS BORN IN NORTHAMPTON,

ENGLAND.HE DIED AT 6 SEPTEMBER 1967 IN CHAMONIX,

FRANCE.

About ALBERT EDWARD INGHAM

EARLY LIFEAlbert Ingham’s father was Albert Edward Ingham

( born about 1875 in Northampton) who was a foreman in a boot manufacturing factory . His mother was Annie Gertrude Ingham (born about 1876 in Northampton) Albert Edward Ingham (our mathematician) had an older brother Christopher Augustus (born about 1897), and two younger sister Phyllis Gertrude ( born about 1904) and Lilian Grace ( born about 1910)

SCHOOL LIFE OF ALBERT EDWARD INGHAMAlbert Ingham was educated at Stafford Grammar School, and

from there he won a scholarship to Trinity College, Cambridge, in December 1917. After spending a few months in the army towards the end of World war I, he began his studies in January 1919. An outstanding undergraduate career saw him awarded distinction in the mathematical Tripos and win a Smith’s prize and the highest honours. In 1922 he was elected to a fellowship at Trinity for a dissertation on the zeta function and his next four years were occupied only with research, a few months of which were spent at Gottingen. During this time Ingham was greatly influenced by Littlewood who gave him the advice to:-

….. Work at a hard problem: you may not solve it but you’ll solve another one.

COLLEGE LIFE OF ALBERT EDWARD INGHAM

In 1926 Ingham was appointed a Reader at Leeds University but four years later returned to Cambridge as a university lecturer and a Fellow of King’s College, on the death of Ramsey, and remained there for the rest of his life. He was elected a Fellow of the Royal Society in 1945 and became a Reader in Mathematical Analysis in 1953.

HOW HE DIED?

He died while on a walking holiday in the mountains. He and his wife Rose Marie Tuper-Carey whom he married in 1932 , had taken his type of holiday every summer for many years.

DAVID GEORGE KENDALL

MAIN DETAILSDavid George Kendall was born on 15 January

1918 in Ripon, Yorkshire, England.He died on 23 October 2007 in Cambridge,

England.

Early life of David George KendallDavid Kendall attended Ripon Grammar School

and then entered Queen’s College, Oxford. He was awarded his M.A. in 1943 but he had already been involved in war work. During these this year of World War II Kendall worked as an Experimental Officer with the Ministry of Supply from 1940 until the end of the war in 1945.Other mathematicians such as Rogers also held similar posts with the Ministry of Supply.

College Life of David George Kendall

In 1946 Kendall was elected a fellow of Magdalen College, Oxford and appointed a lecturer in Mathematics. He spent the Academic Year 1952-53 in the United States as a visiting lecture at Princeton University. Then in 1962 Kendall was appointed as Professor of Mathematical Statics at the University of Cambridge. At the same time he was elected a fellow of Churchill College Cambridge. Kendall held this chair of Mathematical Statistics until he retired in 1985 and which time he became professor emeritus. He also became an Emeritus Fellow of Magdalen College, Oxford in 1989.

WORKS OF DAVID GEORGE KENDALL

Kendall is a leading authority on applied probability and data analysis . He has written on stochastic geometry and its applications, and the statistical theory of shape . His recent work includes two articles How to look at object in a five-dimensional shape space (1994-95) and The Riemannian structure of Euclidean shape spaces: a novel environment for statistics (1993).

EDWARD FOYLE COLLONGWOOD

MAIN DETAILSHe was born on 17 January 1900 in Alnwick,Northumberland, England. He died at 25 October 1970 in Alnwick ,

Norththumberland ,England .

EARLY LIFE OF EDWARD FOYLE COLLINGWOOD

Edward Collingwood’s parents were Dorothy Fawcett and Colonel Cuthbert George Collingwood .Colonel Collingwood had a career in the army ,commanding the Lancashire-Fusiliers in the battle the Anglo –Egyptian force commanded by Kitchener defected the Mahdists and established British dominance in Sudan . Colonel Collingwood retired from army in 1899, the year before his son Edward was born on the family of Lilburn Tower. The estate is in Northumberland in the north of England about 7 km from Wooler on the road to Alnwick (which is about 20 KM to the south east). Edward was the oldest of his parents four children, all boys, and he was brought up on the family estate enjoying.

