Those Amazing Boole Girls

  

From left to right, from top to bottom: Margaret Taylor, Ethel L. Voynich, Alicia Boole Stott, Lucy E. Boole, Mary E. Hinton, Julian Taylor, Mary Stott, Mary Everest Boole, George Hinton, Geoffrey Ingram Taylor, Leonard Stott.

As it happens, it was on Ada Lovelace Day, "an international celebration of the achievements of women in science, technology, engineering and maths" that I first decided I need to know more, and write about the daughters of George and Mary Everest Boole. I was reading Sibohan Robert's, The King of Infinity, about Donald Coxeter (A very entertaining book).
While he was a student of H F Baker at Trinity, Cambridge they attended "tea parties"; tea, biscuits (cookies for US folks), and lots of geometry at Baker's home. When his time to discuss his research Cam, the 21 year old Coxeter introduced his "Aunt Alice", the 68 year old Alicia Boole Stott, to deliver a joint lecture. I had read about Mary E. Boole, and knew a little about her relationship with Hinton (more later) and her teaching and string art and.... Ok, I had a lot of the Gossip, with very little detail. Since it was Ada Lovelace Day, I decided to remind myself, and some of my readers who had not known about them well, to Mary and her daughters, mostly all raised after George Boole had died (Alicia, the middle daughter was four years old, and her baby sister Ethel was only six months). Some of what follows is from notes I have accumulated over the years, and some is from recent searching. If you have access to information about the family not included here, especially about Margaret, I would love to have you share.

Ok, So maybe this event might have happened a little later than Professor Coxeter remembers in his book to Ms. Roberts. It more likely was when Donald was 23 and Alicia was 69/70 since according to most sources she was introduced to young Donald in 1930 by the Cambridge physicist, Geoffrey Ingram Taylor. This Taylor just happened to be Alicia's nephew, the son of her second oldest sister, Margaret. Get used to this, it seems that everyone in the UK is related to everyone else, or at least it seems that way in this exploration.

So let's start with the Mom, Mary Everest Boole (the Everest??? Her uncle was the one for whom they renamed the mountain). Mary got her introduction to mathematics in France where her father had gone to try and cure his health using homeopathic methods. (In fact it seems he was staying at the home of Christian Friedrich Samuel Hahnemann, who is credited with inventing homeopathic medicine. The Reverend Everest was a strong believer in homeopathy, and is said to have preached it from the pulpit. He published A Letter addressed to the Medical Practitioners of Great Britain on the Subject of Homeopathy, 1834, Pickering, London, A Popular View of Homeopathy .)
From about age 11, she used her father's library to teach herself math as she no longer attended school. She met George while visiting relatives in Ireland. Boole had only recently been appointed as the first professor of mathematics at Queen's College, Cork in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was Professor of Greek in the university. (Boole would write a dedication in his "Laws of Thought" to Ryall. )

After she returned to England, they continued to correspond until he came to England to be her tutor during a break from his University duties. About this time, her father died and presently Mary and George were married. During this time he wrote Laws of Thought, and Mary was instrumental in the editing.
It seems she had not been George's first love. In a letter from Ethel Lilian Voynich, the youngest daughter, to her nephew, the previously mentioned G I Taylor on 9 May 1954. she relates a story of the Parry family of Lincoln, a daughter of which Boole is reputed to have fallen in love with in his youth, and never got over until he met Mary Everest. The Miss Parry ahd refused to marry him as he would not sign the 39 Articles of the Church of England (more later on George's strong and unconventional religious leanings). By some accounts, there may have been several infatuations of various levels for young George. In Desmond MacHale's biography, The Live and Work of George Boole, he writes, "Boole... was a romantic at heart and fell in and out of love quite easily. ...a pupil of Boole's both in Lincoln and in Cork, wrote in a letter to his parents, 'Mr Boole is reported to have lost his heart again."

