Category Archives: Ladies of Science

Hypatia – What do we really know?

The fourth century Alexandrian mathematician and philosopher Hypatia has become a feminist icon. She is probably the second most well known woman in #histSTM after Marie Curie. Unfortunately, down the centuries she has been presented more as a legend or a myth intended to fulfil the teller’s purposes rather than a real human being. As Alan Cameron puts it in his excellent essay, Hypatia: Life, Death, and Works:[1]

A pagan in the Christian city of Alexandria, she is one of those figures whose tragic death inspired a legend which could take almost any form because so few facts are known. As a pagan martyr, she has always been a stick to beat Christians with, a symbol in the continuing struggle between science and revealed religion. The memorable account in Gibbon begins wickedly “On a fatal day in the holy season of lent.” As a woman she can be seen as a feminist as well as a pagan martyr. Her name has been a feminist symbol down the centuries more recently a potent name in lesbian and gay circles. As an Egyptian, she has also been claimed as a black woman martyr. There is an asteroid named after her, a crater on the moon, and a journal of feminist studies. As early as 1886, the women of Wichita Kansas, familiar from the movies of our youth as a lawless western cattle town, formed a literary society called the Hypatia Club. Lake Hypatia in Alabama is a retreat for freethinkers and atheists. Rather less in tune with her scholarly activity, there is Hypatia Capital, a merchant bank whose strategy focuses on the top female executives in the Fortune 1000.

A few minutes’ googling will produce countless eulogies of Hypatia as a uniquely gifted philosopher, mathematician and scientist, the second female scientist after Marie Curie, the only woman in antiquity appointed to a university chair, a theorist who anticipated Copernicus with the heliocentric hypothesis. The 2009 movie Agoragoes even further in this direction. A millennium before Kepler, Hypatia discovered that earth and its sister planets not only go round the sun but do so in ellipses, not circles. She remained unmarried, and could therefore be seen as a model of pagan virginity. Alternatively, since the monks are said to have killed her because of her influence on the prefect of Egypt, she could be seen as a slut. It is fascinating to observe how down the centuries she served as a lay figure for the prejudices of successive generations.

So what do we know about the real Hypatia? The answer is almost nothing. We know that she was the daughter of Theon (c.335–c.405) an Alexandrian mathematician and philosopher, most well known for his edition of The Elements of Euclid. We don’t know her birth date with estimates ranging from 350 to 370 CE. Absolutely nothing is known about her mother to whom no references whatsoever exist. It is assumed that she was educated by her father but once again, whilst highly plausible, no real evidence exists for this assumption. If we take a brief looked at the available sources for her biography the reason for all of this uncertainty becomes very clear.

The only source we have from somebody who actually knew Hypatia is Synesius of Cyrene (c.373–probably 413), who was one of her Christian students around 393 CE. In 410 CE he was appointed Bishop of Ptolemais. There was an edition of his letters, which contains seven letters to Hypatia and some to others that mention her. Unfortunately his letters tell us nothing about he death as he predeceased her. His last letter to her was written from his deathbed in 413 CE. Two of his letters, however, request her assistance for acquaintances in civil matters, which indicates that she exercised influence with the civil authorities.

Our second major source is Socrates of Constantinople (c.380–died after 439) a Christian church historian, who was a contemporary but who did not know her personally. He mention her and her death in his Historia Ecclesiastica:

There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, she not infrequently appeared in public in the presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.

The third principle source is Damascius (c.458–after 538) a pagan philosopher, who studied in Alexandria but then moved to Athens where he succeeded his teacher Isidore of Alexandria (c.450–c.520) as head of the School of Athens. He mentions Hypatia in his Life of Isidore, which has in fact been lost but which survives as a fragment that has been reconstructed.

