It all began with the biography of George Boole — a man who went from being a shoemaker's son to a mathematics professor, invented the algebra of logic, and died a century before the first computers, leaving the world the word boolean, which millions of programmers now type every day. At the end of the piece was one line impossible to pass by: "among his descendants — the author of The Gadfly and a Nobel laureate in neural networks."
I wanted to check what lay behind that line. Turned out — an entire family saga: five daughters left without money or university degrees by their father in Victorian England, where a woman couldn't even enter university — and among whom grew a geometer who first visualized four-dimensional space, England's first woman professor of chemistry, the author of the most-read novel in USSR history, and, a few generations down, a physicist who calculated atomic bomb yield from photographs. Separately — a line leading to Geoffrey Hinton, the man who won the Nobel Prize for a machine that thinks by completely different laws than those his great-great-great-grandfather discovered.
In late November 1864, fifty-year-old Professor George Boole walked in pouring rain from his house in Blackrock to the college in Cork — three miles, whether from period custom or economy, history is silent. He gave his lecture in wet clothes and caught pneumonia. What happened next sounds like a cruel joke: his wife Mary was a convinced homeopath and followed the principle "like cures like." If the illness came from wetness — then treatment must be wet. Boole was wrapped in wet sheets. On December 8, 1864, he died of pleural effusion, leaving his wife with five daughters: eldest Mary Ellen eight years old, youngest Ethel about six months.
There was no money at all. Mary Everest Boole returned to England, got work as a librarian at Queen's College — the country's first women's college — and sent the children to relatives: Alicia, who was four, stayed in Cork with her grandmother. Coxeter later described the family's London home without embellishment: "poor, dark, dirty, uncomfortable lodgings in Marylebone." But this poverty had a strange compensation: in her mother's house, in his words, there swarmed "a continuous stream of crusaders and cranks" — Mary corresponded with Darwin, befriended H.G. Wells, and turned the living room into a salon where science mixed with mysticism. The girls received almost no formal education: Alicia, according to biographers, mastered the first two books of Euclid — and that's it. Not a single diploma for the whole family.
Mary Boole couldn't give her daughters school, but she gave them a method — her own pedagogical system, which she later laid out in books like Philosophy and Fun of Algebra. Her principles read today like a manifesto: "Whatever the teacher intends to prove should never be stated — the child should be led to independent discovery by successive questions." Geometric education should begin "as soon as the child's hands are capable of grasping objects" — among the toys must lie the five regular polyhedra and a dissected cone. Compass and set square should become for the child "instruments as familiar as fork and spoon."
The working tool was cardboard. The method Mary called "symbolic" came down to drawing on cardboard, cutting out shapes, sewing with pins and thread on cards — she's actually considered the inventor of curve stitching, "thread graphics," still used to decorate school bulletin boards. The essence — not memorizing formulas but running mathematics through your hands: physically building an object, seeing its cross-section, holding in your fingers what for an adult mathematician lives on paper. Remember this cardboard — in a few pages it becomes the protagonist.
Into the Boole household, when Alicia was about eighteen, came a brother-in-law — Charles Howard Hinton, husband of eldest sister Mary Ellen, obsessed with the idea of the fourth dimension. He brought a box of small wooden cubes from his own system: each cube got a Latin name, younger sisters got the assignment to memorize the list and assemble cubes into figures. According to Coxeter's recollections, for Ethel this was "meaningless tedium," but Alicia was electrified by the task. Within a few months she "began to surpass Hinton in the ability to understand what was happening in hyperspace."
What happened next still doesn't fit in your head. Knowing no analytic geometry at all — biographers record this with pleasure: she "never studied it" — Alicia independently derived all six regular polytopes of four-dimensional space, analogs of the five Platonic solids: bodies bounded by 5, 16, or 600 tetrahedra, 8 cubes, 24 octahedra, or 120 dodecahedra. The method was purely physical: she reasoned that a four-dimensional figure's corner angle at the vertex could only assemble from 4, 8, or 20 tetrahedra (because the near-vertex cross-section is only a tetrahedron, octahedron, or icosahedron), then with purely Euclidean constructions traced how the figure's cross-section passes through our three-dimensional space. The result — cardboard models of cross-sections of all six polytopes, made around 1880, simultaneous with Abbott's Flatland and earlier than the first scientific publication on multidimensional bodies. She considered it a private hobby and told no one about it.
Fifteen years later, Alicia's husband, actuary Walter Stott, happened to see the works of Dutch professor Pieter Schoute on cross-sections of multidimensional bodies — and they suspiciously resembled his wife's constructions. Alicia sent Schoute photographs of her models, the professor was stunned to his core and came in person. An almost twenty-year collaboration ensued: articles in the Proceedings of the Royal Netherlands Academy, discovery of semi-regular (Archimedean) polytopes in 4D, and in 1914 — an honorary doctorate from the University of Groningen, which Alicia, for inexplicable reasons, didn't go to receive: the degree was awarded "in her absence." Her models of the 120-cell and 600-cell still stand in Groningen — kept on permanent exhibition as a monument to geometry made with cardboard and hands. And the word "polytope" — for four-dimensional polyhedra — she coined.
The fourth daughter, Lucy Everest Boole, went into chemistry — also by a roundabout path. She received no university education at all: her mother later summarized her career in one devastating line — "never in any college. Learned chemistry to work as a pharmacist." Through pharmacy school, an assistant position to Professor Wyndham Dunstan, and persistence, Lucy became the first woman co-author of a pharmaceutical study (work on the pungent component of croton oil), in 1894 — the first woman member of the Royal Institute of Chemistry, and then — the first woman professor of chemistry in England. Her gravimetric method for analyzing tartar emetic, met with harsh criticism by colleagues, held in the British Pharmacopoeia from 1898 to 1963 — sixty-five years of official recognition for a method invented by a self-taught woman who was forbidden even to take university exams. She died at 42, bedridden after years of illness.
