Mathematics and Mathematicians at St John's: an exhibition to mark the centenary of the Adams Society
This exhibition celebrates mathematics and mathematicians at St John's. The College has a long tradition of teaching and learning in mathematics, and has produced many notable mathematicians over the years. This exhibition showcases some of the key books and individuals in this tradition. It has been timed to coincide with the centenary of the Adams Society, named after John Couch Adams, who was able to determine the existence and position of the planet Neptune solely by mathematical calculations based on Newtonian principles.
Euclid 1482
The first printed edition of Euclid's Elementa geometrie was published in Venice in 1482. It is printed in Latin, the common language of scholarly works across Europe. It contains the earliest ever printed mathematical diagrams, and is a stunning example of early printing technology. The opening page is adorned with a highly decorative woodcut border, with the title printed in red. Large decorated initials mark the beginnings of each section. The layout of the volume echoes that used in medieval manuscripts. Wide margins allow space for the geometrical diagrams which illustrate the text throughout the volume.
The copy at St John's was given to the Library in 1885 by Richard Pendlebury.
Euclid 1570
The first English edition of Euclid was published in 1570. It was translated by Henry Billingsley, and the preface was written by John Dee. Both men were Johnians. In his preface to Euclid, Dee put forward a defence of mathematics, which was often viewed with suspicion in Tudor times as being allied to magic. Numbers, after all, allowed people to deduce from calculations that which they could not see.
Brook Taylor
One of the leading English mathematicians of his age, Brook Taylor was on the panel that adjudicated between Isaac Newton and Gottfried Leibniz as to who had invented infinitessimal calculus (1712). He was awarded his doctorate the year before he published this work. In it he established the branch of mathematics now known as the calculus of finite differences, and first published his famous theorem, although the full importance of the latter was not grasped until over fifty years later by Lagrange who proclaimed it the principal foundation of differential calculus.
This copy came to the College Library as a gift from another prominent Johnian mathematician, Sir Joseph Larmor.
Mathematical reform
The Analytical Society was established in 1812 by a group of Cambridge students to promote the use of Gottfried Leibnitz's notation for differentiation in calculus, rather than Newton's rather cumbersome symbols. The group was led by Charles Babbage, along with George Peacock, and the Johnian John Herschel. The bill for printing the Analytical Society's memoirs was made out to Herschel, and he contributed an article. The three also published a translation of LaCroix's treatise on calculus in 1816 using the new notation, and it was not long before it was adopted in Cambridge for mathematical examinations.
John Couch Adams
John Couch Adams was born on the 5th of June 1819 in Cornwall, the son of a poor tenant farmer. Few of his peers would have dreamed of studying at Cambridge and becoming a renowned astronomer, but John had some advantages. His mother had received an education from her uncle, John Couch, who had left her his personal library, which included works on astronomy. It was a household where education was valued. Having learned Greek and algebra at a nearby village school, at the age of 12 John moved to a private school run by his cousin, the Reverend John Couch Grylls. There he learned classics, and taught himself mathematics. Adams arrived at St John’s in 1839 having won a scholarship. He was entered as a sizar, the poorest category of student. At St John’s Adams excelled in all subjects. He won the first prize in Greek testament every year. He graduated Senior Wrangler (ie first in the whole University in Mathematics) and first Smith’s prizeman in 1843, and was elected a Fellow of the College.
The discovery of Neptune
Whilst still an undergraduate, Adams noticed that not all of the planets were behaving quite as he would have expected. Something was causing the planet Uranus to move curiously. He suspected the presence of a hitherto unknown planet was exerting a gravitational force. He wrote a note to remind himself that once his examinations were safely out of the way he should investigate.
Adams’s calculations to determine the position of the unknown planet are preserved in a manuscript volume (now designated MS W.16) in St John’s College Library. Adams made six separate solutions of the problem.
This page shows the conclusion of his first solution, made in the Long Vacation of 1843. At the foot of the page he lists the elements of the new planet. By September 1845 he was able to communicate his fourth solution to Challis at the Cambridge Observatory, while the fifth went to the Astronomer Royal, requesting that a search be instigated to prove the existence of the planet by observation. Adams retained much of his methology in his head, only noting down the necessary calculations with the minimum of explanation. His failure to provide evidence for his methods was one of the contributory factors in the delay before observations were finally carried out in the summer of 1846 to confirm his predictions. Concurrently and independently in Paris, Le Verrier was coming to the same conclusions, and published his own predictions in June 1846, initially being given full credit for the discovery.