EDUCATION OF EDWARD FOYLE COLLINGWOOD

Collingwood was educated at the Royal Naval College Osborne , which he entered in 1913 moving to Dartmouth in the following year. He joined the Navy and became a midshipman in 1915 on the ship HMS Collingwood. This ship was named after Vice- Admiral Cuthbert Collingwood who was Nelson’s second in command at the battle of Trafalgar. Vice-Admiral Collingwood was the brother of Edward.

BIOGRAPHY OF COLLINGWOOD

Collingwood’s great – grandfather , and it was no coincidence that Collingwood served on HMS Collingwood for special arrangements had been made for this to happen. However Collingwood’s naval career came to an end when he fell down a hatchway on board ship, broke his wrist and damaged his knee, just before the battle of Jutland. He was transferred to the hospital ship, then invalided out of the Navy. Attempting to go to Woolwich he failed to the medical examination so, in 1918 , he entered Trinity College , Cambridge to study mathematics.

BIOGRAPHY OF COLLINGWOOD• Collingwood became involved with hospital boards in Newcastle, being a founder

member of the Newcastle Regional Hospital Board and its chairmen from 1953 to 1968, then later he was involved with medical affairs on a national and international level. He was vice-president of the International Hospital Federation from 1959 to 1967, a member of the medical research council from 1960 to 1968, and he served on the royal commission on medical education from 1965 to 1968. He was chairman of the Council of Durham University for most of the 1950's and 1960's.

• He was elected to a fellowship of the Royal Society in 1965. He also served the London Mathematical Society in many ways, as a member of the Council and as Treasurer. He wrote an article in 1951 to mark the centenary of the Society. He was knighted in 1962.

• Despite these numerous activities Collingwood still found time for various hobbies. In particular he had a fine collection of eighteenth century paintings, and a collection of Chinese porcelain. As with all his activities Collingwood made a deep study of his hobbies and became a recognized expert on Chinese porcelain.

HOW EDWARD FOYLE COLLINGWOOD MADE MATHEMATICIANS.

Collingwood was influenced by his advisor of studies, Hardy at Cambridge and decided early on that he would undertake research in mathematics . He was also influenced by Littlewood ,but his examination performance was relatively poor and he obtained only a Second Class degree in 1922. Although there were many others in Collingwood‘s year at Cambridge like Burkill Ingham and Newman, he seems to have had little contact with them .A friend, Gilbert Ashton ,writing of these days ,wrote that Collingwood was:-

…always known by his friends and cotemporaries of Trinity as ‘The Admircal’… I remember The Admircal as a quiet , reserved and rather shy person…

WORKS OF EDWARD FOYLE COLLINGWOOD

• He was in charge of the Sweeping Division in 1943, then Chief Scientist in the Admiralty Mine Design Department in 1945. For his war work he was awarded the C.B.E. and received the Legion of Merit from the USA in 1946.

• After the war he returned to his researches on meromorphic functions, publishing an important paper in 1949. He then undertook research work with Mary Cartwright on the theory of cluster sets. Mary Cartwright writes:-

• I tried to contribute what I could to this paper ... my impression is that it was much less than his contribution. I also collaborated in one later paper published in 1961 on an allied topic. ... I found myself quite unable to grasp the deep results in the theory of sets of points on which much of Collingwood's later work in this field depended.

HOW IS CHARACTER IS DESCRIBED?

Collingwood was loved and admired both for his achievements and for the delight of his company. ... he had great intellectual powers which enabled him to achieve excellence in diverse activities conducted in parallel and not in series. Born in Glendale in Northumberland he remained a countrymen at heart with practical knowledge of forestry, farming and gardening. ... He remained a bachelor to the grief of the many dancing partners who had been entranced by his waltzing!