We also have the somewhat bizarre account of the Egyptian Coptic Bishop John of Nikiû (fl. 680–690):

And in those days there appeared in Alexandria a female philosopher, a pagan named Hypatia, and she was devoted at all times to magic, astrolabes and instruments of music, and she beguiled many people through her Satanic wiles. And the governor of the city honoured her exceedingly; for she had beguiled him through her magic. And he ceased attending church as had been his custom… And he not only did this, but he drew many believers to her, and he himself received the unbelievers at his house.

It is often claimed that she was head of The Neo-Platonic School of philosophy in Alexandria. This is simply false. There was no The Neo-Platonic School in Alexandria. She inherited the leadership of her father’s school, one of the prominent schools of mathematics and philosophy in Alexandria. She however taught a form of Neo-Platonic philosophy based mainly on Plotonius, whereas the predominant Neo-Platonic philosophy in Alexandria at the time was that of Iamblichus.

If we turn to her work we immediately have problems. There are no known texts that can be directly attributed to her. The Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world list three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria.

Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary.  Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption.

All of this means that she produced no original mathematics but like her father only edited texts and wrote commentaries. In the history of mathematics Theon is general dismissed as a minor figure, who is only important for preserving texts by major figures. If one is honest one has to pass the same judgement on his daughter.

Although the sources acknowledge Hypatia as an important and respected teacher of moral philosophy there are no known philosophical texts that can be attributed to her and no sources that mention any texts from her that might have been lost.

Of course the most well known episode concerning Hypatia is her brutal murder during Lent in 414 CE. There are various accounts of this event and the further from her death they are the more exaggerated and gruesome they become. A rational analysis of the reports allows the following plausible reconstruction of what took place.

An aggressive mob descended on Hypatia’s residence probably with the intention of intimidating rather than harming her. Unfortunately, they met her on the open street and things got out of hand. She was hauled from her carriage and dragged through to the streets to the Caesareum church on the Alexandrian waterfront. Here she was stripped and her body torn apart using roof tiles. Her remains were then taken to a place called Cinaron and burnt.

Viewed from a modern standpoint this bizarre sequence requires some historical comments. Apparently raging mobs and pitched battles between opposing mobs were a common feature on the streets of fourth-century Alexandria. Her murder also followed an established script for the symbolic purification of the city, which dates back to the third-century. There was even a case of a pagan statue of Separis being subjected to the same fate. There is actually academic literature on the use of street tiles in street warfare[2]. What is more puzzling is the motive for the attack.

The exact composition of the mob is not known beyond the fact that it was Christian. There is of course the possibility that she was attacked simply because she was a woman. However, she was not the only woman philosopher in Alexandria and she enjoyed a good reputation as a virtuous woman. It is also possible that she was attacked because she was a pagan. Once again there are some contradictory facts to this thesis. All of her known students were Christians and she had enjoyed good relations with Theophilus the Patriarch of Alexandria (384–412), who was responsible for establishing the Christian dominance in Alexandria. Theophilus was a mentor of Synesius. Also the Neoplatonic philosophy that she taught was not in conflict with the current Christian doctrine, as opposed to the Iamblichan Neoplatonism. The most probably motive was Hypatia’s perceived influence on Orestes (fl. 415) the Roman Prefect of Egypt who was involved in a major conflict with Cyril of Alexandria (c.376–444), Theophilis’ nephew and successor as Patriarch of Alexandria. This would make Hypatia collateral damage in modern American military jargon. In the end it was probably a combination of all three factors that led to Hypatia’s gruesome demise.

Hypatia’s murder has been exploited over the centuries by those wishing to bash the Catholic Church but also by those wishing to defend Cyril, who characterise her as an evil woman. Hypatia was an interesting fourth-century philosopher and mathematician, who deserves to acknowledged and remembered for herself and not for the images projected on her and her fate down the centuries.

[1]Alan Cameron, Hypatia: Life, Death, and Works, in Wandering Poets and Other Essays on Late Greek Literature and Philosophy, OUP, 2016 pp. 185–203 Quote pp. 185–186

[2]You can read all of this in much more detail in Edward J. Watts’ biography of Hypatia, Hypatia: The Life and Legend of an Ancient Philosopher, OUP, 2017, which I recommend with some reservations.