Adams's later career
In 1848 the Royal Society bestowed its highest award, the Copley Medal, upon Adams in recognition of his discovery of Neptune. Queen Victoria offered Adams a knighthood the same year, but he declined the honour.
Adams became a Fellow of Pembroke in 1853. From 1859 until his death, Adams held the post of Lowndean Professor in the University of Cambridge.
[Institute of Astronomy Library, reproduced under a creative commons licence.]
In 1860, Adams was persuaded to take on the prestigious post of superintendent of the Cambridge Observatory, though only once funding had been put in place for an experienced assistant. Adams took on the role on condition that he should not be expected to undertake observations or process publications.
Adams did not engage in major research or get much involved in the mathematical socieities of the day. For his work on lunar perigee and acceleration he was awarded the RAS gold medal in 1866. Although his position as Director of the Cambridge Observatory gave him scope to exercise patronage and influence Adams remained relatively unengaged with the politics of the scientific world. Always willing to offer information, he avoided controversy. Generous in acknowledging others' achievements he secured an honorary LLD for Le Verrier in 1874 and the gold medal of the Royal Astronomical Society for him in 1876. When Airy retired, Adams was offered and declined the position of Astronomer Royal.
Adams was responsible for cataloguing Newton’s papers when they were left to Cambridge University. From 1869 he was an early and active supporter of provision for higher education for women in the university. He was one of the first Cambridge professors to admit women to his lectures and lobbied for wider and official provision.
Johnian mathematicians
John Dee
John Dee (1527-1609)
Dee entered St John's in 1542 and claimed to have studied for 18 hours a day! In 1546 he was elected a Fellow at the newly founded Trinity College. Difficult to categorise, Dee was a philosopher and astrologer. He was certainly also a mathematician, valuing mathematics for its use in navigation, surveying, and hydraulics, as well as in alchemy and astrology. His mathematical expertise was sufficiently highly regarded that he was chosen to write the preface for the first English translation of Euclid.
Henry Billingsley
Henry Billingsley (d. 1606)
Henry Billingsley matriculated at St John’s in 1550, spending time in Oxford too, though did not take a degree at either university. He became a prosperous haberdasher, but is best known for his translation of Euclid into English, from both the original Greek and a Latin translation. In his preface he explained that ‘without the diligent studies of Euclides Elementes it is impossible to attaine unto the perfect knowledge of Geometrie, and consequently of any other Mathematicall sciences’. His translation was published with a ‘mathematical preface’ by John Dee, the preface becoming better known than the translation itself.
Henry Briggs
Henry Briggs (ca. 1561-1631)
Henry Briggs gained his BA at St John’s in 1581/2, and was admitted as Fellow in 1588. In 1592 he was appointed mathematicus examinator, which implies that he lectured in mathematics. In 1597 he became professor of geometry in the newly founded Gresham College in London, and published works on astronomy, geography, and navigations: A table to find the height of the pole (1602) and Tables for the improvement of navigation (1610). He continued to be involved in College affairs after his move to London. Some of his most important work was on the calculation of logarithms. He was appointed professor of geometry at Oxford University in 1619, and remained in Oxford until his death in 1631.
Brook Taylor
Brook Taylor (1685-1731)
Taylor was admitted to St John’s in 1701. He graduated LLB in 1709 and LLD in 1714, though does not appear to have taken up a legal career. At Cambridge he became proficient in mathematics and physics, and was elected a Fellow of the Royal Society in 1712 and appointed to the committee to adjudicate on the controversy between Newton and Leibnitz over the invention of calculus. He was subsquently to work himself on Newtonian mechanics and fluxional calculus. A book on linear perspective was followed by his chief mathematical work, Methodus incrementorum direct et inversa (1715), propounding a new method of increments, which would become known as finite differences.
James Wood
James Wood (1760-1839)
Wood graduated Senior Wrangler and First Smith’s Prizeman in 1782 and was elected to a Fellowship. He was a College Tutor from 1789 to 1814, during which time he published his Principles of mathematics and natural philosophy, all four volumes of which went through multiple editions, with The elements of algebra being printed in its final edition in 1861. Wood served as Master of St John’s from 1815 until his death in 1839.
John Herschel
Sir John Frederick William Herschel (1792-1871)
The son of the astronomer Sir William Herschel, John graduated as Senior Wrangler and First Smith’s Prizeman in 1813. Known primarily his major contribution to the discovery and cataloguing of stars rather than as a mathematician, Herschel helped to found the Analytical Society in Cambridge along with Charles Babbage.
