## 6 Great Mathematicians of Oxford

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Today, the city of Oxford and its world-class university leads the way for many mathematical pursuits. Working across all fields from pure number theories to understanding the mechanics of its brain, it’s home to over 850 undergraduate students, 350 masters and doctoral students, as well as over 200 academic staff.

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But who are the individuals who shaped the university and its mathematical institute which we know and admire so well today?

The foundations of mathematics in Oxford has a long history - around 800 years to be exact. From Roger Bacon and his thirteenth-century developments to more recently Roger Penrose in the twenty-first, some of the world’s greatest mathematicians have passed through the city walls of Oxford and its world-famous university.

To find out more about those who made phenomenal contributions to the subject we know and love today, take a step back in time with our list of 6 of the great mathematicians of Oxford. With most of them predating the 20th Century, they’re some of the lesser known heroes of the time - but certainly those who have helped to make huge advances in mathematical research and knowledge.

## 1. Godfrey Harold Hardy (1877 - 1947)

“I was at my best a little past forty, when I was a professor at Oxford.”- G H Hardy

G H Hardy is recognised as one of the most important British pure mathematicians of the early twentieth century. His 11 years as Savilian Professor of Geometry at the University of Oxford were some of the most productive of his career, writing over 100 research papers.

His work focused mainly on analysis and number theory, where he became known for over 10 different mathematical principles, including the Hardy-Weinberg principle, the Hardy-Littlewood tauberian theorem, and the Critical line theorem.

**Establishing Hardy as a great mathematician**

G H Hardy began his education at Trinity College, University of Cambridge in 1896, where he excelled in class, being appointed as a Fellow shortly after he graduated in 1899. Much of his academic success began in Cambridge; in 1900 he was elected to a Prize Fellowship at Trinity College; in 1903 he earned his M.A (the highest academic degree at English universities at the time); and was appointed as Trinity staff lecturer in mathematics in 1906.

During his free time, he collaborated on research projects, mainly with classmate John Edensor Littlewood. The first of which was published 1912, contributing to many pure mathematics theories including, the theory of Diophantine analysis; infinite series summation; Fourier series; the Riemann zeta function, and the distribution of primes.

At this time, so early on in his mathematical career, Hardy was unaware that later in his career, J E Littlewood would continue to have such an influential role in his future academic success as a researcher.

**G H Hardy as a tutor**

Despite laying the groundwork for his success at the University of Cambridge, it was his time at the University of Oxford where Hardy really began to use his knowledge to pave the way to academic discovery. Hardy joined the University of Oxford in the year 1919 where he was elected as Savilian Professor of Geometry at New College, Oxford, and entered office on 19th January 1920.

While in Oxford, Hardy established himself both as a great mathematician and as an inspiring tutor. At the time of him lecturing, there was no Mathematical Institute - and so, he taught in his own college, rather than collaborating research with the other colleges in the city.

As a tutor, he was widely admired by his students, with one writing:

“Each lecture was carefully prepared, like a work of art, with the intellectual denouement appearing as if spontaneously in the last five minutes of the hour. For me, the lectures were an intoxicating joy.” - Oxford student

Despite having not trained as a geometer when he studied in Cambridge, many of Hardy’s lectures centres around the geometry topics which he found interest in later in his life, including; Analytics geometry, Applications of analysis to geometry, Solid geometry, and Elements of non-Euclidean geometry. However, he also branched out into other non-geometrical topics too, including; Theory of functions, Mathematical astronomy, and Hydrostatics.

**G H Hardy’s research**

Beyond his work as a tutor, Hardy contributed tremendously to the pursuit of Mathematical research both at the university and with long-term university companion, J E Littlewood.

Before his arrival in Oxford, there was limited research tradition at the university - and Hardy was pioneering in his commitment to change this. Shortly after arriving in Oxford, he began Friday evening advanced classes around pure mathematics, where he and his research students would discuss their current investigations - the first of its time at the university.

But outside of work, Hardy committed a lot of time to developing his research, becoming the author and co-author of more than 300 papers and 11 books, including; *A Course of Pure Mathematics* (1908), *Inequalities* (1934), *The Theory of Numbers* (1938) with E.M. Wright, and the *Divergent Series* (1948).