Filed under History of Mathematics, History of science, Ladies of Science, Myths of Science

Monsieur Joseph Jérôme Lefrançois de Lalande et Les Dames

The cliché concept of a Frenchman is of the prime example of a chauvinist and the eighteenth century is not renowned as a period of equality for women, so it might come as somewhat of a surprise that an eighteenth century Frenchman very much championed the positive role of women in astronomy; that man was Joseph Jérôme Lefrançois de Lalande (1732–1807).


Jérôme Lalande after Joseph Ducreux Source: Wikimedia Commons

Jérôme Lalande illustrates rather well something that is fundamentally wrong with the way that much history of science is conceived and presented. I have a moderately large collection of general reference works on the history of science and the history of astronomy, encyclopaedia, dictionaries, and lexica. In this works Jérôme Lalande almost never appears and if at all usually just as a minor footnote to somebody or something else. However, although he never made a major astronomical discovery, and thus his absence from the reference works, he was in the second half of the eighteenth century a leading figure in the astronomical community, not just in France but throughout the whole of Europe, as a organiser, coordinator, communicator, educator and populariser, all activities very necessary to the evolution of any scientific discipline.

He was born 11 July 1832 in Bourge-en-Bresse and was educated at a Jesuit academy. He went to Paris to study law but having got to know Joseph-Nicolas Delisle (1644­–1720) he became an ardent astronomer and a pupil of both Delisle and Charles Le Monnier (1715–1799).


Joseph Nicolas Delisle by Konrad Westermayr Source: Wikipedia Commons

Despite this passion, he completed his law degree and was about to return to Bourge-en-Bresse to become a lawyer when Lemonnier sent him to Berlin to measure lunar parallax together with Nicolas-Louis de Lacaille (1732–1762) in South Africa. The success of this operation led to his election to the Academy of Berlin, as well as the French Academy of Science. He now devoted his life to astronomy. Over the years he was successively elected to the Royal Swedish Academy of Science and The American Academy of Arts and Sciences. In 1762 he was appointed Delisle’s successor as professor of astronomy at the Collège de France. Amongst his most famous students were Jean-Baptiste Joseph Delambre (1749–1822), Giuseppe Piazzi (1746–1826), Pierre Méchain (1744–1804) and his nephew Michel Lefrançois de Lalande (1766–1839). In 1773 he edited more that 250 articles on astronomy for the supplement to Diderot’s and d’Alembert’s legendary encyclopaedia. From 1760 to 1776 he was editor of the Connaissance des tempsthe official French astronomical year book. From 1795 he also became the director of the Paris observatory in which role he issued a star catalogue of 30,000 stars later expanded to 41,000. As an astronomer his principle activity of the years consisted of carrying out the mathematical calculation of orbits, the paths of comets, solar eclipses and the astronomical unit based on the observations of the Transit of Venus in 1761 and 69, as well as the orbit of Venus.  It was here that the lady astronomers entered his life and his work.

As a young man he assisted Alexis-Claude Clairaut in the recalculation of the orbit of Comet Halley. Lalande was ably assisted in this tedious but complex mathematical work by Nicole-Reine Lepaute (1723–1788). In his publication Clairaut did not acknowledge Lepaute’s contribution, which angered Lalande, who honoured her work so:

We calculated from morning to night for six months…Mme. Lépaute’s help was such that I would not have been able to tackle the enormous task without her.