Honours awarded to Edward Collingwood

• Fellow of the Royal Society of Edinburgh 1954 BMC morning speaker 1956 Fellow of the Royal Society 1965 LMS President1969 - 1970

Alfred Goldie• Alfred William Goldie (December 10, 1920, Coseley, Staffordshire – October

8, 2005, Barrow-in-Furness, Cumbria) was an English Mathematician.• Goldie was educated at Wolverhampton Grammar School and then read

Mathematics at St John's College, Cambridge. His studies were interrupted by war work on ballistics with the Armament Research Department of the Ministry of Supply, eventually taking his BA in 1942 and MA in 1946.

• Goldie became an Assistant Lecturer at the University of Nottingham in 1946. In 1948 he was appointed Lecturer in Pure Mathematics at what was then King's College, Durham (and has been the University of Newcastle upon Tyne since 1963) where he was promoted to Senior Lecturer in 1958 and Reader in Algebra in 1960.

• In 1963 Goldie was appointed Professor of Pure Mathematics at the University of Leeds. He retired from his chair in 1986 with the title Emeritus Professor.

ABOUT Alfred Goldie• Goldie won the 1970 Senior Berwick Prize from the

London Mathematical Society, where he also became Vice-President from 1978-80.

• Goldie worked in ring theory where he introduced the notion of the uniform dimension of a module, and the reduced rank of a module. He is well known for Goldie's theorem, which characterizes right Goldie rings. Indeed, his Independent obituary described him as the "Lord of the Rings".

• Goldie married Mary Kenyon in 1944. They had one son, John, and two daughters, Isobel and Helen. Mary died in 1995 and in 2002 he married Margaret Turner who survived him.

Alfred Goldie's father

Worked as a skilled fitter at Austin Motors, the car manufacturers. The factory employed 1 500 skilled workers serving 15 000 unskilled labourers. The former were responsible for preparing the brass templates used for the accurate positioning of the holes for the screws that held together the various parts of the car. Templates were prepared for new models every two years, and had to be accurate to one thousandth of an inch. The skilled workers often had little work to do, as the actual drilling was done by the unskilled employees.

SCHOOL LIFE OF Alfred Goldie • Alfred attended Wolverhampton Grammar School where he won a scholarship to

St John's College, Cambridge. He entered Cambridge in 1939 just days after World War II began. His scholarship allowed him to complete the usual three year degree in only two years and, indeed, he obtained a First in Part II of the mathematical tripos in 1941. During these two years at Cambridge he was in the Officers Training Corps, and he also took an interest in politics taking a left wing Communist position.

• Because of the war, Goldie did not continue to Part III of the tripos but instead was interviewed for a military position by C P Snow, the novelist, who was acting as scientific adviser to the British Government. Snow realized that, despite Goldie's training in the Officers Training Corps, he would make a more valuable contribution to the war effort using his mathematical skills in Ballistic Research. He was sent to work under C A Clemmow in Cambridge, but soon the Ballistic Research team moved to Shrewsbury. He also spent time at a military base near Glasgow, then towards the end of the war he was sent to the Woolwich Arsenal in London. In October 1944 he married Mary Kenyon; they had one son and two daughters. As the war drew to a close he began to think about restarting his mathematical education

HOW HE CHARACTER IS DESCRIBED

He was a vivid personality with an individual mind, full of opinions and strongly argued positions on mathematics but also on the wider world, including politics, where his views moved rightwards over the years - starting with Communism whilst a student at Cambridge, and ending well within traditional Conservatism. ... Alfred Goldie was a very practical man, particularly enjoying working with wood. He also had a love of the outdoors, which he shared with his first wife, Mary, a geographer. Despite somewhat incompatible personalities, they still managed to give their three children a stable and happy upbringing.

John Wallis

MAIN DETAILS OF JOHN WALLISHe was born on 23 November 1616 in Ashford,

Kent, England.He died on 28 October 1703 in Oxford, England.

