John Dee

John Dee (1527–1608) was an English mathematician, natural philosopher, and student of the occult.[2] Astrologer, astronomer, mathematician and alchemist, John Dee is famously known as the 'conjurer' to Queen Elizabeth I[1] and stands as one of the most fascinating and complex figures of the English Renaissance. His mathematical contributions were multifaceted and profoundly influential in establishing England as a center for mathematical learning during the Renaissance, spanning theoretical mathematics, practical applications, and the promotion of mathematical education.

Early Life and Education

John Dee's father was Roland Dee who was of Welsh descent. Roland Dee dealt in textiles and, in addition, was a gentleman sewer at the court of Henry VIII. In this latter capacity he would have made clothing for the royal household as well as buying and supplying fabrics for the King. John Dee's mother was Jane Wild. Jane married Roland when she was fifteen years of age and, three years later, John (who was their first and only child) was born.[7] John Dee was born on July 13, 1527, in London[2], specifically in Tower Ward, London, to a Welsh family with modest means but ambitious ties[6].

At the age of eight Dee was sent to be educated at Chelmsford Chantry School. At fifteen he started his studies at St John's College, Cambridge, where he studied Greek, Latin, Philosophy, Geometry, Arithmetic and Astronomy.[16] He was so eager to learn, he later recalled, so "vehemently bent to study", that he worked eighteen hours a day, allowing just four hours for sleep and two for meals.[7]

Dee entered St. John's College, Cambridge, in 1542, where he earned a bachelor's degree (1545) and a master's degree (1548); he also was made a fellow of Trinity College, Cambridge, on its founding in 1546.[2] Henry VIII founded Trinity College, the largest of the Cambridge colleges, in 1546 and Dee became one of its founding Fellows.[7]

European Education and Key Influences

Being unhappy with the scientific attitude in England, Dee travelled on the Continent between 1548 to 1551. He first made a visit to Louvain near Brussels, arriving on 24 June 1548, where he studied with Gemma Frisius and Gerardus Mercator. Soon Mercator became a particularly close friend of Dee's and together they discussed new models for the universe.[7] Dee later wrote:- It was the custom of our mutual friendship and intimacy that, during three whole years, neither of us lacked the other's presence for as much as three whole days.[7]

Already a keen astrologer, John Dee's studies abroad at Louvain University had led him into contact with famed cosmographers such as Gemma Frisius and cartographer Gerardus Mercator, which deepened his mathematical knowledge. Mercator and Dee established such a rapport that Dee brought back two of Mercator's globes and various astronomical instruments and gave them to Cambridge University to be used by their scholars and fellows[2].

Dee furthered his scientific studies on the Continent with a short visit in 1547 and then a longer stay from 1548 to 1551 (both times to the Low Countries) under the mathematician-cartographers Pedro Nuñez, Gemma Frisius, Abraham Ortelius, and Gerardus Mercator, as well as through his own studies in Paris and elsewhere.[2] In the same year Dee went to Paris where he lectured on Euclid's Elements. He must have been an impressive lecturer for it was reported that people flocked to hear his lectures which filled the lecture rooms to overflowing.[7]

Professional Development and Career Choices

In 1551 Dee was offered an appointment as professor of mathematics in Paris but declined. He also declined a lectureship in mathematics at Oxford three years later.[7] Dee turned down a mathematical professorship at the University of Paris in 1551 and a similar position at the University of Oxford in 1554, apparently in hopes of obtaining an official position with the English crown.[2]

Back in England Dee entered the service of the Earl of Pembroke in February 1552, then he entered the service of the Duke of Northumberland near the end of the same year.[7] Dee became a Rector at Upton-upon-Severn from 1553, at which point Dee was offered a readership in mathematics at Oxford University in 1554, which he declined. The reason for his decline was that he thought it was offensive that English universities chose to focus on Rhetoric and grammar rather than philosophy and science.[5]

Relationship with the Tudor Court

Under Mary I

In 1555, Dee was arrested and charged with the crime of "calculating". This was because he had cast horoscopes of Queen Mary and Princess Elizabeth. These charges were then changed to treason against the Queen.[5] The latter activity landed him in jail in 1555 on the charge of being a conjurer, but he was soon released.[2]

