Category Archives: History of science

Christmas Trilogy 2016 Part 3: The English Keplerians

For any scientific theory to succeed, no matter how good or true it is; it needs people who support and propagate it. Disciples, so to speak, who are prepared to spread the gospel. Kepler’s astronomical theories, his three laws of planetary motion and everything that went with them, were no different from every other theory in this aspect; they needed a fan club. On the continent of Europe the reception of Kepler’s theories was initially lukewarm to say the least and it was not only Galileo, who did his best to ignore them. Therefore it is somewhat surprising that they found a group of enthusiastic supporters right from the beginning in England. Surprising because in general in the first half of the seventeenth century England lagged well behind the continent in astronomy, as in all things mathematical.

The first Englishmen to pick up on Kepler’s theories was the small group around Thomas Harriot, who did so immediately after the publication of the Astronomia nova in 1609.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

The group included not only Harriot but also his lens grinder Christopher Tooke, the Cornish MP Sir William Lower (c.1570–1615) and his Welsh neighbour John Prydderch (or Protheroe). Lower had long been an astronomical pupil of Harriot’s and had in turn introduced his neighbour Prydderch to the science.

The cartoon of Lower and Prydderch on page 265 of Seryddiaeth a Seryddwyr By J.S. Evans. Lower looks through a telescope while Prydderch holds a cross-staff. The cartoon had been used earlier by Arthur Mee in his book The Story of the Telescope in 1909. The artist was J. M. Staniforth, the artist-in-chief of the Western Mail newspaper.

The cartoon of Lower and Prydderch on page 265 of Seryddiaeth a Seryddwyr By J.S. Evans. Lower looks through a telescope while Prydderch holds a cross-staff. The cartoon had been used earlier by Arthur Mee in his book The Story of the Telescope in 1909. The artist was J. M. Staniforth, the artist-in-chief of the Western Mail newspaper.

This group was one of the very earliest astronomical telescopic observing teams, exchanging information and comparing observations already in 1609/10. In 1610 they were enthusiastically reading Astronomia nova and discussing the new elliptical astronomy. It was Lower, who had carefully observed Halley’s comet in 1607 (pre-telescope) together with Harriot, who first suggested that the orbits of comets would also be ellipses. Kepler still thought that comets move in straight lines. The Harriot group did not publish their active support of the Keplerian elliptical astronomy but Harriot was well networked within the mathematical communities of both England and the Continent. He had even earlier had a fairly substantial correspondence with Kepler on the topic of atmospheric refraction. It is a fairly safe assumption that Harriot’s and Lower’s support of Kepler’s theories was known to other contemporary English mathematical practitioners.

Our next group of English Keplerians is that initiated by the astronomical prodigy Jeremiah Horrocks (1618–1641). Horrocks was a self-taught astronomer who stumbled across Kepler’s theories, whilst on the search for reliable astronomical tables. He quickly established that Kepler’s Rudolphine Tables were superior to other available tables and soon became a disciple of Kepler’s elliptical astronomy. Horrocks passed on his enthusiasm for Kepler’s theories to his astronomical helpmate William Crabtree (1610–1644). In turn Crabtree seems to have been responsible for converting another young autodidactic astronomer William Gascoigne (1612–1644) to the Keplerian astronomical gospel. Crabtree referred to this little group as Nos Keplari. Horrocks contributed to the development of Keplerian astronomy with an elliptical model of the Moon’s orbit, something that Kepler had not achieved. This model was the one that would eventually make its way into Newton’s Principia. He also corrected and extended the Rudolphine Tables enabling Horrocks and Crabtree to become, famously, the first people ever to observe a transit of Venus.


Like Harriot’s group, Nos Keplari published little but they were collectively even better networked than Harriot. Horrocks had been at Oxford Emmanual College Cambridge with John Wallis and it was Wallis, a convinced nationalist, who propagated Horrocks’ posthumous astronomical reputation against foreign rivals, as he also did in the question of algebra for Harriot. Both Gascoigne and Crabtree had connections to the Towneley family, landed gentry who took a strong interest in the emerging modern science of the period. Later the Towneley’s who had connections to the Royal Society ensured that the work of Nos Keplari was not lost and forgotten, bringing it, amongst other things, to the attention of a young John Flamsteed, who would later become the first Astronomer Royal. . Gascoigne had connections to William Cavendish, the later Duke of Newcastle, under whose command he served at the battle of Marston Moor, where he died. William, his brother Charles and his wife Margaret were all enthusiastic supporters of the new sciences and important members of the English scientific and philosophical community. Gascoigne also corresponded with William Oughtred who served as private mathematics tutor to many leading members of the burgeoning English mathematical community. It is to two of Oughtred’s students that we now turn

William Oughtred by Wenceslas Hollar 1646

William Oughtred
by Wenceslas Hollar 1646

Seth Ward (1617–1689) studied at Oxford Cambridge University from 1636 to 1640 when he became a fellow of Sidney Sussex College.

Greenhill, John; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660) Source: Wikimedia Commons

Greenhill, John; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660)
Source: Wikimedia Commons

In the same year he took instruction in mathematics from William Oughtred. In 1649 he became Savilian Professor of Astronomy at Oxford University the same year that John Wallis was appointed Savilian Professor of Mathematics. Whilst serving as Savilian Professor, Ward became embroiled in a dispute about Keplerian astronomy with the French astronomer and mathematician Ismaël Boulliau.

Ismaël Boulliau  Source: Wikimedia Commons

Ismaël Boulliau
Source: Wikimedia Commons

Boulliau was an early and strong defender of Keplerian elliptical astronomy, who however rejected Kepler’s attempts to create a physical explanation of planetary orbits. Boulliau published his Keplerian theories in his Astronomia philoaïca in 1645. Ward attacked Boulliau’s model in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis from 1653, presenting his own model for Kepler’s planetary laws. Boulliau responded to Ward’s attack in his De lineis spiralibus from 1657. Ward had amplified his own views in his Astronomia geometrica from 1656. This public exchange between two heavyweight champions of the elliptical astronomy did much to raise the general awareness of Kepler’s work in England. It has been suggested that the dispute was instrumental in bringing Newton’s attention to Kepler’s ideas, a claim that is however disputed by historians.

Ward went on to make a successful career in the Church of England, eventually becoming Bishop of Salisbury his successor, as Savilian Professor of Astronomy was another one of Oughtred’s student, Christopher Wren (1632–1723).