After a brief, but apparently happy nine years of married life, George died leaving Mary with five young girls all less than age ten. The details of George's unusual death are in some part related to Mary's father's influence and their mutual attraction to homeopathic medicine. One day in 1864, George walked three miles in the drenching rain and lectured wearing wet clothes. He soon became ill, developing a severe cold and high fever. His wife felt that a remedy should resemble the cause. She put George to bed and threw buckets of cold water over him (cold water and ice baths were a common part of homeopathic treatment at the time), since his illness had been caused by getting cold and wet. George Boole's condition worsened and on 8 December 1864, Boole died of an attack of fever, ending in pleural effusion.
In the earlier mentioned letter from Ellen Boole Voynich to G. I. Taylor she also includes that a bitter rivalry had existed between her mother and her aunt Maryann Boole (This most likely refers to George's sister, Mary Ann, the same as her mother.) as Maryann believed Mary E. Boole hastened her husband's death by following the recommendations of a doctor who advocated cold water cures, and making Boole lie shivering between the sheets. Ethel remarks "The Everests do seem to have been a family of crooks and cranks."
It should be pointed out that George was also a follower of homeopathic practices, but perhaps with a little less enthusiasm than his wife. In a letter to Augustus DeMorgan on 17 July, 1860 he writes, "The moral is - if you are ever attacked with inflammation and homeopathy does not produce decided effects soon, do not sacrifice you life to an opinion...but call in some accredited... Esculapius (Aesculapius was the Latin god of medicine, son of Apollo and Coronis. The first temple, with a sanatorium, was erected to him in Rome in 293) with all his weapons of war and do as your ancestors did - submit to being killed or cured according to the rule." In the mid 19th century, homeopathic followers were not all "crooks and cranks. DeMorgan believed he had been cured by homeopathy, and was a follower as well.

After George Boole died, Mary returned to London with four of the five children, Alicia stayed for about seven years with family in Cork.

Although one frequently reads that they were essentially impoverished, (Coxeter writes,... "the five girls were reunited with their mother (whose books reveal her as one of the pioneers of modern pedagogy) in a poor, dark, dirty, and uncomfortable lodging in London."   ) It seems this might well have exaggerated the case. After a London newspaper, reporting on Boole's death, suggested that the Boole family had been left unprovided for, donations poured in from their friends in London and around the UK. That the "unprovided for" seems not to have been the case is attested to by a letter (3 Feb 1865) from Isaac Todhunter of St. John's College Cambridge. He apologizes for any upset caused and states the subscriptions were refunded.

Mary took a job as a librarian at Queens College, probably through her knowledge of Reverend F. D. Maurice, who was one of several religious reformers with unconventional views that George admired. George had strong disagreements with many authoritarian views of religion, but never wrote on these ideas himself, although he was openly a supporter of several others, including Maurice, and John W. Colenso, the Bishop of Natal ( Colenso was a better than average mathematician himself, having been Second Wrangler and a Smith's Prize winner, and had taught at Harrow School as mathematical tutor for awhile and was the author of a popular arithmetic.).
Maurice was also one of the founders of Queens College, which was  England's first women's college. Working with the students there she, and others around her, realized that she was an exceptional teacher. It was during this time that she created the idea of "string art" for teaching students about mathematical and geometric ideas. Many years later the art form would become very popular in the US. Her approach to teaching would fit very neatly among many reform minded educators of the last thirty years. She once wrote, "The geometric education may begin as soon as the child’s hands can grasp objects. Let him have, among his toys, the five regular solids and a cut cone."  She also suggested that no child should be given a multiplication table until they have produced one on their own.

"She wrote several books which were published much later but she certainly had the ideas for them when unofficially tutoring at Queen's College. Examples of these books are (i) Logic Taught By Love (1890), (ii) Lectures on the Logic of Arithmetic (1903), (iii) The preparation of the child for science (1904), and (iv) Philosophy and the fun of algebra (1909).  " (St Andrews History of Math web site)
Her "Philosophy and the fun of algebra" is available, read aloud. [This link appeared to have changed, will pursue reconstruction]The introduction alone is worth the visit. 
Mary was interested in spiritualism and as a result of a book she wrote caused her to lose her library job. She found employment with a friend of her father, the surgeon, spiritualist and reformer, James Hinton. He was also, according to his son, a radical advocate of polygamous relationships.
"James Hinton’s writing, focused on domestic life, was outside of mainstream philosophical and cultural thought, and radical in its avocation of polygamous relationships, freer relations between the sexes, and the benefits of female nudity." (M J Blackloc, A cultural history of higher space, 1869-1909)

In 1880, Mary's oldest daughter, Mary Ellen, married James Hinton's son, another unusual character, named Charles Howard Hinton. I have written about Hinton's unusual life and some notable achievements here. His book on the fourth dimension was influential on Coxeter, and he was known to work with the three younger children during his courtship by showing them colored blocks he had made for studying 4-D. This would seem to have a special effect on the middle daughter, Alica. Hinton was Science Master at Uppingham School in the early 1880's at the same time that the Maths Master there was Abbott's friend Howard Candler, the "H.C." to whom Flatland was dedicated.