Much of this work was co-completed with his old Cambridge companion, J E Littlewood. Together, the pair produced around fifty joint research papers together and co-authored almost one hundred, making them one of the most prolific partnerships in mathematical history.

**G H Hardy returns to Cambridge**

Although Hardy enjoyed his role at the University of Oxford, he chose to resign and return to Cambridge in later life, where he began his education. Despite his efforts to create an analytical mathematical school in Oxford, Cambridge (at the time) was the central Mathematical hub of England, and Hardy was keen to take a place in one of the most prestigious roles at the university.

Joined by his co-researcher and long-time friend, Littlewood, Hardy remained in Cambridge throughout his retirement, returning to Oxford for several weeks every summer to catch up with his old colleagues and soak up the atmosphere. Whilst here, he also captained the New College Senior Common Room cricket team in their annual matches against the college servants and choir school.

## 2. Charles Dodgson (Lewis Carroll)

Despite Lewis Carroll being recognised as the prolific writer of *Alice’s Adventures in Wonderland* and *Through the Looking Glass*, he actually held a ‘day job’ as a tutor in Mathematics at Christ Church, University of Oxford, which also landed him the title as one of the great mathematicians of Oxford.

Once you learn about his education and professional history, it seems to make sense. Mathematical language can be seen in much of Dodgson’s literature works for children, particularly in his novels about Alice in Wonderland:

*“Can you do addition? What’s one and one and one and one and one and one and one and one and one and one?*

*[I don’t know, I lost count]*

*She can’t do addition. Can you do subtraction? Take nine from eight.*

*[Nine from eight I can’t, you know, but-]*

*She can’t do subtraction. Can you do division? Divide a loaf by a knife*

*[I suppose-]*

*Bread and butter of course. She can’t do sums a bit!*

**Charles Dodgson’s early years**

As one of eleven children, Charles Dodgson was initially home-schooled by his parents where he began to show an interest in mathematics. From 1843, when his family moved to Croft Rectory in Yorkshire, Dodgson’s father was able to afford to send him to private school, where he demonstrated his mathematical talent, winning many academic awards.

One of these was awarded when Charles was just 12 years old, after having produced a two-page note on trisecting a right angle - which his teachers recognised as remarkable for a child of his age.

**Charles Dodgson’s education in Oxford**

On 23 May 1850, Dodgson was officially enrolled as a member of the University of Oxford, after passing his matriculation exams in Latin, Green, and mathematics. He began studying at Christ Church in January 1851, where he was elected for a four-year Honours degree in Classics and Mathematics.

After his four years of study, Dodgson sat his Finals examinations in 1854, which included topics on pure and applied mathematics, calculus, astronomy, geometry and algebra. He came top of the entire class and was awarded a First Class degree in December of that year.

**Charles Dodgson as a tutor at Christ Church**

From 1856 to 1881, Charles Dodgson was a Mathematical tutor at Christ Church, teaching the subject for students preparing for Responsions, Moderations and Finals.

After graduating, his initial work was privately tutoring pupils who were preparing for special examinations, particularly Responsions. In 1856, the Mathematics tutor Robert Faussett had left Oxford to fight in the Crimean War, and so Dodgson was appointed in his place, where he ended up holding the position for twenty-five years.

During his free time, Dodgson took up the hobby of photography, taking hundreds of pictures of his Oxford contemporaries and portraits of children, including his well-known photo of Alice Liddell, who went on to be long-associated with the name of Lewis Carroll.

**Charles Dodgson’s Mathematical Research**

From his earliest days, Dodgson had been primarily interested in geometry. Particularly, Dodgson admired a book titled Elements by Euclid, which became a central text for teaching geometry in the 19th Century.

To help teach geometric theory to his students, Dodgson produced many pamphlets explaining the ideas involved - which were often quite whimsical and written in the style of a play, thanks to his creativity and passion for writing.