Christopher Wren by Godfrey Keller 1711  Source: Wikimedia Commons

Christopher Wren by Godfrey Keller 1711
Source: Wikimedia Commons

Wren is of course much better known as the foremost English architect of the seventeenth-century but started out as mathematician and astronomer. Wren studied at Wadham College Oxford from 1650 to 1653, where he was part of the circle of scientifically interested scholars centred on John Wilkins (1614–1672), the highly influential early supporter of heliocentric astronomy. The Wilkins group included at various times Seth Ward, John Wallis, Robert Boyle, William Petty and Robert Hooke amongst others and would go on to become one of the groups that founded the Royal Society. Wren was a protégé of Sir Charles Scarborough, a student of William Harvey who later became a famous physician in his own right; Scarborough had been a fellow student of Ward’s and was another student of Oughtred’s. Wren was appointed Gresham Professor of Astronomy and it was following his lectures at Gresham College that the meetings took place that would develop into the Royal Society. As already noted Wren then went on to succeed Ward as Savilian Professor for astronomy in 1661, a post that he resigned in 1673 when his work as Surveyor of the King’s Works (a post he took on in 1669), rebuilding London following the Great Fire of 1666, became too demanding. Wren enjoyed a good reputation as a mathematician and astronomer and like Ward was a convinced Keplerian.

Our final English Keplerian is Nicolaus Mercator (1620–1687), who was not English at all but German, but who lived in London from 1658 to 1682 teaching mathematics.

Nicolaus Mercator © 1996-2007 Eric W. Weisstein

Nicolaus Mercator
© 1996-2007 Eric W. Weisstein

In his first years in England Mercator corresponded with Boulliau on the subject of Horrock’s Transit of Venus observations. Mercator stood in contact with the leading English mathematicians, including Oughtred, John Pell and John Collins and in 1664 he published a defence of Keplerian astronomy Hypothesis astronomica nova. Mercator’s work contained an acceptable mathematical proof of Kepler’s second law, the area law, which had been a bone of contention ever since Kepler published it in 1609; Kepler’s own proof being highly debateable, to put it mildly. Mercator continued his defence of Kepler in his Institutiones astronomicae in 1676. It was probably through Mercator’s works, rather than Ward’s, that Newton became acquainted with Kepler’s astronomy. We still have Newton’s annotated copy of the latter work. Newton and Mercator were acquainted and corresponded with each other.

As I hope to have shown there was a strong continuing interest in England in Keplerian astronomy from its very beginnings in 1609 through to the 1660s when it had become de facto the astronomical model of choice in English scientific circles. As I stated at the outset, to become accepted a new scientific theory has to find supporters who are prepared to champion it against its critics. Kepler’s elliptical astronomy certainly found those supporters in England’s green and pleasant lands.





Filed under History of Astronomy, History of Mathematics, History of science, Renaissance Science

Christmas Trilogy 2016 Part 1: Is Newtonian physics Newton’s physics?

Nature and nature’s laws lay hid in night;

God said “Let Newton be” and all was light.

Isaac Newton's Tomb in Westminster Abbey Photo: Klaus-Dieter Keller Source: Wikimedia Commons

Isaac Newton’s Tomb in Westminster Abbey
Photo: Klaus-Dieter Keller
Source: Wikimedia Commons

Alexander Pope’s epitaph sets the capstone on the myth of Newton’s achievements that had been under construction since the publication of the Principia in 1687. Newton had single-handedly delivered up the core of modern science – mechanics, astronomy/cosmology, optics with a side order of mathematics – all packed up and ready to go, just pay at the cash desk on your way out. We, of course, know (you do know don’t you?) that Pope’s claim is more than somewhat hyperbolic and that Newton’s achievements have, over the centuries since his death, been greatly exaggerated. But what about the mechanics? Surely that is something that Newton delivered up as a finished package in the Principia? We all learnt Newtonian physics at school, didn’t we, and that – the three laws of motion, the definition of force and the rest – is all straight out of the Principia, isn’t it? Newtonian physics is Newton’s physics, isn’t it? There is a rule in journalism/blogging that if the title of an article/post is in the form of a question then the answer is no. So Newtonian physics is not Newton’s physics, or is it? The answer is actually a qualified yes, Newtonian physics is Newton’s physics, but it’s very qualified.

Newton's own copy of his Principia, with hand-written corrections for the second edition Source: Wikimedia Commons

Newton’s own copy of his Principia, with hand-written corrections for the second edition
Source: Wikimedia Commons

The differences begin with the mathematics and this is important, after all Newton’s masterwork is The Mathematical Principles of Natural Philosophy with the emphasis very much on the mathematical. Newton wanted to differentiate his work, which he considered to be rigorously mathematical, from other versions of natural philosophy, in particular that of Descartes, which he saw as more speculatively philosophical. In this sense the Principia is a real change from much that went before and was rejected by some of a more philosophical and literary bent for exactly that reason. However Newton’s mathematics would prove a problem for any modern student learning Newtonian mechanics.

Our student would use calculus in his study of the mechanics writing his work either in Leibniz’s dx/dy notation or the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). He won’t be using the dot notation developed by Newton and against which Babbage, Peacock, Herschel and the Analytical Society campaigned so hard at the beginning of the nineteenth century. In fact if our student turns to the Principia, he won’t find Newton’s dot notation calculus there either, as I explained in an earlier post Newton didn’t use calculus when writing the Principia, but did all of his mathematics with Euclidian geometry. This makes the Principia difficult to read for the modern reader and at times impenetrable. It should also be noted that although both Leibniz and Newton, independently of each other, codified a system of calculus – they didn’t invent it – at the end of the seventeenth century, they didn’t produce a completed system. A lot of the calculus that our student will be using was developed in the eighteenth century by such mathematicians as Pierre Varignon (1654–1722) in France and various Bernoullis as well as Leonard Euler (1707­1783) in Switzerland. The concept of limits that are so important to our modern student’s calculus proofs was first introduced by Bernard Bolzano (1781–1848), Augustin-Louis Cauchy (1789–1857) and above all Karl Theodor Wilhelm Weierstrass (1815–1897) in the nineteenth century.

Turning from the mathematics to the physics itself, although the core of what we now know as Newtonian mechanics can be found in the Principia, what we actually use/ teach today is actually an eighteenth-century synthesis of Newton’s work with elements taken from the works of Descartes and Leibniz; something our Isaac would definitely not have been very happy about, as he nursed a strong aversion to both of them.