Taken from Winterburn The Quite Revolution of Caroline Herschel see footnote 1

Nicole-Reine Étable de la Briere was born 5 January 1723 in Paris began to take an interest in mathematics and astronomy in around the time she married her husband Jean-André Lepaute the royal clock maker. Together with her husband she designed and constructed an astronomical clock, which was presented to the French Academy of Science in 1753. She, her husband and Lalande worked on a book entitled Traite d’horologerie(Treatise on Clockmaking) that was published under her husbands name in 1755. Although she was not mentioned as author Lalande honoured her contribution as follows:

“Madame Lepaute computed for this book a table of numbers of oscillations for pendulums of different lengths, or the lengths for each given number of vibrations, from that of 18 lignes, that does 18000 vibrations per hour, up to that of 3000 leagues.”

Following her work with Lalande on Comet Halley, she again collaborated with him on the ephemeris for the 1761 Transit of Venus.  She also collaborated with Lalande for fifteen years on the calculations for the Connaissance des temps. In 1762 she calculated the exact time for a solar eclipse that occurred on 1 April 1764. She also wrote an article on the eclipse with an eclipse map. She produced star catalogues and calculated an ephemeris of the sun, moon and the planets from 1774 to 1784. Although childless she adopted and trained he husband nephew, Joseph Lepaute Dagelet (175116788) in astronomy and mathematics. He went on to become professor of mathematics at the French Military School and later deputy astronomer at the French Academy of Science, where he had a distinguished career. A comet and a crater on the moon are named in her honour.

Lalande’s second lady ‘computer’ (the term used for the people, usually women, employed to do the often complex but tedious and repetitious astronomical calculations was Elisabeth Louise Félicité du Pierry, née Pourra de la Madeleine, who was born 1746 but who’s date of death is unknown/disputed, possibly 1807. She met Lalande in 1779 and began to study astronomy under him after the death of her husband. Her main work was on eclipses of the sun and moon based on historical data that she collected. Lalande based his own lunar orbit work on her research. She is said to have been the first woman to have offered lecture courses at a French university when she lectured at the Sorbonne on astronomy for women­–Cours d´astronomie ouvert pour les dames et mis à leur portée. Lalande dedicated his book, Astronomie des Dames(of which more later) to her stating: “She represents a model for all women through her high intellectual qualities.” She later dropped out of astronomy and took up chemistry instead.

Lalande’s third lady computer was his own illegitimate daughter Marie-Jeanne-Amélie Harley (1768–1832), who married his nephew Michel Lefrançois de Lalande. The young couple studied astronomy together under Lalande and were his assistants at the Paris Observatory helping to calculate and complete the star catalogues. Marie-Jeanne-Amélie work very closely with her father contributing to many of his publications. Gauss is reputed to have said that he knew only one French women working in science, Madame Lefrançois de Lalande. She had two children, a daughter named Caroline after Caroline Herschel and a son named Isaac after Newton. The De Lalande crater on the moon is named after her.

In the naming of his grand daughter we get a strong clue that Lalande’s respect for female astronomers was not restricted to his own assistants and family. In fact Lalande was one of the strongest male supporters of Caroline Herschel, who he respected immensely, which is reflected by her writing directly to him rather than communicating through her brother William, although William was a close colleague and friend of Lalande’s.


Caroline Herschel Source: Wikimedia Commons

Without a doubt Lalande’s greatest contribution to the support of women in astronomy was his Astronomie des Dames published in 1785 with two further updated and expanded editions in 1795 and 1806,which explains various aspects of astronomy for the female reader and praises the work of famous female astronomers beginning with Hypatia, including his own co-workers and going up to Caroline Herschel, who was added in the second edition. Lalande was a renowned and successful author of popular books on astronomy so his decision to write about female astronomers in a laudatory manner had quite a lot of impact. The second editions from 1795 covers the following women:

Hypatia (the ancient Greek philosopher)

Maria Cunitz

Maria-Claire Eimart Muller

Jeanne Dumée

Hevelius’s wife (this is how he describes her, not by name but by association)

Manfredi’s sisters (as above)

Kirch’s thre sisters and his wife, née Winkelmann

La Marquise de Châtelet

Madame Lapute

Mrs Edwards (from the Nautical Almanacin England)