There is even a well-known story that relates Queen Victoria’s love for Dodgson’s love for *Alice’s Adventures in Wonderland*. Apparently, the Queen demanded “send me the next book that Carroll produces,” which, much to her disappointment, was titled; *An Elementary treatise on Determinants with their Application to Simultaneous Linear Equations and Algebraical Geometry.*

However, it was Dodgson’s contributions to mathematical logic and the theory of voting which earned him credit as one of the great Mathematicians of Oxford. Towards the end of his life, he wrote extensively about logic, specifically, presenting symbolic logic as entertaining for children to develop their own powers of logical thought. As such, he devised *The Game of Logic* to help children understand and sort out syllogisms, using familiar and real-life situations to help them apply their knowledge.

## 3. John Wallis (1616 - 1703)

“Wallis drew on ideas originally developed in France, Italy and the Netherlands...he handled them in his own way, and the resulting method of quadrature, based on the summation of indivisible or infinitesimal quantities, was a crucial step towards the development of of a fully fledged integral calculus some ten years later.”- Jacqueline Stedall

Considered one of the most influential English mathematicians before the rise of Isaac Newton, John Wallis is regarded as one of the great mathematicians of the 17th Century, having produced important works on the Arithmetic of Infinitesimals and Conic Sections - both of which were critical to helping Newton discover his version of the binomial theorem.

**John Wallis appointed as Savilian Professor in Oxford**

During the English Civil War (in 1649), John Wallis was appointed Savilian Professor of Geometry at the University of Oxford. His appointment came from a time of political unrest, when the original Savilian professors were expelled in 1648 for their Royalist sympathies, and the Parliamentary Commissioners replaced Wallis as Professor of Geometry.

Prior to taking his role as Savilian Professor, John Wallis had little mathematical experience, however he ended up holding the chair until his death fifty-four years later. His role marked the beginning of an intense period of activity which established Oxford as a mathematical powerhouse of the nation, and earned Wallis his credit as one of Oxford’s great mathematicians, long before Isaac Newton became established.

**John Wallis and his mathematical research**

John Wallis’s most significant contribution to the field of mathematics was through two major publications: *Arithmetica Infinitorum* and *De Sectionibus Conicis*.

His first publication, *Arithmetica Infinitorum* (Arithmetic of Infinitesimals, or a New Method of Inquiring into the Quadrature of Curves, and Other Difficult Mathematical Problems) came at a critical time for the development of mathematics. His exploration of the fundamental engine of discovery, and the exploration and recognition of patterns allowed great mathematicians such as Sir Isaac Newton to discover the general binomial theorem.

Meanwhile, his other important contribution, *De Sectionibus Conicis* which was published in the 1650s laid out his investigations into conic sections and their properties. It was during this publication that he introduced two new symbols which we still use in today’s mathematical world: the ‘infinity’ sign and the symbol for ‘greater than or equal to.’

**The final years of John Wallis**

In his final years as Savilian Professor at the University of Oxford, Wallis published his influential *A Treatise of Algebra, Both Historical and Practical* (1685).

The publication provides a fully astute survey of the great mathematical achievements of past centuries. This was the first substantial history of mathematics recorded in the English language, as well as being one of the few works which presented modern mathematical advances alongside its historical developments.

At the time, the work was controversial, as Wallis made accusations about fellow mathematician and philosopher, Descartes - claiming that he had plagiarised another mathematician (Thomas Harriot’s) work. However, the book was the most widely read over the next hundred years and continues to hold great significance in the world of mathematics.

In the 1690s, John Wallis’s *Collected Works* were published in honour of his achievements. Towards the latter stages of the decade (1969), the University of Oxford established the *Wallis Chair of Mathematics*, as well as commissioning a portrait of himself which today is hung in the Examination Schools in Oxford.

## 4. Edmond Halley

Throughout the 18th Century, the University of Oxford was central in the development of Newtonian philosophy. Edmond Halley, one of the most famous English astronomers of all time, was Oxford’s Savilian Professor of Geometry at the time - leading him to be recognised as one of the greatest mathematicians of Oxford to have ever lived.

**Edmond Halley’s education at the University of Oxford**

At just 17 years-old, Halley astonished professors at the University of Oxford with his astronomical observations, securing him a place at The Queen’s College, Oxford, in 1673.