A notable example of this synthesis concerns the relationship between mass, velocity and energy and was brought about one of the very few women to be involved in these developments in the eighteenth century, Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French aristocrat, lover of Voltaire and translator of the first French edition of the Principia.

In the frontispiece to Voltaire's book on Newton's philosophy, du Châtelet appears as Voltaire's muse, reflecting Newton's heavenly insights down to Voltaire. Source: Wikimedia Commons

In the frontispiece to Voltaire’s book on Newton’s philosophy, du Châtelet appears as Voltaire’s muse, reflecting Newton’s heavenly insights down to Voltaire.
Source: Wikimedia Commons

One should remember that mechanics doesn’t begin with Newton; Simon Stevin, Galileo Galilei, Giovanni Alfonso Borelli, René Descartes, Christiaan Huygens and others all produced works on mechanics before Newton and a lot of their work flowed into the Principia. One of the problems of mechanics discussed in the seventeenth century was the physics of elastic and inelastic collisions, sounds horribly technical but it’s the physics of billiard and snooker for example, which Descartes famously got wrong. Part of the problem is the value of the energy[1] imparted upon impact by an object of mass m travelling at a velocity v upon impact.

Newton believed that the solution was simply mass times velocity, mv and belief is the right term his explanation being surprisingly non-mathematical and rather religious. Leibniz, however, thought that the solution was mass times velocity squared, again with very little scientific justification. The support for the two theories was divided largely along nationalist line, the Germans siding with Leibniz and the British with Newton and it was the French Newtonian Émilie du Châtelet who settled the dispute in favour of Leibniz. Drawing on experimental results produced by the Dutch Newtonian, Willem Jacob ‘s Gravesande (1688–1742), she was able to demonstrate the impact energy is indeed mv2.

Willem Jacob 's Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759) Source: Wikimedia Commons

Willem Jacob ‘s Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759)
Source: Wikimedia Commons

The purpose of this brief excurse into eighteenth-century physics is intended to show that contrary to Pope’s epitaph not even the great Isaac Newton can illuminate a whole branch of science in one sweep. He added a strong beam of light to many beacons already ignited by others throughout the seventeenth century but even he left many corners in the shadows for other researchers to find and illuminate in their turn.





[1] The use of the term energy here is of course anachronistic


Filed under History of Physics, History of science, Myths of Science, Newton, Uncategorized

Werner von Siemens and Erlangen

I (almost)[1] live in the town of Erlangen in Franconia, in Southern Germany. Erlangen is a university town with an official population of about 110 000. I say official because Erlangen has a fairly large number of inhabitants, mostly student, who are registered as living elsewhere with Erlangen as their second place of residence, who are not included in the official population numbers. I suspect that the population actually lies somewhere between 120 and 130 000. Erlangen is dominated by the university, which currently has 40 000 students, although several departments are in the neighbouring towns of Furth and Nürnberg, and is thus the second largest university in Bavaria, and the company Siemens. Siemens, one of Germany’s largest industrial firms, is a worldwide concern and Erlangen is after Berlin and Munich the third largest Siemens centre in Germany, home to large parts of the company’s research and development. It is the home of Siemens’ medical technology branch, Siemens being a world leader in this field. 13 December is the two hundredth anniversary of the birth of Werner von Siemens the founder of the company.

Werner von Siemens (Portrait by Giacomo Brogi) Source: Wikimedia Commons

Werner von Siemens (Portrait by Giacomo Brogi)
Source: Wikimedia Commons

Werner Siemens (the von came later in his life) was born in Lenthe near Hanover the fourth child of fourteenth children of the farmer Christian Ferdinand Siemens and his wife Eleonore Henriette Deichmann on13 December 1894. The family was not wealthy and Werner was forced to end his education early. In 1835 he joined the artillery corps of Prussian Army in order to get an education in science and engineering; he graduated as a lieutenant in 1838.

Werner Siemens as Second-Lieutenant in the Prussian Artillery, 1842 Source: Wikimedia Commons

Werner Siemens as Second-Lieutenant in the Prussian Artillery, 1842
Source: Wikimedia Commons

He was sentenced to five years in military prison for acting as a second in a duel but was pardoned in 1842 and took up his military service. Whilst still in the army he developed an improved version of Wheatstone’s and Cooke’s electrical telegraph in 1846 and persuaded the Prussian Army to give his system field trials in 1847. Having proved the effectiveness of his system Siemens patented it and in the same year founded together with the fine mechanic Johann Georg Halske the Telegraphen-Bauanstalt von Siemens & Halske. They received a commission to construct Prussia’s first electrical telegraph line from Berlin to Frankfurt, which was completed in 1849, when Werner left the army to become an electrical engineer and entrepreneur. The profession of electrical engineer didn’t exist yet and Werner Siemens is regarded as one of its founders.

Pointer telegraph, 1847 (replica) Source: Siemens

Pointer telegraph, 1847 (replica)
Source: Siemens

Already a successful electrical telegraph construction company the next major step came when Werner discovered the principle of dynamo self-excitation in 1867, which enabled the construction of the worlds first practical electric generators. Werner was not alone in making this discovery. The Hungarian Anyos Jedlik discovered it already in 1856 but didn’t patent it and his discovery remained unknown and unexploited. The Englishman Samuel Alfred Avery patented a self-exciting dynamo in 1866, one year ahead of both Siemens and Charles Wheatstone who also independently made the same discovery.

Structure (with cross section) of the dynamo machine 1866 Source: Siemens

Structure (with cross section) of the dynamo machine 1866
Source: Siemens

Throughout his life Werner Siemens combined the best attributes of a scientists, an engineer, an inventor and an entrepreneur constantly pushing the range of his companies products. He developed the use of gutta-percha as material for cable insolation, Siemens laying the first German transatlantic telegraph cable with their own specially constructed cable laying ship The Faraday in 1874. The world’s first electric railway followed in 1879, the world’s first electric tram in 1881 and the world’s first trolleybus in 1882.