EARLY LIFE OF JOHN WALLIS• John Wallis's father was the Reverend John Wallis who had

become a minister in Ashford in 1602. He was a highly respected man known widely in the area. The Reverend Wallis married Joanna Chapman, who was his second wife, in 1612 and John was the third of their five children. When young John was about six years old his father died.

• John went to school in Ashford but an outbreak of the plague in the area led to his mother to decide that it would be best for him to move away. He went to James Movat's grammar school in Tenterden, Kent, in 1625 where he first showed his great potential as a scholar. Writing in his autobiography, Wallis comments

SCHOOL LIFE OF JOHN WALLIS

However he spent 1631-32 at Martin Holbeach's school in Felsted, Essex, where he became proficient in Latin, Greek and Hebrew. He also studied logic at this school but mathematics was not considered important in the best schools of the time, so Wallis did not come in contact with that topic at school. It was during the 1631 Christmas holidays that Wallis first came in contact with mathematics when his brother taught him the rules of arithmetic. Wallis found that mathematics .

COLLEGE LIFE OF JOHN WALLIS• From school in Felsted he went to Emmanual College Cambridge,

entering around Christmas 1632. He took the standard bachelor of arts degree and, since nobody at Cambridge at this time could direct his mathematical studies, he took a range of topics such as ethics, metaphysics, geography, astronomy, medicine and anatomy. Although never intending to follow a career in medicine, he defended his teacher Francis Glisson's revolutionary theory of the circulation of the blood in a public debate, being the first person to do so.

• In 1637 Wallis received his BA and continued his studies receiving his Master's Degree in 1640. In the same year he was ordained by the bishop of Winchester and appointed chaplain to Sir Richard Darley at Butterworth in Yorkshire. Between 1642 and 1644 he was chaplain at Hedingham, Essex and in London. It was during this time that the first of two events which shaped Wallis's future took place:-

Honours awarded to John Wallis

Fellow of the Royal Society Biography in Aubrey's Brief Lives Popular biographies list

MATHEMATICIAMS OF EGYPT

• ABU KAMIL SHUJA• HYSPSICLES• EUCLID• SERENUS

ABU KAMIL SHUJA

MAIN DETAILS OF ABU KAMIL SHUJAHe born on about 850 in (possibly) EgyptHe died about 930

ABOUT ABU KAMIL SHUJA • Abu Kamil Shuja is sometimes known as al-Hasib al-Misri, meaning the

calculator from Egypt. Very little is known about Abu Kamil's life - perhaps even this is an exaggeration and it would be more honest to say that we have no biographical details at all except that he came from Egypt and we know his dates with a fair degree of certainty.

• The Fihrist (Index) was a work compiled by the bookseller Ibn an-Nadim around 988. It gives a full account of the Arabic literature which was available in the 10th century and it describes briefly some of the authors of this literature. The Fihrist includes a reference to Abu Kamil and among his works listed there are: (i) Book of fortune, (ii) Book of the key to fortune, (iii) Book on algebra, (vi) Book on surveying and geometry, (v) Book of the adequate, (vi) Book on omens, (vii) Book of the kernel, (viii) Book of the two errors, and (ix) Book on augmentation and diminution. Works by Abu Kamil which have survived, and will be discussed below, include Book on algebra, Book of rare things in the art of calculation, and Book on surveying and geometry.

ABOUT ABU KAMIL SHUJA • Although we know nothing of Abu Kamil's life we do understand

something of the role he plays in the development of algebra. Before al-Khwarizmi we have no information of how algebra developed in Arabic countries, but relatively recent work by a number of historians of mathematics as given a reasonable picture of how the subject developed after al-Khwarizmi. The role of Abu Kamil is important here as he was one of al-Khwarizmi's immediate successors. In fact Abu Kamil himself stresses al-Khwarizmi's role as the "inventor of algebra". He described al-Khwarizmi as (see for example [4] or [5]):-

• ... the one who was first to succeed in a book of algebra and who pioneered and invented all the principles in it.

• Again Abu Kamil wrote:- • I have established, in my second book, proof of the authority and

precedent in algebra of Muhammad ibn Musa al-Khwarizmi, and I have answered that impetuous man Ibn Barza on his attribution to Abd al-Hamid, whom he said was his grandfather.