As an undergraduate in Oxford, Halley was making significant contributions to the world of astronomy, collaborating with fellow scientist John Flamsteed - the Astronomer Royal. One of these was published in 1676 in the Royal Society’s *Philosophical Transactions* and explained the process of occultation of Mars by the Moon.

At the age of 20, Halley decided to leave his undergraduate studies and sail to the island of St Helena, with a set of instruments to map and explore the skies of the southern hemisphere - with objects such as nebulae and star clusters which cannot be seen from European latitudes.

Despite leaving Oxford without taking his final degree examinations, he earned an international reputation at just the age of 22 when he published these ground-breaking findings in his journal *Catalogus Stellarum Australium* in 1678. As a result, the Royal Society elected him as one of its youngest ever Fellows, and Charles II commanded the University of Oxford to grant him an MA degree - which is considered to be the first degree awarded in recognition of research achievements.

**Edmond Halley’s election as Savilian Professor**

Despite being the place where he launched his career, it wasn’t for twenty-six years until Edmond Halley was then offered his first formal appointment at the University of Oxford. This took place in 1704, when he succeeded John Wallis as Savilian Professor of Geometry, where he remained in post until his death in 1742.

It’s not surprising that it took this long for Halley to take the Chair as Savilian Professor. As a young graduate, Halley was keen to explore and would have found the university lifestyle too limiting for his intellectual pursuits at that age. Instead, for many years he involved himself with the Royal Society where he could research and work alongside budding academics of the time, including Sir Isaac Newton. Research which, he brought back with him to shape his teaching at the University of Oxford when he finally took the role as Savilian Professor in 1704.

**Halley’s work as Savilian Professor at the University of Oxford**

As his first point of call, Halley set out to prepare what would become the definitive edition of Apollonius’s *Conics* - a task which was left unfinished by his predecessor John Wallis. His hope was that helping on such a major scholarly project would silence any critics who had frequently labelled him as an opportunist throughout his career.

But Halley had also developed a career as a scientist, so undertook a lot of research in the field during his time as Savilian professor. One of these was a theory to explain the variations in the Earth’s magnetic field - something which had been a serious topic of study earlier in the 17th Century.

In 1705, he published *A Synopsis of the Astronomy of Comets*, where he showed how three historic comets were so similar in characteristics that they must have been successive returns of one original object. A prediction later proved accurate when a similar comet returned in 1758. The findings created the term ‘Halley’s Comet’ and is still used today to explain these astronomical matters.

## 5. Baden Powell (1786 - 1860)

Baden Powell was a British mathematician and Church of English Priest. Between the years of 1827 to 1860, he was Savilian Professor of Geometry at the University of Oxford, where his work led Powell to be recognised as one of the great mathematicians of the Victorian era - laying the foundations for the University of Oxford to become a hub for mathematical research.

**Baden Powell’s earlier years**

Having originated from a farming family with roots in Suffolk, Powell’s father established himself in southern England, where he worked as a wine merchant and High Sheriff of Kent - yielding a significant role within the local community.

In 1814, Powell, thanks to his academic interests and father’s position, had him admitted as an undergraduate at Oriel College in Oxford, where he graduated with a First Class Honours degree in Classics and Mathematics three years later.

After graduating from university, he returned to his home county of Kent. In 1821, he was ordained as a priest of the Church of England, having served as Curate of Midhurst in Sussex for the few years after university. His first role was as Vicar of Plumstead in Kent, where he began experimenting with his scientific interests, starting with physics experiments on radiant heat.

**Baden Powell elected as Savilian Professor at University of Oxford**

In 1827, Stephen Rigaud, a keen astronomer, migrated from his role as Savilian Chair of Geometry over to Astronomy, leaving Powell to be elected as his successor.

At the time, the University of Oxford was not a hub for mathematics, shocking Powell as he entered his new role. Ever since the Honours School in Mathematics had been introduced in 1800, students had allegedly become more exam-focused and less interested in contributing to the subject as a whole. According to historians, he was even advised against giving an inaugural lecture as it was almost certain that it would not attract an audience.