The Faraday, cable laying ship of Siemens Brothers & Co. 1874 Source: Wikimedia Commons

The Faraday, cable laying ship of Siemens Brothers & Co. 1874
Source: Wikimedia Commons

Werner Siemens was a great believer in scientific research and donated 500,000 Marks (a fortune), in land and cash, in 1884 towards the establishment of the Physikalisch-Technische Reichsanstalt a state scientific research institute, which finally came into being in 1887 and lives on today under the name Physikalisch-Technische Bundesanstalt (PTB). From the very beginning Werner Siemens thought in international terms sending his brother Wilhelm off to London in 1852 to represent the company and another brother Carl to St Petersburg in 1853, where Siemens built Russia’s first telegraph network. In 1867 Halske left the company and Carl and Wilhelm became partners making Siemens a family company. In 1888, four years before his death, Werner was ennobled becoming Werner von Siemens.

The research and development department of Siemens moved to Erlangen after the Second World War, as their home in Berlin became an island surrounded by the Russian occupation zone. Erlangen was probably chosen because it was already the home of Siemens’ medical technology section. In order to understand how this came to be in Erlangen we need to go back to the nineteenth century and the live story of Erwin Moritz Reiniger.

Siemens-Administration in the 1950s „Himbeerpalast“ Designed by  Hans Hertlein  Note the Zodiac clock dial Source: Wikimedia Commons

Siemens-Administration in the 1950s „Himbeerpalast“ Designed by Hans Hertlein
Note the Zodiac clock dial
Source: Wikimedia Commons

Reiniger born 5 April 154 in Stuttgart was employed as an experiment demonstrator at the University of Erlangen in 1876. He was also responsible for the repair of technical equipment in the university institutes and clinics. Realising that this work could become highly profitable, Reiniger set up as a self-employed fine mechanic in Schlossplatz 3 next door to the university administration in the Schloss (palace) in 1877, producing fine mechanical, physical, optical and simple electro-medical instruments.

Schloss Erlangen (university Administration) Source: Wikimedia Commons

Schloss Erlangen
(University Administration)
Source: Wikimedia Commons

Schlossplatz 3. Site of Reindeer's original workshop Source: Wikimedia Commons

Schlossplatz 3. Site of Reiniger’s original workshop
Source: Wikimedia Commons

Plaque on Schlossplatz 3

Plaque on Schlossplatz 3

By 1885 Reiniger was employing fifteen workers. In 1886 he went into partnership with the mechanics Max Gebbert and Karl Friedrich Schall forming the Vereinigte physikalisch-mechanische Werkstätten von Reiniger, Gebbert & Schall– Erlangen, New York, Stuttgart (RGS). The workshops in New York and Stuttgart were soon abandoned and the company concentrated on Erlangen. Karl Schall left the company in 1888 and Reiniger was bought out by Gebbert in 1895.

Reiniger Gebiert & Schall Letterhead 1896 Source: Wikimedia Commons

Reiniger Gebiert & Schall Letterhead 1896
Source: Wikimedia Commons

Wilhelm Conrad Röntgen discovered X-rays on 8 November 1895 and published his discovery in three scientific papers between then and January 1896.

Wilhelm Conrad Röntgen Source: Wikimedia Commons

Wilhelm Conrad Röntgen
Source: Wikimedia Commons

Famously he didn’t patent his discovery and RGS were already, as the very first company in the world, producing X-ray tubes and X-ray machines in 1896 and this would become the mainstay of their business. There is a rather sweet letter in the Siemens archive from Röntgen, who was professor in Würzburg, not too far away from Erlangen, asking if he could possibly get a rebate if he purchased his X-ray tubes from RGS.

Reiniger, Gebbert & Schall AG Factory in Erlangen constructed in 1883. Now a protected building. Source: Wikimedia Commons

Reiniger, Gebbert & Schall AG Factory in Erlangen constructed in 1883. Now a protected building.
Source: Wikimedia Commons

Following the First World War, RGS got into financially difficulties due to bad management and in 1925 the company was bought by Siemens & Halske, who transferred their own medical technology production to Erlangen thus establishing the medical technology division of Siemens in Erlangen where it still is today. Originally called the Siemens-Reiniger-Werke AG it has gone through more name changes than I care to remember currently being called ‘Healthineers’ to the amusement of the local population, who on the whole find the name ridiculous.

Siemens Medical Museum in the Reiniger, Gebbert & Schall AG Factory Building

Siemens Medical Museum in the Reiniger, Gebbert & Schall AG Factory Building

What of the future? Last week saw the laying of the foundation stone of the new Siemens Campus in Erlangen a 500 million Euro building project to provide Siemens with a new R&D centre for the twenty-first century.

Siemens Campus Architects Model

Siemens Campus Architects Model



[1] I actually live in a small village on the outskirts of Erlangen but the town boundary is about 150 metres, as the crow flies, from where I am sitting typing this post.


Filed under History of Physics, History of science, History of Technology

History (of Science) Books by Women

Last weekend saw several major newspapers publishing their books of the year list. Unfortunately these displayed, in several aspects, a serious lack of balance. Science and history of science books came up more than somewhat short and in some categories the male dominance was glaring. The latter problem provoked the following tweet by historian and history book author Lucy Worsley:

8 of 9 of the ‘history books of the year’ in today’s Times, and 19 out of 21 of ditto in today’s Telegraph, are by men. I’m not impressed. Lucy Worsley

In reaction to this tweet a hash tag sprang into life, #HistoryBooksbyWomen, under which some just listed the names of female history book authors and others tweeted names and book titles. My discipline the history of science is blessed with many excellent female historians, authors of many first class books. This being the case I thought that I might cruise along my bookshelves and present here a lightly annotated list of some of those books by women that have enriched and informed my career as a historian of science.

I start with my #histsci soul sisterTM, Rebekah ‘Becky’ Higgitt, whose volume in the way the nineteenth century saw Isaac Newton, Recreating Isaac, I reviewed here.

Becky is also co-author of the beautiful Finding Longitude, which I reviewed here. (Her co-author Richard Dunn is a man but we won’t hold it against him).

Staying with Newton we have Sarah Dry telling us what happened to his manuscripts in The Newton Papers and Lesley Murdin Under Newton’s Shadow: Astronomical Practices in the Seventeenth Century.


In the world of navigation, cartography and geodesy we have Christine Garwood Flat Earth: The History of an Infamous Idea, Joyce E. Chaplin Round About the Earth: Circumnavigation from Magellan to Orbit, Silvia Sumira Globes: 400 Years of Exploration Navigation and Power and Rachel Hewitt Map of a Nation: A Biography of the Ordnance Survey.