J.J. Sylvester
James Joseph Sylvester (1814-1897)
Sylvester entered the University of London the year that it opened, when he was just 14. London’s non-sectarian policies allowed him, as a Jew, both to study and to take a degree, though he stayed only 5 months there. In 1831 he was entered as a sizar at St John’s, being readmitted as a pensioner in 1836 following illness. In January 1837 he finished second Wrangler in the mathematical tripos, but could not take his degree nor compete for prizes or Fellowships, as he could not subscribe to the 39 articles of the Church of England. (Following the repeal of the Test Acts in 1872, the University awarded him the degrees of BA and MA honoris causa and made him an honorary ScD in 1890.) Ineligible for Oxbridge positions he held mathematical posts at London, Virginia, the Royal Military Academy at Woolwich, whilst pursuing a parallel legal career, before taking up a professorship at Johns Hopkins where his mathematics gained international recognition. 1884 saw his appointment to the Savilian Chair in Geometry at Oxford. The Royal Society honoured his memory with the establishment of its Sylvester Medal, an award ‘for the encouragement of mathematical research irrespective of nationality, and not confined to pure mathematical research’.
Isaac Todhunter
Isaac Todhunter (1820-1884)
Isaac Todhunter came to St John’s via a circuitous route. Whilst working as an assistant schoolmaster he managed to attend evening classes run by University College London, where one of his teachers was J.J. Sylvester. In 1842 he obtained his BA at UCL, proceeding to MA two years later, whilst still working as a maths teacher in Wimbledon. In 1844, he entered St John’s where he was to achieve the Senior Wranglership and First Smith’s Prize. He was elected a Fellow of the College in 1849. As lecturer and tutor in mathematics he produced numerous mathematical works: algebra (1858), trigonometry (1859), an edition of Euclid (1862), mechanics (1867) and mensuration (1869), which became the standard textbooks for the remainder of the nineteenth century. He also wrote on the history of mathematics. He resigned his Fellowship in 1864 in order to marry. In 1871 he was awarded the Adams Prize for his ‘Researches on the calculus of variables’, and was elected a member of the council of the Royal Society. In 1874 St John’s made him an honorary Fellow.
Baron Kikuchi Dairoku
Baron Kikuchi Dairoku (1855-1917)
Kikuchi was born into a scholarly family in Edo (Tokyo), and was educated in England. He came to St John’s in 1873 to study mathematics and was the first Japanese student to graduate at Cambridge. In his career in educational administration, he became president of Toyko Imperial University, Minister of Education (1901-1903) and president of Kyoto Imperial University. He wrote a textbook on elementary geometry which was widely used for over 50 years.
Louis Mordell
Louis Joel Mordell (1888-1972)
Born in Philadelphia, the son of Lithuanian immigrants, in 1906 Mordell paid for a one-way ticket to England to sit the Cambridge University scholarship exam. He finished top of the list and was awarded a scholarship at St John’s. In 1909 he finished third Wrangler, and was subsequently awarded the Smith’s Prize, even though his chosen subject of number theory was not particularly regarded at the time. Mordell lectured at Birkbeck, with an interruption for war work, and then the Manchester College of Technology, where he produced his most important work, his ‘finite base theorem’. In 1945, Mordell returned to Cambridge to take up the Sadleirian Chair and a Fellowship at St John’s. He was awarded the Sylvester Medal of the Royal Society, and was President of the London Mathematical Society.
Max Newman
Max Newman (1897-1984)
Newman entered St John’s in 1915, though his studies were interrupted by war work 1916-19. He graduated in 1921, and became a Fellow of St John’s in 1923. From 1927 he was a lecturer in mathematics. His work on combinatorial topology revolutionized the field. He wrote just one book Elements of the topology of plane sets of points, published in 1939. In 1942 he joined the Government Code and Cipher School at Bletchley Park, working with Turing in designing and building code-breaking machines, culminating in the ‘Colossus’. Between 1945 and 1964 Newman was Fielden Professor of Mathematics at Manchester University. In 1973 he was made an Honorary Fellow of St John’s.
Maurice Wilkes
Sir Maurice Wilkes (1913-2010)
Wilkes gained his BA in mathematics in 1934 and his PhD in 1938. He was a university demonstrator in mathematics from 1937 until 1946, at which point he became Director of the Mathematical Laboratory, remaining its head for a further decade after it became the Computer Laboratory. He was Professor of Computer Technology 1965-1980. He designed the EDSAC programmable computer. Honoured as a pioneer of computing in the UK, Maurice Wilkes was knighted in 2000.