Service to Elizabeth I

However, when Elizabeth succeeded to the throne in 1558, events changed for Dee as he became her astrological and scientific advisor. He, amazingly was allowed to chose her coronation date and through this closeness with the queen, Dee even became a Protestant, himself.[5] In 1564 Dee was 'appointed Royal Advisor in mystic secrets', roughly translated as Court Astrologer. Appreciating royal support Dee applied himself to his studies with such diligence that he only allowed himself four hours sleep and two for his meals and recreation. Dee's status as the court conjurer for Queen Elizabeth had begun. The virgin queen often depended on Dee for matters in science, medicine and exploration.[1]

Mathematical and Scientific Contributions

Mathematical Education and Advocacy

Dee's efforts were crucial in transforming England from a world in which mathematics did not play a very significant role and this was particularly true of England, which in this sense lagged severely behind the continent[3]. He also used his writings to argue that mathematics did not necessarily deserve its wicked reputation[2], addressing the Tudor-era suspicion of mathematics that some circles in Tudor society were suspicious of a subject which analysed the relationship between numbers and the stars, seeing it as a gateway to demonic magic[2].

Dee became a founding figure of what historians call the English School of Mathematics. It should be pointed out that this is not a school in any formal sense by rather an informal group of scholars spread over several generations who shared a common interest in promoting the mathematical sciences outside of the system, so to speak, and did so largely in the vernacular, the English referring to the language used rather than the nationality of those involved. This school in considered to have begun with Robert Recorde and John Dee and to have ended around the time of Isaac Newton's rise to fame[3].

Mathematical Preface to Euclid

In addition to editing the first English translation of Euclid's Elements (1570), Dee added an influential preface that offered a powerful manifesto on the dignity and usefulness of the mathematical sciences.[2] John Dee's main contribution to the sixteenth-century Euclidean tradition was the important Mathematicall preface he wrote for Henry Billingsley's 1570 translation and commentary on Euclid's Elements.[27] In 1570, Dee wrote a new mathematical preface to Henry Billingsley's translation of Euclid. This preface introduced the public to the signs of addition (+), subtraction (-), multiplication (x), and division (÷).[25]

John Dee's mathematical interests have principally been studied through his Mathematicall praeface to Henry Billingsley's 1570 translation of Euclid's Elements[7]. In this preface, Dee provided a comprehensive classification of mathematical sciences and their applications. This article considers John Dee's famous classification and justification of 'the Sciences, and Artes Mathematicall' in his Mathematicall praeface to Henry Billingsley's Elements of geometrie of Euclid of Megara (1570), the first English translation of Euclid[10].

The preface was remarkably influential in its time and beyond. Although this preface would fade into obscurity somewhat, it was widely read by many in the 17th century, including natural philosopher John Wilkins who, inspired by Dee's work, wrote 'Mathematical Magick', one of Isaac Newton's favourite books[2].

Theoretical Mathematical Work

#### Fundamental Mathematical Concepts

Dee made important contributions to mathematical theory, particularly in his definitions and conceptual framework. In his Mathematical Preface, he established clear definitions: Number, we define, to be, a certayne Mathematicall Sũme, of Vnits[6] and Magnitude is a thing Mathematicall, by participation of some likenes of whose nature, any thing is iudged long, broade, or thicke[6].

#### Geometric Studies

The focus here is broadened to include the notes he added to Books X–XIII of the Elements. I argue that this additional material drew on a manuscript text, the Tyrocinium mathematicum, that Dee wrote a decade earlier, probably as tutor to the youthful Thomas Digges[7]. His geometric work demonstrated that Unlike Ramus, Dee was not a pugnacious advocate of radical reform, yet he did look beyond the limits of Euclid's geometry towards deeper disciplinary visions of knowledge[7].

#### Integration of Mathematics with Natural Philosophy

Although Dee's reputation as an astrologer and natural magician has endured, it is important to realize that he was also an extremely accomplished mathematician, and Dee himself (like most of his contemporaries) would not have considered astrology and mathematics to be discrete subjects. In 1558, for example, he published Propaedeumata aphoristica (John Dee on Astronomy , 1978), a work that explicitly connects the study of astrology and mathematics by arguing that the universe is structured mathematically and harmonically[5].

Navigation and Exploration

Dee was intimately involved in laying the groundwork for several English voyages of exploration, instructing captains and pilots in the principles of mathematical navigation, preparing maps for their use, and furnishing them with various navigational instruments. He is most closely associated with the expeditions to Canada led by Sir Martin Frobisher in 1576–78 and with discussions in 1583 regarding a proposed but never commissioned search for the Northwest Passage.[2] His mathematical work was used by navigators of the time[9].