Representing the Middle Ages we have two biographies Nancy Marie Brown The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages and Louise Cochrane Adelard of Bath: The First English Scientist. For fans of automata there is E. R. Truitt’s delightful Medieval Robots: Mechanism, Magic, Nature, and Art.


In the early modern period and the emergence of modern science we have Pamela O. Long Artisan/Practitioners and the Rise of the New Science, Pamela H. Smith The Body of the Artisan, Paula Findlen Possessing Nature: Museums, Collecting, and Scientific Culture in Early Modern Italy, Deborah E. Harkness The Jewel House: Elizabethan London and the Scientific Revolution, Eileen Reeves Galileo’s Glassworks, Lisa Jardine Ingenious Pursuits: Building the Scientific Revolution, her Going Dutch: How England Plundered Holland’s Glory, her On a Grander Scale: The Outstanding Life and Tumultuous Times of Sir Christopher Wren, and her The Curious Life of Robert Hooke: The Man Who Measured London, Ulinka Rublack The Astronomer & the Witch: Johannes Kepler’s Fight for His Mother, Sachiko Kusukawa Picturing the Book of Nature: Image, Text, and Argument in Sixteenth-Century Human Anatomy and Medical Botany and Susan Dackerman ed. Prints and the Pursuit of Knowledge in the Early Modern Period Featuring essays by Susan Dackerman, Lorraine Daston, Katherine Park, Susanne Karr Schmidt and Claudia Swann.


Turning to the eighteenth century we have Patricia Fara A Entertainment for Angels: Electricity in the Enlightenment, Susannah Gibson Animal, Vegetable, Mineral? How eighteenth-century science disrupted the natural order and Jenny Uglow The Lunar Men: The Friends Who Made the Future.


No Renaissance Mathematicus book list would be complete without some esoteric history. We start with Monica Azzolini The Duke and the Stars: Astrology and Politics in Renaissance Milan that I reviewed here, Louise Hill Cuth English almanacs, astrology & popular medicine: 1550–1700, Tamsyn Barton Ancient Astrology, Pamela H. Smith The Business of Alchemy: Science and Culture in the Holy Roman Empire, Frances A. Yates The Rosicrucian Enlightenment and her Giordano Bruno and the Hermetic Tradition as well as Ingrid D. Rowland Giordano Bruno: Philosopher/Heretic. Somewhere between the stools Lorraine Daston & Katherine Park Wonders and the Order of Nature.


Mathematics are represented by Kim Plofker Mathematics in India and Serafina Cuomo Ancient mathematics. Astronomy and cosmology by M. R. Wright Cosmology in Antiquity, Kitty Ferguson Measuring the Universe and Jessica Ratcliff The Transit of Venus Enterprise in Victorian Britain.


We close with a potpourri of titles that don’t quite fit into any of the categories above. We start with two excellent books by Laura J. Snyder, her four-way biography of nineteenth-century Cambridge polymaths The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World and her double seventeenth-century art and science biography Eye of the Beholder: Johannes Vermeer, Antoni van Leeuwenhoek, and the Reinvention of Seeing. Two further biographies are Brenda Maddox Rosalind Franklin: The Dark Lady of DNA and Dorothy Stein Ada: A Life and a Legacy. Patricia Fara gives us a general survey of science history in Science A Four Thousand Year History and a look at the role some women played in that history in Pandora’s Breeches: Women, Science & Power in the Enlightenment. Deborah Jaffé also looks at the role of women in science and technology in Ingenious Women: From Tincture of Saffron to Flying Machines. Last but by no means least we have Ingrid D. Rowland’s translation of Vitruvius: Ten Books of Architecture.


This list is of course fairly random and somewhat arbitrary and is in no way comprehensive or exhaustive. All of the books that I have included are in my opinion good and quite a lot of them are excellent. They demonstrate that there is width, depth and variety in the writings produced by women in the history of science taken in its widest sense. Should any misogynistic male of the species turn up in the comments and claim that the above list is only so impressive, and I find it very impressive, because I, in some way, privilege or favour female historians then I must point out that I have many more history of science books by male authors than by female ones on my bookshelves.

If you wish to add your own favourite history of science books authored by women in the comments you are more than welcome.


Filed under Book Reviews, History of science, Ladies of Science

A Herschel comes seldom alone.

On the excellent website Lady Science Anna Reser and Leila McNeill recently posted an article entitled Well, Actually Mythbusting History Doesn’t Work, which I shall not be addressing. However it contained the interesting statement, When the likes of Caroline Herschel and Ada Lovelace are brought up, a common response is a historical version of “what about the men?!” The men in this case being William Herschel and Charles Babbage. Ignoring Lovelace and Babbage I would like to address the case of the siblings Caroline and William Herschel.

Of course Caroline Herschel is a very important figure in the history of astronomy and deserves to be recognised on her own extensive merits but is it possible to discuss her life and work without mentioning her elder brother? The answer to this question is a clear yes and no. If one were to present a brief bullet point outline of her life then yes, as follows.

Caroline Herschel Source: Wikimedia Commons

Caroline Herschel
Source: Wikimedia Commons

Caroline Herschel German/ British Astronomer

  • Born Hanover 16 March 1750
  • Lived in England 1772–1822
  • Died Hanover 9 January 1848
  • Discoverer of eight comets
  • Recipient of a pension from George III 1787
  • Recipient of the Gold Medal of the Royal Astronomical Society 1828
  • One of the first Woman members of the Royal Astronomical Society, elected 1835
  • Awarded Gold Medal for Science by the King of Prussia 1846

However if one goes beyond the highly impressive outline and starts to examine her biography in depth then it is impossible not to mention her brother William who played a decisive role at almost every stage of her live.

Stunted and disfigured by a bout of typhus in her childhood, Caroline was not considered a suitable candidate for marriage. Her illiterate mother did not hold much of education for women so it seemed that Caroline was destined for a life of domestic drudgery. However William her elder brother, having established himself as a professional musician in the city of Bath, fetched her from Hanover to come and live with him as his housekeeper in 1772. In Bath she shared the attic flat with their younger brother Alexander, of whom more later, whilst William lived on the first floor, which was also his music studio where amongst other things he delivered music lessons. The ground floor was occupied by a married couple, who worked as William servants, also paying rent for their accommodation. Caroline took over the running of this household.