Abdus Salam
Abdus Salam (1926-1996)
Born in a poor district of the Punjab in 1926, Salam’s outstanding performance in his matriculation examinations won him a full scholarship to the University of Lahore where he specialised in mathematics. An MA in 1946 was followed by a scholarship to St John’s where he excelled, achieving firsts in both mathematics and natural sciences. He lectured in mathematics at Cambridge 1954-6, but research physics was his field, and he moved to Imperial College where he became Professor of Theoretical Physics. In 1964 he helped to found the International Centre for Theoretical Physics in Trieste, of which he remained Director for 30 years until his retirement. In 1979 he shared the Nobel prize with Steven Weinberg and Sheldon Glashow for the historic unification of the weak nuclear force with electromagnetic force. As scientific advisor to the Government of Pakistan he was at the forefront of his country’s scientific advancement, promoting and developing research infrastructure.
Roger Penrose
Sir Roger Penrose (1931-) 
Roger Penrose was awarded a PhD in algebraic geometry at St John’s in 1957, staying for three further years as a Title A Fellow. After leaving St John’s, his career took in work for NATO, King’s College London, the University of Texas, and Birkbeck, before moving to Oxford as Fellow of Wadham College and Rouse Ball Professor of Mathematics (1973-93), both of which positions he continues to hold in emeritus. He has made numerous contributions to the mathematical physics of general relativity and cosmology, being especially well-known for his 1974 discovery of Penrose tilings, which can only tile the plane aperiodically and were the first tilings to exhibit five-fold rotational symmetry, an example of which can be seen in the entrance to the Working Library. He has won numerous awards, including in 2020 the Nobel Prize in Physics “for the discovery that black hole formation is a robust prediction of the general theory of relativity”. Sir Roger is an Honorary Fellow of St John’s, and delivered the first Penrose lecture in 2022.
The Adams Society
Account of the founding of the Adams Society from the Eagle, Easter 1923
UNLIKE a considerable number of other Societies, the Adams (Mathematical) Society is not the oldest in the College. In fact, it began last term. Taking into account the great reputation of our College in the mathematical world, it may be a matter of surprise to some that, while for many years flourishing societies should have discussed legal, economical, historical, classical, theological and other subjects, mathematics has not been, till now, similarly favoured. Probably there is some truth in the idea that, in order to discuss mathematics - at least as that term is understood in this College - we require to say something, and that is not always easy. The proposal to have a mathematical society originated mainly with the second year students, and Mr. Cunningham, when approached, at once gave his most hearty support. The inaugural meeting was held in Mr. Cunningham's rooms, on 27th February.
After the company had been entertained to coffee by their host, the society was formally inaugurated, and the following officers were elected : President: J. Hyslop ; Vice-Pres.: T. G. Room ; Secretary: T. A. A. Broadbent : Treasurer: J. W. Harmer.
Mr. White then gave a most interesting and amusing account of the work of some Johnian mathematicians, including such men as John Dee, Henry Billingsley, Henry Briggs, Brook Taylor, John Couch Adams, and Sir John Herschel. We gravely fear that John Dee's habit of studying for eighteen hours every day is not generally imitated by present Johnians!
At the second meeting, held in Mr. White's Rooms, W. Wilson treated us to some examples of an important theorem regarding the connectivity of manifolds. Either Wilson's knowledge, or our own ignorance, is very profound.
Our vice-president, T. G. Room, gave the first paper this term, in Mr. Greaves' Rooms, on the history of Conics. Room was decidedly good, and decidedly entertaining. How we wish some of our Trinity friends could have heard him!
At the last meeting of the session, after election of new officers, the retiring president held forth on the Dynamics of the Aeroplane. He also assured us that his discourse would have been perfectly intelligible if he had been able to produce a model flying machine.
The attendance at all the meetings was good. The thanks of the Society are due to the senior members, who have given hospitality, have graced the meetings with their presence, and in every way have given all the assistance in their power. The officers for next session are :-President : R. Schlapp ; Vice-Pres. : T. A. A. Broadbent ; Secretary : S. Goldstein ; Treasurer : P. Fletcher.
Over the last century, the society has invited many mathematicians, including Nobel Laureates, to speak on a wide variety of topics. They have been amused, baffled, and awed in turn. They have enjoyed many dinners often with humorous speeches, and have triumphed over and been utterly thrashed by various other Colleges' mathematical societies at a range of sports.