Madam du Piery

His niece Lefrançois de Lalande

Miss Caroline Herschel[1]

 (you can read about Maria Cunitz, Maria Kirch née Winkelmann, Elisabeth Koopman Hevelius and Maria Clara Eimart here)

As Emily Winterburn explains (see footnote 1) Lalande’s book follows in a tradition of popular science books written specifically for ladies. This starts with Bernard Le Bovier de Fontenelle’s Entretiens sur la pluralité des mondes(Conversations on the Plurality of Worlds) (1686) and includes John Harris’ Astronomical Dialogues Between a Gentleman and a Lady(1719), Benjamin Martin’s Gentlemen and Ladies Philosophy(1759) and Francesco Algarotti’s Il newtonianismo per le dame(1737) (Sir Isaac Newton’s Philosophy Explained for the use of Ladies, in six dialogues on Light and Colour(1739)). Lalande acknowledges Fontenelle’s influence on his own work.

Although with Lalande we still have a man employing women in a subservient position and then writing about them rather than women working for and writing about themselves, we have in the way that he supported, acknowledged and praised women in his work a major advance on nearly everything that had gone before.







[1]This list is taken from Emily Winterburn’s excellent The Quite Revolution of Caroline Herschel:The Lost Heroine of Astronomy, The History Press, Stroud, 2017 pp. 221-222, which I reviewed here. Winterburn’s book together with a tweet from RAS Women in STEM @RAS_Women about Marie-Jeanne-AmélieLefrançois de Lalande inspired this blog post.

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Filed under History of Astronomy, Ladies of Science

Can we please stop (mis)quoting Albert on Emmy, it’s demeaning?

Emmy Noether, whom I’ve blogged about a couple of times in the past, is without any doubt one of the greats in the history of mathematics, as is well documented by the testimonials written by some of the greatest contemporary mathematicians and physicists and collected in Auguste Dick’s slim but well research biography, Emmy Noether: 1882–1935.

Emmy Noether c. 1930
Source:Wikimedia Commons

Yesterday was World Maths Day and the Royal Society tweeted portraits of mathematicians with links to articles all day, one of those tweets was about Emmy Noether. The tweet included a paraphrase of a well known quote from Albert Einstein, after all what could be better than a quote from old Albert the greatest of the great? Well almost anything actually, as the Einstein quote is highly demeaning. As given informally by the Royal Society it read as follows:

Emmy Noether was described by Einstein as the most important woman in the history of mathematics.

What Einstein actually wrote in a letter to the New York Times on the occasion of her death in 1935 was the following:

In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered, methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.

In the same year, but before she died, Norbert Wiener wrote:

Miss Noether is… the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of Madame Curie.

Now I’m sure that the Royal Society, Albert Einstein and Norbert Wiener all meant well, but take a step back and consider what all of them said in their different ways, Emmy Noether was pretty good for a woman [my emphasis].

Emmy Noether was one of the greatest mathematicians of the twentieth century, male or female, man or woman, about that there is absolutely no doubt, to qualify that praise with the term woman is quite simple demeaning.

In my mind it triggers the text of Melanie Safka’s mega pop hit from 1971, Brand New Key:

I ride my bike, I roller skate, don’t drive no car

Don’t go too fast, but I go pretty far

For somebody who don’t drive

I been all around the world

Some people say, I done all right for a girl [my emphasis]

On twitter, space archaeologist, Alice Gorman (@drspacejunk) took it one stage further, in my opinion correctly, and asked, “Dare I cite Samuel Johnson’s aphorism about the talking dog?” For those who are not up to speed on the good doctor’s witticisms:

I told him I had been that morning at a meeting of the people called Quakers, where I had heard a woman preach. Johnson: “Sir, a woman’s preaching is like a dog’s walking on his hind legs. It is not done well; but you are surprised to find it done at all.” – Boswell: Life

Can we please in future when talking about Emmy Noether resist the temptation to quote those who affix their praise of her mathematical talents with the term woman and just acknowledge her as a great mathematician?