William Herschel 1785 portrait by Lemuel Francis Abbott Source: Wikimedia Commons

William Herschel 1785 portrait by Lemuel Francis Abbott
Source: Wikimedia Commons

William took over Caroline’s education teaching her to sing as well as instructing her in arithmetic and English. Soon she began to appear as a soloist in William public recitals and made such a positive impression that am impresario offered her the opportunity of going on tour as a singer, an offer that she declined preferring to stay in Bath with her brother.

When William developed his passion for astronomy Caroline became his assistant, rather grudgingly at first but later with enthusiasm, recording and tabulating her brother telescopic observations. When William began to manufacture his own telescopes Caroline was once again at hand, as assistant. When I visited the Herschel Museum in Bath I learnt that one of Caroline’s tasks was to sieve the horse manure that they used to embed the cast telescope mirrors to grind and polish them. I highly recommend visiting this museum, where you can view the Herschel’s telescope workshop in the cellar. Caroline also took over the task of calculating and compiling the catalogue of William’s observation. It should be very clear that the siblings worked as a team, each playing an important role in their astronomical endeavours.

Later after the discovery of Uranus, when William became the King’s astronomer and they moved to Datchet near Windsor, he encouraged Caroline to become an astronomer in her own right teaching her how to sweep the skies looking for comets and constructing a small reflecting telescope for this purpose. Caroline would go on to have a very successful career as a comet hunter, as already noted above.

I hope that in this very brief sketch that I have made it clear that William played a key role at each juncture in Caroline’s life and that without him she never would have become an astronomer, so any full description of her undoubted achievements must include her bother and his influence. However there is a reverse side to this story, as should be very clear from my brief account, any description of William Herschel’s achievements, as an astronomer, must include an explanation of Caroline’s very central role in those discoveries.

Any account of William’s and Caroline’s dependency on each other in their astronomical careers should also include the role played by their younger brother Alexander. Like William and their father, Alexander was a highly proficient professional musician, who had moved into William’s house in Bath, as Caroline was still living in Hanover. Alexander apparently played a role in the decision to bring Caroline to Bath. As well as being a talented musician Alexander was a highly skilled craftsman and when William decided to start building his own Newtonian telescopes, it was Alexander who provided the necessary metal components including the telescope tubes for the small objective scopes used to view the image in a Newtonian. The Herschel telescope production was very much a family business. The Herschel telescopes enjoyed a very good reputation and manufacturing and selling them became a profitable sideline for the siblings. The two sides of the Herschel’s astronomical activities fertilised each other. The quality of the telescopes underlined the accuracy of the observations and the accuracy of the observations was positive advertising for the telescopes.

Replica of a Herschel Newtonian Reflector. Herschel Museum Bath Source: Wikimedia Commons

Replica of a Herschel Newtonian Reflector. Herschel Museum Bath
Source: Wikimedia Commons

It should be now clear that when considering the Herschel’s astronomical activities we really have to view all three siblings as a unit, as well as viewing them as individuals but our collection of Herschels does not end here. As should be well known William’s son John would go on to be a highly significant and influential polymath in the nineteenth century, amongst other things setting forth the family’s astronomical tradition. John was very close to his aunt Caroline and it was she and not his father who first introduced the young Herschel sprog to the joys and fascinations of astronomical observation.

ohn Frederick William Herschel by Alfred Edward Chalon 1829 Source: Wikimedia Commons

ohn Frederick William Herschel by Alfred Edward Chalon 1829
Source: Wikimedia Commons

Although the Herschels form a relatively closed family unit in their astronomical activities, they also employed a joiner to make the tubes and stands for their reflectors, they also provide a very good example of they fact that observational astronomy, and in fact much scientific activity, is team work and not the product of individuals.




Filed under History of Astronomy, History of science, Ladies of Science

Why there weren’t any scientists before the late nineteenth century.

It has become common practice for historians of science to admonish people who use the term scientist when applied to people who lived before the nineteenth century. They point out, correctly, that the word was first coined by Cambridge polymath William Whewell in 1833 at the British Association for the Advancement of Science meeting in Cambridge and first used in print by him a year later in his review of Mary Somerville’s On the Connection of the physical sciences. As Melinda Baldwin has shown in her guest post, The history of “scientist”, the term didn’t really become established until late in the nineteenth century or even early in the twentieth. On being thus admonished many people react negatively and ask pointedly whether historians of science mean that there was no science before 1833. On being told that this is not the case they argue that if people were doing science then it is perfectly acceptable to call them scientists. If they are doing science then they are scientists, end of story!

Unfortunately it is not as easy as that, because terms have connotations, which extend well beyond their simple denotations. For those readers who are not up on the jargon of linguistics or the philosophy of language I will try to explain the terms denotation and connotation with a simple example. Expert linguists and philosophers of language should look the other way for a minute or two. The name Sascha denotes the dog whose picture you can see in the top right hand corner of this blog. The name Sascha connotes, for me, all of the things that I experienced with him throughout the ten years that we shared our lives, a wild mixture of a thousand different emotions. Returning to the term scientists, it denotes quite simply someone who does science (whatever that may be, a can of worms I don’t intend to open today). To the distress of real life scientists, cartoonists, playwrights, film directors and others often present a sort of cardboard cut out generic figure as a scientist: white, male, bearded, wearing glasses and a white lab coat. Even the sexy female scientist presented in more up to date TV series is usually given the glasses and the white lab coat to establish their professional identity. This clichéd list of characteristics is the superficial connotation that is generated in their minds and often in that of their readers and viewers by the term scientist.

On a less superficial level the word scientists, as used since the beginning of the twentieth century, has a very strong set of characteristics, its connotation, that spring to the reader’s or listener’s mind when confronted with the term. This list of characteristic’s are usually centred round the scientist’s education, training and professional experience; the clue here lies in the word professional. The scientist is an expert who has undergone a lengthy and extensive specialist education and training to qualify them for their profession and who has enough experience in that profession to justify their being called a scientist. This set of characteristics for the scientist is something that only came into being, rather gradually, over the course of the nineteenth century. If we go back before that time the set of characteristics that we find associated with people doing what we would recognise as science is very different and in fact changed over the centuries, since science began to emerge in Europe in the High Middle Ages. In what follows I shall restrict my remarks to Europe and the period between about twelve hundred CE and eighteen hundred CE. The problems of using the term scientist for earlier periods and other cultures are even greater than those I will outline here.