ABOUT ABU KAMIL SHUJA

Abu Kamil had begun to understand what we would write in symbols as xnxm = xn+m. For example he uses the expression "square square root" for x5 (i.e. x2.x2.x), "cube cube" for x6 (i.e. x3.x3), "square square square square" for x8 (i.e. x2.x2.x2.x2). In fact Abu Kamil works easily with the powers up to x8 which appear in the text. The algebra contains 69 problems which include many of the 40 problems considered by al-Khwarizmi, but with a rather different approach to them.

WORKS OF ABU KAMIL SHUJA

The work also deals with circles and here Abu Kamil takes π = 22/7. A whole section is devoted to calculating the area of the segment of a circle. The final part of the work gives rules for calculating the side of regular polygons of 3, 4, 5, 6, 8, and 10 sides either inscribed in, or circumscribed about, a circle of given diameter. For the pentagon and decagon the rules which Abu Kamil gives, although without proof in this work, were fully proved in his algebra book.

Hypsicles of Alexandria

MAIN DETAILS OF Hypsicles of AlexandriaHe was born on about 190 BC in Alexandria,

Egypt.He died on about 120 BC.

About Hypsicles of Alexandria • Hypsicles of Alexandria wrote a treatise on regular polyhedra. He is the

author of what has been called Book XIV of Euclid's Elements, a work which deals with inscribing regular solids in a sphere.

• What little is known of Hypsicles' life is related by him in the preface to the so-called Book XIV. He writes that Basilides of Tyre came to Alexandria and there he discussed mathematics with Hypsicles' father. Hypsicles relates that his father and Basilides studied a treatise by Apollonius on a dodecahedron and an icosahedron in the same sphere and decided that Apollonius's treatment was not satisfactory.

• In the so-called Book XIV Hypsicles proves some results due to Apollonius. He had clearly studied Apollonius's tract on inscribing a dodecahedron and an icosahedron in the same sphere and clearly had, as his father and Basilides before him, found it poorly presented and Hypsicles attempts to improve on Apollonius's treatment.

About Hypsicles of Alexandria • Arab writers also claim that Hypsicles was involved with the so-called Book

XV of the Elements. Bulmer-Thomas writes in [1] that various aspects are ascribed to him, claiming that either:-

• ... he wrote it, edited it, or merely discovered it. But this is clearly a much later and much inferior book, in three separate parts, and this speculation appears to derive from a misunderstanding of the preface to Book XIV.

• Diophantus quotes a definition of polygonal number due to Hypsicles (see either [1] or [2]):-

• If there are as many numbers as we please beginning from 1 and increasing by the same common difference, then, when the common difference is 1, the sum of all the numbers is a triangular number; when 2 a square; when 3, a pentagonal number [and so on]. And the number of angles is called after the number which exceeds the common difference by 2, and the side after the number of terms including 1.

• This says that, in modern notation, the nth m-agonal number is • n [2 + (n - 1) (m - 2)]/2.

WORK OF Hypsicles of Alexandria • The work which involves arithmetic progressions is

Hypsicles' On the Ascension of Stars. In this work he was the first to divide the Zodiac into 360°. He says (see [1] or [2]):-

• The circle of the zodiac having been divided into 360 equal arcs, let each of the arcs be called a spatial degree, and likewise, if the time taken by the zodiac circle to return from a point to the same point is divided into 360 equal times, let each of the times be called a temporal degree.

• Hypsicles considers two problems in this work [2]:-. • (i) Given the ratio of the longest to the shortest day at any

place, how long does it take any given sign of the zodiac to rise there?(ii) How long does it take any given degree in a sign to rise?

MISTAKES OF Hypsicles of Alexandria

The mistake which Hypsicles makes is to assume that the rising times form an arithmetical progression. Having made this assumption his results are correct and Neugebauer certainly values this work much more highly than Heath does. In fact without the aid of the sine function and trigonometry it is hard to see how Hypsicles could have done better.

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