Filed under History of Mathematics, Ladies of Science

A Lady Logician

Today George Boole is regarded as one of the founders of the computer age that now dominates our culture.

George Boole
Source: Wikimedia Commons

His algebra lies at the base of computer circuit design and of most computer programming languages and Booleans power the algorithms of the ubiquitous search engines. As a result two years ago the bicentenary of his birth was celebrated extensively and very publically. All of this would have been very hard to predict when his work on the algebra of logic first saw the light of day in the nineteenth century. His first publication Mathematical Analysis of Logic (1847) was largely ignored by the wider world of mathematics and his definitive presentation of his logic An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities fared little better, initially attracting very little attention. It was only some time after his death that Boole’s logical works began to attract deeper interest, most notably in Germany by Ernst Schröder and in America by Charles Sanders Peirce.

Charles Sanders Peirce
Source: Wikimedia Commons

In 1883 Peirce published Studies in Logic: by Members of the Johns Hopkins University, edited by himself it contained seven papers written largely by his students. Of central interest is the fact that it contains a doctoral thesis, On the Algebra of Logic, written by a women, Christine Ladd.

Christine Ladd’s life story is a casebook study of the prejudices that women, who wished to enter academia suffered in the nineteenth and early twentieth centuries. Born 1 December 1847 (the year Boole published his first logic book) in Windsor, Connecticut the daughter of Eliphalet and Augusta Ladd, she grew up in New York and Windsor. Her mother and her aunt Julie Niles brought her up to believe in education for women and women’s rights. Her mother died in 1860 but her father initially supported her wish for advanced education and enrolled her at Welshing academy in a two year course for preparing students for college; she graduated as valedictorian in 1865 but now her father opposed her wish to go on to college. Only by arguing that she was too ugly to get a husband was she able to persuade her father and grandmother to allow her to study at the women’s college Vassar. She entered Vassar in 1866 but was forced by financial difficulties to leave before completing her first year. She now became a schoolteacher until her aunt helped her to finance her studies and she returned to Vassar.

At Vassar the pioneering female astronomer Maria Mitchell took her under her wing and fostered her developing interest in physics and mathematics.

Due to the fact that women could not do experiment work in laboratories she was forced to choose mathematics[1] over physics, a decision that she regretted all of her life. She graduated from Vassar in 1869 and became a secondary school teacher of mathematics and science in Washington, Pennsylvania. Over the next nine years she published six items in The Analyst: A Journal of Pure and Applied Mathematics and three in the American Journal of Mathematics. More importantly she took a very active part in the mathematical questions column of the Educational Times, the journal of the College of Preceptors in London, a profession body for schoolteachers. This mathematical questions column was a very popular forum for nineteenth century mathematicians and logicians with many leading practitioners contribution both question and solutions. For example the nineteenth-century Scottish logician Hugh McColl published his first logical essays here and Bertrand Russell’s first mathematical publication can also be found here[2]. Ladd contributed a total of seventy-seven problem and solution to the Education Times, which would prove highly significant for her future career.

In 1878 she applied for and won a fellowship to study mathematics at the Johns Hopkins University. Her fellowship application was simply signed C. Ladd and the university had assumed that she was male. When they realised that she was in fact a woman, they withdrew their offer of a fellowship. However the English professor of mathematics at Johns Hopkins, James J. Sylvester, who knew of Ladd’s abilities from those Educational Times contribution insisted on the university honouring the fellowship offer.

James Joseph Sylvester
Source: Wikimedia Commons

At the time Johns Hopkins did not have a very good reputation but Sylvester did, in fact he was a mathematical star, not wishing to lose him the university conceded and allowed Ladd to take up her three-year scholarship. However her name was not allowed to be printed in circulars and basically the university denied her existence. At the beginning she was only allowed to attend Sylvester’s classes but as it became clear that she was an exceptional student she was allowed to attend classes by other professors.