100 years of the Adams Society
There follows a very partial selection of events from the first one hundred years of the Adams Society's existence.
1923
The society's inaugural meeting takes place in Mr Cunningham's rooms. Mr White addresses the meeting.
1927
Bertha Swirles is the first woman to be invited to give a talk, addressing a joint meeting of the Adams Society and Girton Mathematical Society. It would be many years before female mathematicians were awarded Cambridge degrees.
1930
Arthur Eddington gives a paper on the constant
after which he and Paul Dirac discuss many of the fundamental concepts of physics. What a discussion to have attended!
1931
The society issues its first fixture cards.
1932
Mr White delivers the first of several entertaining talks on the subject of ‘Eggs’, producing from the egg a bowler hat, a spindle and a Dutch cheese!
1936
The Society reaches the milestone of its 100th meeting! It celebrates this by getting Mr White back to talk on Johnian mathematicians.
1939
Frank Smithies addresses the Society.
1939
Maurice Wilkes, pioneer of early computing, who was later to develop the EDSAC computer, gives a talk on 'calculating machines'.
1942
Due to depleted numbers in wartime, the Society combines its meetings with those of the University's Quintic Society.
1944
Mr White regales the Society with another of his entertaining talks on the subject of Eggs!
1947
Miss Cartwright lucidly expounded “Non-Linear Differential Equations and their Topology” as probably only the second woman to address the Society. Mary Cartwright was elected a Fellow of the Royal Society in 1947, and became Mistress of Girton in 1949, having been a University Lecturer in Mathematics from 1935. She later became the first woman to serve as president of the London Mathematical Society.
1948
The 200th meeting of the Society being so nearly coincident with the discovery of the planet Neptune, it is marked by Mr Cunningham giving a talk on John Couch Adams.
1949
Professor Hartree gives an account of a search bearing a curious resemblance to the Hunting of the Snark. He found his Snark, and was even able with a dramatic flourish, to show his audience a diagram of it. Fortunately the Snark was not a Boojum, so Professor Hartree survived.
1950
Not one, but two female speakers are invited to address the Society this year, and a talk by Fred Hoyle, fresh from his popular cosmology talks on the radio, achieves record attendance.
1954
The 250th meeting of the Society! Back comes Mr White with his ever popular 'Some Johnian mathematicians'. None of the current students would have heard it before though.
1955
The Society learns about 'Elementary particles' from Dr Abdus Salam, later to be awarded the Nobel prize in physics.
1958
Harold Jeffreys is one of the guests of honour at the Adams Society dinner, entertaining attendees with reminiscences of Cambridge mathematics before the First World War.
1959
Johnian, Roger Penrose, who was to become a Nobel laureate in 2020, addresses the Society, and the eighth triennial dinner is held.
1968
The Society is revived after a year of being dormant, and George Reid baffles members with a talk on the first six letters of the alphabet.
Early 1970s
Bertha Swirles (now Bertha Jeffreys) is invited to address the Society again. The draft of her talk is preserved in her papers in the College Library.
1976
Taking a break from mathematics the Society triumphantly defeats all its nearest neighbours and rivals among the Colleges' mathematical societies at the seasonal sport of punt jousting.
1980s
With the admission of women to St John’s, the first female committee members are appointed.
2000
The Society suffers humiliating defeat in its regular cricket fixture with Trinity’s Mathematical Society, their opponents having distracted the opening bowlers by the underhand tactic of bowling an apple first ball.
2006
At the annual cricket match versus Trinity it is reported that “as tradition dictates the first ball was bowled with an apple” How quickly do traditions emerge!
2008
Having suffered its 8th cricketing defeat of the century by the Trinity mathematicians the Adams Society holds its best attended lecture for three years, with 125 coming to hear Dr Piers Bursill-Hall on ‘1001 reasons to thank the gods that you aren’t a Trinity Mathmo’.
2009
The Adams Society finally wins a cricket match…
2015
Professor Amanda Turner, herself a Johnian, presented the Adams Society with the challenge of describing random processes ‘from lichen to lightning’ mathematically.
2015
Adams Society members are spotted training for their annual cricket fixture! Is that fair play?
2022
At a recent meeting of the Adams Society, Dr Vicky Neale explores how the symmetry of knitted scarf patterns connects to solving polynomial equations. Attendees are invited to bring coloured pencils to doodle along.