Hinton created several new words to describe elements in the fourth dimension. According to OED, he first used the word tesseract in 1888 in his book A New Era of Thought. He also invented the words "kata" (from the Greek "down from") and "ana" (from the Greek "up toward") to describe the two opposing fourth-dimensional directions—the 4-D equivalents of left and right, forwards and backwards, and up and down.  

In the 80's Mary Ellen traveled with Hinton to Japan. Her long letters [1888 - 1891] back to her family indicate she was teaching school there (she mentions giving her students essays on the customs of Japan so that she can learn about them, as Yokohama is very westernized). They traveled frequently, and she speaks often of the beauty of the country. She makes no mention of her own writing, or of C. H. Hinton's work there.

Then around 1893 Hinton has a job as a professor in Princeton. It was here that he invented the gunpowder charged pitching machine that would. with modifications for safety, find its way into baseball forever. The machine was featured in an article in Harper's Weekly, for March 20, 1897. He apparently was quite popular with students, who nicknamed him "bull", supposedly for his great strength. After a Pennsylvania-Princeton football game, Prof. Hinton became the hero of the students by physically throwing a large Pennsylvania supporter over a fence after the man had attempted to snatch a yellow chrysanthemum from Hinton's Coat.
For whatever reason, he left for a position as Assistant Professor at the University of Minnesota, where he seemed to stay only a short time. In 1900 he resigned the university and went to work at the Naval Observatory in Washington, D.C. Simon Newcomb, recently retired, was still active in direction of the affairs of the observatory, and had also written on the fourth dimension, so he may have been essential in Hinton's new position there. Hinton would also have an unusual death.

Hinton suffered a cerebral hemorrhage and dropped dead on the spot while leaving the annual banquet of the Washington, D.C., Society of Philanthropic Inquiry. He was a prominent member of the Society and had wound up the evening by complying with the toastmaster's request for a toast to "female philosophers." His death is described in an article called "Scientist Drops Dead" in the Washington Post of Wednesday, May 1,1907.
(Rudy Rucker's introduction to Speculations on the Fourth Dimension: Selected Writings  of Charles H. Hinton,)

Mary Ellen would take her own life the following year. She was found dead of asphyxiation in her home on May 28 of 1908. The short article in the New York Times described her as "a frequent contributor to English and American Magazines." The article also quoted her as having recently written that, "life is something we have the privilege of ending when we choose. When think it is time to die, I shall end it all." There is a book of poetry, Other Notes by Mary Boole Hinton, published in 1901 that I take to be hers.

Margaret, the second of the girls would marry the artist Edward Ingram Taylor, and give birth to the Geoffrey Taylor mentioned earlier and a second son, Julian. One of Edward Taylor's works, titled Lambert Castle, is in the Fitzwilliam Museum, in Cambridge, but It seems that his real source of income was designing decorations for cruise lines. I am more partial to this charcoal sketch of his son at about age three.

Geoffrey was a major figure in fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". In 1944 he would be knighted, and awarded the Copley Medal from the Royal Society.
Son Julian was an accomplished surgeon. He also would distinguish himself during World War II when he volunteered, at the age of fifty. Shortly after his arrival there, Malaya and Singapore were overwhelmed by the Japanese and he was taken prisoner. After an interval an order was issued that all senior officers were to be transferred to camps in Formosa but, following universal request and pressure, Julian Taylor was permitted to remain in Changi Prison with the others, where for the next three and a half years he carried out remarkable work, not only in the field of surgery working with negligible facilities but, even more, in the field of morale by his inspiration to men much younger than himself. With his wide range of knowledge and experience he could lecture on English history, French history, the City of London, the tides round the English Coasts and the sailing of small boats, thus relieving the tedium and hopelessness of the situation. He was awarded the CBE for this service. Margaret, seems to be the most difficult of the five sisters to find information about. Perhaps she simply chose to be the wife and mother who would raise incredible children.  Perhaps she had a life full of richness that many people have who lead quiet lives.  Perhaps both of these are true. 