Eldest daughter Mary Ellen married that same Hinton — and here the family chronicle turns into an adventure novel. Hinton, polymath genius and future author of the philosophical system of "the fourth dimension as consciousness expansion," secretly married a second time in the 1880s to a girl under a false name, fathered twins with her — and in October 1886 himself went first to his school's headmaster, then to the police station on Bow Street to confess bigamy. Trial within a week, second wife as witness, prison. After release the family emigrated to Japan, where Hinton served as headmaster of a school for British expat children and befriended Lafcadio Hearn, then moved to Princeton in 1893. He died spectacularly: at a scientific dinner in Washington in April 1907 he raised a toast "to women philosophers" and dropped dead in the lobby. The philosophy of the fourth dimension ended where it should have — in the third.
The youngest, Ethel, had the hardest childhood: at eight she was sent from London to Lancashire to her brother, a colliery manager, whom biographers describe as "a religious fanatic and sadist" — he beat children and forced Ethel to play piano for hours. She returned from there dressed in black, withdrawn, calling herself "Lily." Then — Berlin and the music academy, Russian language with émigré Stepniak, governessing in St. Petersburg with entry into narodnik circles, translations of Shevchenko, meeting Ivan Franko in Lviv and co-founding with Stepniak the Society of Friends of Russian Freedom. In 1890 she met Polish revolutionary Michał Wojnicz, escaped from Siberian exile — and soon became Mrs. Voynich.
The world knows his name for another reason: antiquarian and book dealer Wilfrid Voynich in 1912 acquired a mysterious medieval manuscript in an unknown language that still hasn't been deciphered — the Voynich Manuscript bears the surname that Boole's daughter brought into this family. But Ethel owes her fame not to her husband: her novel The Gadfly (1897) about a revolutionary in Italy became an international bestseller, and in the USSR — a phenomenon: by the author's death in 1960 circulation reached 2.5 million copies, the novel was required reading, filmed twice, and the second time — in 1955 — the film got music by Dmitri Shostakovich, whose "Romance" from The Gadfly suite still circulates concert programs. The most touching thing about this story — that Ethel Voynich, who lived to 96 in New York, learned of her Soviet fame only in 1955 from a Soviet diplomat; royalties of $15,000 were then obtained for her by US Ambassador to the UN Adlai Stevenson. There's also a spy branch: according to one version, The Gadfly's hero was based on Sidney Reilly — "ace of spies," whom Ian Fleming considered one of the prototypes for James Bond. Asteroid 2032 Ethel bears her name since 1970.
The third branch of the family led to two unexpected finishes. Granddaughter Margaret, whose daughters were an artist and a neurosurgeon, gave birth to Geoffrey Ingram Taylor — one of the greatest physicists of the 20th century. When in July 1945 the first atomic bomb was tested in New Mexico, and in 1949 the photographs were declassified, Taylor did what became classic: calculated the explosion yield from civilian photographs in Life magazine, measuring the fireball's expansion from frames and applying a relationship known today as the Taylor-Sedov formula. The estimate — about twenty kilotons, matching the secret figure within percentage points. In 2024 researchers recalculated his work with modern computational tools — the method confirmed with even greater precision. Boole's daughter's grandson, having no connection to the nuclear project, cracked a state secret from photos in an illustrated magazine.
And Mary Ellen's line through generations — from George Boole Hinton the botanist to entomologist Howard Everest Hinton — led to Geoffrey Hinton, "godfather of AI." He received the Turing Award in 2018 for deep learning, and in 2024 — the Nobel Prize in Physics for artificial neural networks. The middle name "Everest" he bears in memory of that same Sir George Everest, whose name stands on the planet's highest mountain — Mary Boole's sister was the great geodesist's niece. And here's the final irony that gives me chills: Geoffrey Hinton, who built a machine that thinks by statistics and weights, not Boolean laws of thought — became the first major voice warning about the dangers of this very machine. The descendant of the man who formalized logic — the first to say aloud: "what we built is no longer logic."
The first thought that suggests itself — this is a story not about heredity but about method. Not one of the daughters inherited "genius" from their father in the genetic sense; they inherited cardboard. Mary Boole's pedagogy — running abstraction through your hands — gave the world a woman who visualized four-dimensional space with her hands before professionals, and a chemist whose method outlived six shifts of scientific paradigms. I think this is more honest than any stories about "noble blood": what's given is not a gift but a tool.
Second thought — about how time marinates ideas. Boolean algebra lay dormant until Shannon for eighty years; the family method lasted four generations to the Turing Award; The Gadfly waited sixty years for Soviet readers. In this family nobody waited for anything at all — they built cardboard models in poverty, not knowing that a century later their models would stand in university display cases. This family's investment horizon measured in generations, and none of them believed in these investments.
And the third, most uncomfortable. All five daughters grew up in a world that officially forbade them everything: universities, professorships, scientific societies. Not one broke — all found workarounds: pharmacy school instead of university, an antiquarian husband instead of a career, cardboard instead of lecture halls. The barrier didn't stop a single one of them — it just defined the form of their victories. Sometimes I think this is the main lesson of this family: a system that closes doors inadvertently forces those it closed out to invent unconventional passages — and it's precisely these passages that are remembered longer than the doors themselves.