In the year 1879 to 1880 she studied mathematics, logic and psychology under Charles Sanders Peirce becoming the first American women to be involved in psychology. Under Peirce’s supervision she wrote her doctoral thesis On the Algebra of Logic, which was then, as mentioned above, published in 1883. Although she had completed all the requirements of a doctoral degree Johns Hopkins University refused to award her a doctorate because she was a woman. They only finally did so forty-four years later in 1927, when she was already seventy-eight years old.

In 1882 she married fellow Johns Hopkins mathematician Fabian Franklin and became Christine Ladd-Franklin, the name by which she is universally known today. As a married woman she was barred from holding a paid position at an American university but she would lecture unpaid for five years on logic and psychology at Johns Hopkins and later at Columbia University for thirty years.

In the 1880s she developed an interest in vision and theories of colour perception publishing her first paper on the subject in 1887. She accompanied her husband on a research trip to Germany 1891-92 and used the opportunity to study with the psychologist Georg Elias Müller (1850–1934) in Göttingen

George Elias Muller
Source: Wikimedia Commons

and with the physiologist and physicist Hermann von Helmholtz (1821-1894) in Berlin.

Hermannvon Helmholtz in 1848
Source: Wikimedia Commons

In 1894 she returned alone to Germany to work with physicist Arthur König (1856–1901), with whom she did not get on and whom she accused of having stolen her ideas, and again in 1901 to work with Müller.

Portrait of Arthur Konig from Pokorny, J.
Source: Wikimedia Commons

As a result of her researches she developed and published her own theories of colour vision and the causes of colour blindness that were highly influential.

Ladd-Franklin was a tireless campaigner for women’s rights and even persuaded the inventor of the record player, Emile Berliner, to establish a fellowship for female professors, the Sarah Berliner postdoctoral endowment, in 1909, which she administered for the first ten years and which is still awarded annually.

Emile Berliner
Source: Wikimedia Commons

She herself continued to suffer rejection and humiliation as a female academic. In 1904 the British psychologist Edward Titchener (1867–1927) founded a society for experimental psychologists, “The Experimentalists”, and although he knew Ladd-Franklin well her barred her, as a woman, from membership. A decision, which she fought against in vain for many years. Women were only permitted to attend following Titchener’s death.

Edward Bradford Titchener
Source: Wikimedia Commons

Despite the discrimination that she suffered Christine Ladd-Franklin published many papers in the leading journals and her work was held in high regard. She died of pneumonia, aged 82, in 1930. Today the American Association for women in Psychology have an annual Christine-Ladd Franklin Award, awarded for significant and substantial contributions to the Association.

Christine Ladd-Franklin
Source: Wikimedia Commons

Although she struggled against prejudice and discrimination all of her life and never received the formal recognition that should have been her due, Christine Ladd-Franklin made significant contributions to the fields of Boolean algebra and colour vision for which she is highly regarded today. Through her fighting spirit and unbending will she helped open the doors of scientific research and academia for later generations of women.



[1] It is interesting to note that barred from access to academia and its institutions a small but significant number of women managed to some extent to break through the glass ceiling in logic and the mathematics in the nineteenth century, because these are subjects in which one can make an impression with nothing more than a pencil and a piece of paper.

[2] In my days as a logic historian I spent a not very pleasant two weeks in the British Newspaper Library in Colindale (the tenth circle of hell), amongst other things, going through the Educational Times looking for contributions on the algebra of logic. During this search I came across the Bertrand Russell contribution, which I showed, some time later, to a leading Russell scholar of my acquaintance, who shall remain here nameless. Imagine my surprise when shortly afterwards an article was published by said Russell expert explaining how he had discovered Russell’s first ever mathematical publication in the Mathematical Questions column of The Educational Times. He made no mention of the fact that it was actually I who had made the discovery.