Alicia Boole, the "Aunt Alice" mentioned in the beginnings of this blog, was surely the most mathematical of these unusual women.  Her only education was from her mother, but given that Mary E. had proven herself an outstanding teacher, perhaps her mothers use of models prepared her for the incredible capacity she would have to visualize higher dimensions.  By whatever means, when Charles Hinton walked in to visit the home and pulled out his colored blocks of the 3D projections of four dimensional solids, Alicia was enthralled.  She quickly outpaced her brother-in-law. During this time she was only 17, and developed the ability to visualize in a fourth dimension.
She found that there were exactly six regular polytopes in four dimensions and developed the term polytope. She also produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods and made cardboard models of all these sections. Later she was a contributor to his book. For Hinton's, A new era of thought published in 1888, (in which he introduces the term tesseract) Alicia Boole wrote part of the chapters on sections of 3-dimensional solids.
After her sister and brother-in-law departed England for Japan, she took a job as a secretary in Liverpool where she would meet and marry her husband, the actuary, Walter Stott the following year. She had two children in the first two years of marriage, and little time it would seem to talk about the fourth dimension, but she or her husband noticed an appeal by the Dutch mathematician Schoute for the solution to the other half of some four-dimensional geometry program he had partially resolved. Alice had the other half in the models she had made.

Schoute and Alicia Boole Stott

Schoute came thereafter each summer, and they continued to work together. Schout persuaded her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.

At the tercentenary of the University of Groningen, they made a big deal about the collaboration and the models, and they sent back to Alice a fancy scroll, in Latin, which she couldn't read. Later her son read it and exclaimed, "Jesus Christ, they're making you a Doctor."  (This story seems almost unbelievable as arrangements had been made for Alicia to stay with Schoute's widow.  It is hard to imagine that she was unaware of the reason for her visit, but she lived in a world of hard to imagine things, so I include the story.)
Leonard would have been about 23 years old by this time and may have been very fluent in Latin. He went on to be a doctor of merit, "a pioneer in the treatment of tuberculosis, and invented a portable x-ray machine." (Vita Mathematica: Historical Research and Integration with Teaching edited by Ronald Calinger) For his 30 plus years at the Papworth Village settlement which was tried to provide a "normal" life to sufferers of tuberculosis allowing them to be with their families, have and raise children, etc. Fears for the young death of children born into such an environment proved unfounded. For his service to the country he was awarded the OBE.

Using the special capacity of her mind, she developed a new method to visualize four-dimensional polytopes. In particular, she constructed the three-dimensional sections of these four-dimensional objects. The result is a series of three-dimensional polyhedra, which she illustrated making drawings and three-dimensional models. The presence of an extensive collection in the University of Groningen (The Netherlands) reveals a collaboration between Boole Stott and the Groningen professor of geometry P. H. Schoute. This collaboration lasted more than 20 years and combined Schoute’s analytical methods with Boole Stott unusual ability to visualize the fourth dimension. After Schoute’s death (1913), the University of Groningen in 1914 awarded an honorary doctorate to Boole Stott.

For whatever reason, Alicia did not make the trip to Groningen and the award was made in her absence.
After that she seemed to quit working on her polytopes for a period of about 15 years, then the introduction to Coxeter gave renewed life to her work and they corresponded and visited until he left for Canada in 1936. She would die four short years later.
For people who imagine that all mathematicians have some special knack for seeing the fourth dimension, a story that may illustrate somewhat how profound was Alicia's talent. One of the great (some say greatest) geometers alive today is John H Conway.  He told this story to Siobhan Roberts during a conference in Japan :