In the high Middle Ages most of the sciences, as we now know them, simply didn’t exist. Alchemy/chemistry, including much that we would now call applied or industrial chemistry, was regarded as an art practiced by artisans. Where art here means technique or technology or even handcraft. Whilst its practitioners might regard themselves as seekers after or even possessors of knowledge their image was not even remotely like that of our image invoked by the word scientist. Mathematicus, astrologus, astronomus were all synonyms for the same profession, again the practitioner of an art, artisans. Mostly employed outside of the universities, often in the courts of rulers, these ‘mathematicians’ were usually principally employed as astrologers but their full job description included many other functions. Astronomer, horologist (that is designer and maker of sundials), hydraulic engineer in charge of designing water features in ornamental gardens and a whole host of other activities we would normally associate with a technician or engineer. Their social status was that of a craftsman, albeit an upper grade one, rather than that of an academic, also far from out image of the scientist.

Physics belonged in the universities, practiced by philosophers, but this was the physics of Aristotle, the study of nature and contained much that is foreign to our concept of physics. Also this was mostly a qualitative descriptive study and not a quantitative empirical one. Although some of its practitioners, such as for example Robert Grosseteste of Roger Bacon, espoused ideas similar to our concept of the scientific method in their writings their actually their actually practice bears little resemblance to that of modern scientists. Although bearing the same name, their institutions, the medieval universities, have very little in common with our modern institutes of higher educations.

There is very little change in this state of affairs up to the sixteenth century, as the demand for the use of mathematics in astronomy for cartography and navigation as well as astrology in medicine began to change the status of its practitioners. It is first in the seventeenth century when the work of people such as Kepler, a court mathematicus, and Galileo, a university teacher of astrology for medical students, began to intrude into the traditional domain of the philosophers and redefine the nature and subject matter of physics that quantitative empirical research began to make inroads into the universities. In this context it is highly relevant that when Galileo left the university for the Medici court in Florence he insisted on the title philosophicus as well as mathematicus because of the lowly status of the latter in comparison to the former, These practitioners became known not as scientists but as natural philosophers and their career profiles and public image were still substantially different to that of modern scientists. The seventeenth century also saw the gradual emergence of geology, zoology, biology and botany as separate disciplines with expert practitioners from the philosophers’ earlier domain of natural history. Chemistry didn’t make its way into the universities until the eighteenth century and then only as a handmaiden to medicine, only gaining recognition as a discipline in its own right in the nineteenth century.

Let us pause for a while and look at the career profiles of the most well known figures, who contributed to the evolution of the mathematical sciences in the sixteenth and seventeenth centuries. Copernicus was a canon of the cathedral chapter of Frombork and basically an administrator or civil servant of the prince-bishopric of Ermland (Warmia). Astronomy was so to speak his hobby. His life has nothing in common with our concept of a scientist. Tycho Brahe was a Danish aristocrat, who set up a research institute for astronomy and Paracelsian medicine on a Scandinavian island in something resembling a castle and which included a court jester and a pet elk, which got drunk and broke its neck falling down some stairs. Tycho’s life was about as far removed from the twenty first century idea of a scientist as you can get. As already mentioned Johannes Kepler was a schoolteacher and district mathematicus, meaning amongst other things astrologer, who went on to become a court mathematicus, meaning principally astrologer; once again almost nothing in common with a modern scientist. Galileo was actually a university professor for mathematics but his principle activity would have been teaching astrology to medical students. He later became a court philosopher, basically an intellectual court jester. Descartes was a mercenary or soldier of fortune, who then retired to the live of a gentleman of leisure, alternating with periods of being a court philosopher with the same function as Galileo. None of these people had any real formal education or training as a ‘scientist’. There were no white coats and with the exception of Tycho nothing even remotely resembling a laboratory. Neither Copernicus nor Kepler even had an observatory. Today, we would tend to regard Newton as a physicist but he was actually a professor of mathematics in Cambridge. However a professor, who had almost no students and whose lectures appear to have been very scantily attended. He abandoned academia to become Warden and then Master of the Mint a post with little to do with his scientific activities. None of these figures who are leading lights in the pantheon of scientific heroes even remotely fulfils our connotations of a scientist.

The term physics was first used in the way we use it at the beginning of the second decade of the eighteenth century and didn’t become common usage in this sense until the nineteenth century. The term physicist was first coined even later than the term scientist. It really was first in the nineteenth century that the people doing science first began to fulfil the connotations that we have when we hear or read the word scientist, so it really is for the best if we refrain from using the term for researchers who lived in earlier periods.






Filed under History of science

A spirited defence

After I had, in my last blog post, mauled his Scientific American essay in my usual uncouth Rambo style, Michael Barany responded with great elegance and courtesy in a spirited defence of his historical claims to which I now intend to add some comments, thus extending this exchange by a fourth part.

On early practical mathematicians Michael Barany acknowledges that their work is for the public good but argues correctly that that doesn’t then a “public good”. I acknowledge that there is a difference and accept his point however I have a sneaky feeling that something is only referred to as a “public good” when somebody in power is trying to put one over on the great unwashed.

Barany thinks that the Liber Abbaci and per definition all the other abbacus books, only exist for a closed circle of insider and not for the general public. In fact abbacus books were used as textbooks in so-called abbacus schools, which were small private schools that taught the basics of arithmetic, algebra, geometry and bookkeeping open to all who could pay the fees demanded by the schoolteacher, who was very often the author of the abbacus book that he used for his teaching. It is true that the pupils were mostly the apprentices of tradesmen, builders and artists but they were at least in theory open to all and were not quite the closed shop that Michael Barany seems to be implying. In this context Michael Barany says that Recorde’s Pathway to Knowledge, a book on elementary Euclidean geometry, is eminently impractical. However elementary Euclidean geometry was part of the syllabus of all abbacus schools considered part of the necessary knowledge required by artist and builder/architect apprentices. In fact the first Italian vernacular translation of Euclid was made by Tartaglia, an abbacus schoolteacher.

Michael Barany makes some plausible but rather stretched argument to justify his couterpositioning of Recorde and Dee, which I don’t find totally convincing but slips into his argument the following gem. If you don’t like Dee as your English standard bearer for keeping mathematics close to one’s chest, try Thomas Harriot. Now I assume that this flippant comment was written tongue in cheek but just in case.