Filed under History of Logic, History of Mathematics, History of science, Ladies of Science, Uncategorized

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


DO IT! is the title of a book written by 1960s Yippie activist Jerry Rubin. In the 1970s when I worked in experimental theatre groups if somebody suggested doing something in a different way then the response was almost always, “Don’t talk about it, do it!” I get increasingly pissed off by people on Twitter or Facebook moaning and complaining about fairly trivial inaccuracies on Wikipedia. My inner response when I read such comments is, “Don’t talk about it, change it!” Recently Maria Popova of brainpickings posted the following on her tumblr, Explore:

The Wikipedia bio-panels for Marie Curie and Albert Einstein reveal the subtle ways in which our culture still perpetuates gender hierarchies in science. In addition to the considerably lengthier and more detailed panel for Einstein, note that Curie’s children are listed above her accolades, whereas the opposite order appears in the Einstein entry – all the more lamentable given that Curie is the recipient of two Nobel Prizes and Einstein of one.

How ironic given Einstein’s wonderful letter of assurance to a little girl who wanted to be a scientist but feared that her gender would hold her back. 

When I read this, announced in a tweet, my response was a slightly ruder version of “Don’t talk about it, change it!” Within minutes Kele Cable (@KeleCable) had, in response to my tweet, edited the Marie Curie bio-panel so that Curie’s children were now listed in the same place as Einstein’s. A couple of days I decided to take a closer look at the two bio-panels and assess Popova’s accusations.

Marie Curie c. 1920 Source Wikimedia Commons

Marie Curie c. 1920
Source Wikimedia Commons

The first difference that I discovered was that the title of Curie’s doctoral thesis was not listed as opposed to Einstein’s, which was. Five minutes on Google and two on Wikipedia and I had corrected this omission. Now I went into a detailed examination, as to why Einstein’s bio-panel was substantially longer than Curie’s. Was it implicit sexism as Popova was implying? The simple answer is no! Both bio-panels contain the same information but in various areas of their life that information was more extensive in Einstein’s life than in Curie’s. I will elucidate.

Albert Einstein during a lecture in Vienna in 1921 Source: Wikimedia Commons

Albert Einstein during a lecture in Vienna in 1921
Source: Wikimedia Commons

Under ‘Residences’ we have two for Curie and seven for Einstein. Albert moved around a bit more than Marie. Marie only had two ‘Citizenships’, Polish and French whereas Albert notched up six. Under ‘Fields’ both have two entries. Turning to ‘Institutions’ Marie managed five whereas Albert managed a grand total of twelve. Both had two alma maters. The doctoral details for both are equal although Marie has four doctoral students listed, whilst Albert has none. Under ‘Known’ for we again have a major difference, Marie is credited with radioactivity, Polonium and Radium, whereas the list for Albert has eleven different entries. Under ‘Influenced’ for Albert there are three names but none for Marie, which I feel is something that should be corrected by somebody who knows their way around nuclear chemistry, not my field. Both of them rack up seven entries under notable awards. Finally Marie had one spouse and two children, whereas Albert had two spouses and three children. In all of this I can’t for the life of me see any sexist bias.

Frankly I find Popova’s, all the more lamentable given that Curie is the recipient of two Nobel Prizes and Einstein of one, comment bizarre. Is the number of Nobel Prizes a scientist receives truly a measure of their significance? I personally think that Lise Meitner is at least as significant as Marie Curie, as a scientist, but, as is well known, she never won a Nobel Prize. Curie did indeed win two, one in physics and one in chemistry but they were both for two different aspects of the same research programme. Einstein only won one, for establishing one of the two great pillars of twentieth-century physics, the quantum theory. He also established the other great pillar, relativity theory, but famously didn’t win a Nobel for having done so. We really shouldn’t measure the significance of scientists’ roles in the evolution of their disciplines by the vagaries of the Nobel awards.



Filed under History of Chemistry, History of Physics, History of science, Ladies of Science