Understandably, his work set out to reverse this mindset of the students and academics. In 1832, he gave a public lecture on *The Present State and Future Prospects of Mathematical and Physical Sciences* in the University of Oxford, where he expressed his discontent over the declining numbers of science students.

During his 33 years in the role, he committed a lot of energy to changing things, with one of his most innovative ideas being to create scholarships for the promotion of mathematics as a subject. These were founded in 1831 and were awarded to a number of Oxford’s great mathematicians, including William Spottiswoode and Bartholomew Price.

**Baden Powell’s work**

Although chairing a role as a mathematics professor, Powell had keen interest in other subjects, including physics, theology, and philosophy. One of his most pioneering and controversial essays was published Essays and Reviews in 1860, where he acknowledged that scientific advances were not incompatible with Christian religion - joining in with evolutionary theories pitched by Charles Darwin in his book, *On the Origin of Species*.

However, he did of course produce many mathematical publications in his years as Savilian Professor at the University of Oxford, including; *The elements of curves* (1828); *A short treatise on the principles of the differential and integral calculus*(1829); *An elementary treatise on the geometry of curves and curved surfaces, investigated by the application of the differential and integral calculus* (1830); *On the nature and evidence of the primary laws of motion* (1837); and, *On necessary and contingent truth, considered in regard to some primary principles of mathematical and mechanical science* (1849).

A full list of Baden Powell’s published work and essays can be found here.

## 6. Thomas Harriot (1560 - 1621)

Despite travelling around the world using nothing more than a map and his mathematical logic, it is only recently that Thomas Harriot has been recognised as one of the most significant original thinkers of his time. Leaving over 8,000 manuscript pages of his research into key mathematical principles in geometry, algebra, optics, mechanics, astronomy, and navigation, he was also the first astronomer to use a telescope to map the moon.

**Thomas Harriot’s earlier years**

Thomas Harriot, ‘by birth and by education an Oxonian’ spent much of his early life inspired by the great academic centre which he knew as home. Quite fittingly, it seemed like a natural place for him to be matriculated at the University of Oxford in 1577 as a member of St Mary Hall (which eventually united and formed under Oriel College in 1902).

During his time at university, he developed the skills of astronomical navigation, which, after earning his BA degree at Oriel College in 1580, led him to join Sir Walter Raleigh’s colonising ventures to America, advising him on navigation, astronomy and surveying. He was a member of the colony which landed on Roanoke Island in June 1585, and then returned to England the following year. A summary of his time on the island and its people was then published by Harriot in 1588, titled; *A Briefe and True Report of the New Land of Virginia.*

**Thomas Harriot’s research**

As demonstrated by his earlier expedition, Harriot was an extremely skilful mathematician and astronomer, and was endless in his pursuit to find answers to some of science’s most talked about questions.

One of Harriot’s greatest accomplishments was discovering how to find the length of an equiangular spiral by approximating it by a polygon, cutting it up, and rearranging the pieces into a triangle whose dimensions can be calculated.

Amongst other things, he was also the first person to observe and map the moon with a telescope in 1609, several months ahead of Galileo. And, in 1614, Harriot created a table which allowed navigators to set a fixed compass course when sailing between two points - offering a solution to the ‘Mercator problem’ of the time.

**Thomas Harriot’s legacy**

When he passed away in 1621, Harriot left thousands of pages of manuscripts detailing his research, which had never been published during his lifetime. Except for his book on algebra, *Artis Analyticae Praxis*, which was published in Latin in 1631, the rest of his manuscripts have been published by historians and academics over the years since his passing.

However, despite being part of huge research, development, and findings, it has only been in the past 50 or so years that his importance has been fully recognised. Today, Oriel College now holds a Thomas Harriot Lecture in Trinity Term of each year, in recognition of his tremendous contribution to the mathematical world.

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## Summary

Oxford is renowned for its mathematicians like G.H. Hardy, Charles Dodgson (Lewis Carroll), and John Wallis. Their contributions in analysis, number theory, and infinitesimals have left a lasting impact. Oxford's mathematical legacy continues to inspire students worldwide.