while he was at Cambridge circa 1960, he made an earnest attempt to think in four dimensions.  Being a geometer, Conway naturally preferred contemplating a fourth dimension in terms of space. 　In attempting to visualize a fourth coordinate or dimension in space, Conway built a device that allowed him to see with what he called “double parallax” ─ in addition to the displacement that occurs horizontally when you look at an object by closing one eye and then the other, he tried to train himself to see vertical parallax. If he could experience both horizontal and vertical parallax, he would have four coordinates for every point in space, and thus would be seeing four dimensions. In his attempt to do so, Conway donned a recycled motorcycle helmet, adapted with a flat visor and cheap, old war- surplus periscopes. The periscopes were bolted to the visor (not very well; they rattled when he walked) and extended from his right eye up to his forehead and his left eye down toward his chin. The only name Conway had for the helmet was“that damned contraption”because it was rather uncomfortable, his nose pressed up against the visor, as a child’ s to a toy shop window at Christmas. 　Conway had a strong desire to see four dimensions, which he truly believed was possible (Conway died in 2020, perhaps he now can see in much higher dimensions). He regularly walked around wearing his helmet in the Fellows Garden of his college at Cambridge, and in a flash of daring (or stupidity) during one Saturday in the downtown streets busy with shoppers.“I suppose I had a limited amount of success in that quixotic quest,”he told me.“I got to the point where I could see four dimensions, but there was no hope of going beyond, so what’ s the point?

Lucy Everest Boole, sister number four, was an Irish chemist and pharmacist and professor at the London School of Medicine for Women. She was the first female Fellow of the Royal Institute of Chemistry. Lucy Boole never married and lived with her mother. She became ill in 1897 and died in 1904 at the age of 42.

In 1902 Ethel Lilian Boole, the youngest of the girls, married Wilfrid Michael Voynich, a Polish revolutionary, antiquarian, and bibliophile, the eponym of the Voynich manuscript (I first learned of the Voynich manuscript in exploring Belphagor's Prime, the number 100000000000000666000000000000001. This beautiful palindromic prime has a 1 at each end, with 666, the number of the beast in the middle, and thirteen ones on each side separating the 666 from the units. The symbol even had its own symbol, a sort of inverted π. The symbol itself comes from the Voynich Manuscript.) She is most famous for her novel The Gadfly, first published in 1897 in the United States (June) and Britain (September), about the struggles of an international revolutionary in Italy. This novel was very popular in the Soviet Union and was the top bestseller and compulsory reading there, and was seen as ideologically useful; for similar reasons, the novel has been popular in the People's Republic of China as well. By the time of Voynich's death The Gadfly had sold an estimated 2,500,000 copies in the Soviet Union and was made into a movie in 1928 in Soviet Georgia (Krazana) and in 1955. (At the time I am writing this, the book is available in Kindle edition for free. The mysterious Voynich Manuscript, was \($4.99 \)US) 

In 1955, the Soviet director Aleksandr Fajntsimmer adapted the novel into a film of the same title (Russian: Ovod). Composer Dmitri Shostakovich wrote the score (see The Gadfly Suite, like everything else in the universe, it's on Youtube). Along with some other excerpts, the Romance movement has since become very popular. Shostakovich's Gadfly theme was also used in the 1980s, in the BBC TV series Reilly, Ace of Spies. In 1980 the novel was adapted again as a TV miniseries The Gadfly, featuring Sergei Bondarchuk as Father Montanelli.

I mentioned Geoffrey Taylor, the physicist son of Margaret.  Mary Ellen's two sons distinguished themselves as well. George Hinton worked as a metallurgist in Mexico, and  made extensive classifications of the flora and fauna of central and southern Mexico with his son.  His collections included well in excess of 300 new species and four new genera. His son, Howard Everest, extended the education provided in the fields by his father to become one of Englands outstanding entomologists, and perhaps the worlds foremost expert on Dryopoidea, (a taxonomic superfamily of beetles).  And in 2024 the recognition of this line continued to grow when Geoffrey Everest Hinton, son of Howard Everest Hinton, the beetle guy, and great great grandson of George and Mary Boole,  was jointly awarded the Nobel Prize in Physics with John Hopfield "for foundational discoveries and inventions that enable machine learning with artificial neural networks." His development of the Boltzmann machine was explicitly mentioned in the citation.  When the New York Times reporter Cade Metz asked Hinton to explain in simpler terms how the Boltzmann machine could "pretrain" backpropagation networks, Hinton quipped that Richard Feynman reportedly said: "Listen, buddy, if I could explain it in a couple of minutes, it wouldn't be worth the Nobel Prize." [Showing that he had a sense of humor, something most people doubted about his father, H.E Hinton.]