Michael Barany’s whole essay contrasts what he sees as two approaches to mathematics, those who see mathematics as a topic for everyone and those who view mathematics as a topic for an elitist clique. In the passage that I criticised in his original essay he presented Robert Recorde as an example of the former and John Dee as a representative of the latter. A contrast that he tries to defend in his reply, where this statement about Harriot turns up. Now his elitist argument is very much dependent on a clique or closed circle of trained experts or adepts who exchanged their arcane knowledge amongst themselves but not with outsiders. A good example of such behaviour in the history of science is alchemy and the alchemists. Harriot as an example of such behaviour is a complete flop. Thomas Harriot made significant discoveries in various fields of scientific endeavour, mathematics, dynamics, chemistry, optics, cartography and astronomy, however he never published any of his work and although he corresponded with other leading Renaissance scholars he also didn’t share his discoveries with these people. A good example of this is his correspondence with Kepler, where he discussed over several letters the problem of refraction but never once mentioned that he had already discovered what we now know as Snell’s Law. Harriot remained throughout his life a closed circle with exactly one member, not a very good example to illustrate Michael Barany’s thesis.

I claimed that there was no advance mathematics in Europe from late antiquity till the fifteenth century. Michael Barany counters this by saying: This cuts, for instance, the rich history of Islamic court mathematics out of the European history in which it emphatically belongs; it doesn’t cut it. Ignoring Islamic Andalusia, Islamic mathematics was developed outside of Europe and although it started to reappear in Europe during the twelfth and thirteen centuries during the translator period nobody within Europe was really capable of doing much with those advanced aspects of it before the fifteenth century, so I stand by my claim.

We now turn to Michael Barany’s defence of his original: In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty. This he contrast with a, in his opinion, eighteenth century where mathematicians help sway over the scientific community. I basically implied that this claim was rubbish and I still stand by that to that, so what does Michael Barany produce in his defence.

In my original post I listed seven leading scholars of the seventeenth century who were mathematicians and whose very substantive contributions to the so-called scientific revolution was mathematical, on this Barany writes:

Thony pretends that naming some figures remembered today both for mathematics and for their contributions to the scientific revolution contradicts this well-established historical claim.

The, without any doubt, principle figures of the so-called scientific revolution are just some figures! Interesting? So what is Michael Barany’s well-established historical claim? We get offered the following:

Following Steven Shapin and many who have written since his classic 1988 article on Boyle’s relationship to mathematics, I chose to emphasize the conflicts between the experimental program associated with the scientific revolution and competing views on the role of mathematics in natural philosophy.

What we have here is an argument by authority, that of Steven Shapin, whose work and the conclusions that he draws are by no means undisputed, and one name Robert Boyle! Curiously a few days before I read this, science writer, John Gribbin, commentated on Facebook that Robert Hooke had to work out Boyle’s Law because Boyle was lousy at mathematics, might this explain his aversion to it? However Michael Barany does offer us a second argument:

But to take just his most famous example, Newton’s prestige in the Royal Society is generally seen today to have had at least as much to do with his Opticks and his other non-mathematical pursuits as with his calculus, which contemporaries almost uniformly found impenetrable.

Really? I seem to remember that twenty years before he published his Opticks, Old Isaac wrote another somewhat significant tome entitled Philosophiæ Naturalis Principia Mathematica [my emphasis], which was published by the Royal Society. It was this volume of mathematical physics that established Newton’s reputation, not only with the fellows of the Royal Society, but with the entire scientific community of Europe, even with those who rejected Newton’s central concept of gravity as action at a distance. This book led to Newton being elected President of the Royal Society, in 1704, the same year as the Opticks was published. The Opticks certainly enhanced Newton’s reputation but he was already considered almost universally by then to be the greatest living natural philosopher.

Is the Opticks truly non-mathematical? Well, actually no! When it was published it was the culmination of two thousand years of geometrical optics, a mathematical discipline that begins with Euclid, Hero and Ptolemaeus in antiquity and was developed by various Islamic scholars in the Middle Ages, most notably Ibn al-Haytham. One of the first mathematical sciences to re-enter Europe in the High Middle Ages it was propagated by Robert Grosseteste, Roger Bacon, John Peckham and Witelo. In the seventeenth-century it was one of the mainstream disciplines contributing to the so-called scientific revolution developed by Thomas Harriot, Johannes Kepler, Willebrord van Roijen Snell, Christoph Scheiner, René Descartes, Pierre Fermat, Christiaan Huygens, Robert Hooke, James Gregory and others. Newton built on and developed the work of all these people and published his results in his Opticks in 1706. Yes, some of his results are based on experiments but that does not make the results non-mathematical and if you bother to read the book you will find more than a smidgen of geometry there in.

In my opinion trying to recruit Newton as an example of non-mathematical experimental science is an act of desperation.

To be fair to Michael Barany the division between those who favoured non-mathematical experimental science and the mathematician really did exist in the seventeenth century, however it was largely confined to England and most prominently in the Royal Society. This is the conflict between the Baconians and the Newtonians that I have blogged about on several occasions in the past. Boyle, Hooke and Flamsteed, for example, were all Baconians who, following Francis Bacon, were not particularly fond of mathematical proofs. This conflict has an interesting history within the Royal Society, which led to disadvantages for the development of the mathematical sciences in England in the eighteenth century.

When the Royal Society was initially founded some mathematician did not become members because of the dominance of the Baconians and that despite the fact that the first President, William Brouncker, was a mathematician. Later under Newton’s presidency the mathematicians gained the ascendency, but first in 1712 after an eight-year guerrilla conflict between Newton and Hans Sloane, a Baconian and the society’s secretary. Following Newton’s death in 1727 (ns) the Baconians regained power and the result was that, whereas on the continent the mathematical sciences flourished and evolved throughout the eighteenth century, in England they withered and died, leading to a new power struggle in the nineteenth century featuring such figures as Charles Babbage and John Herschel.

To claim as Michael Barany does that this conflict within the English scientific community meant that mathematics played an inferior role in the seventeenth century is a bridge too far and contradicts the available historical facts. Yes, the mathematization of nature was not the only game in town and interestingly non-mathematical experimental science was not the only alternative. In fact the seventeenth century was a wonderful cuddle-muddle of conflicting meta-physical views on the sciences. However whatever Steven Shapin might or might not claim the seventeenth century was a very mathematical century and mathematics was the principle driving force behind the so-called scientific revolution. As a footnote I would point out that many of the leading experimental natural philosophers of the seventeenth century, such as Galileo, Pascal, Stevin and Newton, were mathematicians who interpreted and presented their results mathematically.


Filed under History of Mathematics, History of science, Newton