From the 1550s to at least the 1570s, he worked as an advisor to England's voyages of discovery, in this role he provided technical aid with navigation and even political support to create a "British Empire", a term he was purportedly the first to use.[5] He was equally active in publicly advocating a British empire in General and Rare Memorials Pertayning to the Perfect Arte of Navigation (1577).[2]

Astronomical Observations

Dee observed the "new star" which is often called "Tycho Brahe's supernova of 1572" and in the following year he wrote Parallacticae commentationis praxosque which gives trigonometric methods which were applied to find the distance to the new star. He had made accurate observations with his assistant Thomas Digges and the two probably corresponded with Brahe about the star. Certainly Brahe greatly admired Dee's contributions[4].

Occult and Mystical Works

Monas Hieroglyphica

In 1564, while studying at Antwerp, Dee published Monas Hieroglyphica, a series of twenty-four theorems interpreting the Hieroglyphic Monad, a symbol of Dee's own devising which carried associations with both creation and unity. The glyph first appeared in Dee's earlier text on astronomy, Propaedeumata Aphoristica (1558), but in the Monas Hieroglyphica it became the central focus of the work.[19] Dee continued to discuss his occult views in 1564 with the Monas hieroglyphica (The Hieroglyphic Monad [2000], Monas hieroglyphica), wherein he offered a single mathematical-magical symbol as the key to unlocking the unity of nature.[2]

Angelic Conversations

Perhaps frustrated by his failure to arrive at a comprehensive understanding of natural knowledge, Dee sought divine assistance by attempting to converse with angels.[2] The pivot to Enochian magick began in 1581 when Dee, frustrated by his inability to pierce the veil alone, met Edward Kelley (sometimes spelled Kelly), a 26-year-old scryer with a murky past—rumored to have lost his ears for forgery. From 1582 to 1587, in settings ranging from Dee's Mortlake home to European courts, the duo developed Enochian magick—a system rooted in a supposed angelic tongue delivered by entities like Uriel and Raphael.[6]

Personal Life and Family

John Dee was married three times and had eight children. His first wife, Katherine Constable, died in 1574. His second wife died in 1576. Neither of them had children. In 1578, when he was 51, he married Jane Fromond, who was 23. They had seven or eight children together.[15] Jane died during the plague in Manchester in 1605, along with a number of his children, including his son Theodore. The fates of his daughters Madinia, Frances and Margaret are uncertain, as Dee had by this time ceased keeping his diary.[13]

Library and Scholarship

There he built a laboratory and amassed the largest private library in England at that time, which was said to number more than 4,000 books and manuscripts. He was as generous in making his library accessible to scholars as he was in assisting numerous practitioners who applied for advice.[2] Dee returned to Mortlake after six years abroad to find his home vandalised, his library ruined and many of his prized books and instruments stolen. Furthermore, he found that increasing criticism of occult practices had made England still less hospitable to his magical practices and natural philosophy.[9]

Later Years and Financial Struggles

When James I came to power in 1603, he had no time for superstition or magic and Dee's influence declined. He spent the end of his life in poverty, dying in either 1608 or 1609.[3] Though she appointed him warden of Manchester College in 1596, Dee's final years were marked by poverty and isolation.[2] Dee left Manchester in 1605 to return to London, but remained Warden until his death. By that time, Elizabeth was dead and James I gave him no support. Dee spent his final years in poverty at Mortlake, forced to sell off various possessions to support himself and his daughter, Katherine, who cared for him until his death in Mortlake late in 1608 or early in 1609 aged 81.[9]

Legacy and Impact

For all people's thoughts about Dee and his association with 'angels', his mathematical genius, giving us today the universal symbols used in maths, as well as his understanding of astronomy, were groundbreaking, leading to the development of advanced theories like gravity.[1] Furthermore, as passionately as he believed in the utility of mathematics for mundane matters, Dee expressed conviction in the occult power of mathematics to reveal divine mysteries.[2]

It is almost certain that William Shakespeare (1564–1616) modeled the character of Prospero in The Tempest (1611) on the career of John Dee, the Elizabethan magus.[2] Dee's influence extended far beyond his lifetime, bridging the worlds of Renaissance science and occultism in ways that continue to fascinate scholars and the public alike.