Sebastian Hinton, Charles and Mary Ellen's youngest son and a Chicago Lawyer (the firm had the Wrigley's Gum acct) is credited with the invention of that school yard staple, the Jungle Jim. He hit on an idea of bringing his father's work somewhat into the hands of the public-at-large--specifically, into the hands of children, who would be able to play and climb and swing in Charles' fourth dimensional idea.  He applied for a patent in 1920 which was granted in 1923."

"Evidently the term "monkey bars" didn't take hold until the 1950's, though Hinton referred to "monkey-like play" in his patent application. Also Charles had built a version of these of bamboo for the children to play on and help them understand the concept of moving through three (four) dimensional space.  " *JF Ptak Science Books 

Sebastiane married Carmelita Chase who founded the Putney School in Vermont and   who was a personal friend, it seems, of Chairman Mao.  Sebastian seemed to have lived much of his adult life fearing that he was genetically predisposed to suicide because of his mother.  In 1923 he checked into a clinic for treatment, but while there committed suicide. After his suicide, thirty-three-year-old Carmelita was a single parent raising three young children. Jean was six, William four, and Joan not quite two. Fortunately, Carmelita was not without financial resources. One of them was the just approved Jungle Gym patent.

Their daughter, Joan Hinton,was a physics graduate student at the University of Wisconsin when she was tapped for Los Alamos. She worked on a team building the first reactor able to use enriched uranium as fuel. Hinton also witnessed the Trinity Test. She was one of only one or two woman taking part in Manhattan Project developing the A-bomb, in 1948.  Shortly afterward she went to China to join the revolution and ran a dairy farm near Beijing. She would die there on June 8, 2010.  Her brother, William,is best known for his book Fanshen, published in 1966, a "documentary of revolution" which chronicled the land reform program of the Communist Party of China (CPC) in the 1940s in Zhangzhuangcun.  

The other daughter, Jean was a life long environmentalist and activist.  She once said,

".. her mission in life became clear to her one day in 1941, when she helped a group of black activists storm a whites-only cafeteria in Washington, D.C."

An interesting tie between members of the family also occurred at the first atomic bomb explosion at White Sands, N.M. Working on the project, it would be expected that Mary Ellen's granddaughter Joan would be there, but it appears she only got to witness it by avoiding cars with a friend on a wild motorcycle ride into the hills about 25 miles away. Geoffrey Taylor's work in in turbulent motion and shock waves allowed him to contribute to problems that they were having with the implosion instability needed to trigger the chain reaction. To this end he visited the US in 1944, and again in 1945 to be at the same Bomb Blast. 

Joan Hinton had a son with her husband, Erwin Engst, an American (Cornell trained) dairy farmer, and together they started dairy farms in Xi'an and Beijing.  Their son Fred Engst is a  professor of Economics at the University of International Business and Economics  in Beijing.
William Hinton's daughter, Carma, also has distinguished herself.  She was born in Beijing in 1949 and stayed until 1971.  She is most famous for her documentary (co-produced with her husband Richard Gordon) “Gate of Heavenly Peace” of the 1989 Tiananmen Square protests.
And the family has yet another social activist in a newer generation.  Gina Engst , granddaughter of Joan Hinton, is a graduate of the Putney School created by great-grandmother, and is now based in Spain, where, by some estimates, the latest housing bubble left some 8 million housing units (new and old) unoccupied. Gina is part of a group helping older people squat. The group also helped turn one of the mansions in Barcelona into a community center for Latin American immigrant workers.


Well that's it, the state of my knowledge to date on the incredible daughters of George and Mary E. Boole.  I hope to keep updating this as good people with more information than I have share their knowledge with me.  So check back and see what I have learned, corrected, etc.  My thanks to many people who gave me leads to resources on the internet and off.  A 20 year old communication between Prof. Thomas Banchoff of Brown University and Rudy Rucker, author and (to my last knowlege)  webzine editor was especially fruitful, and a personal letter from Prof Banchoff pointed me to some more recent information on the descendents of Joan Hinton.  I have also taken liberally from a blog at A New Yorker in  Beijing .