A Boolean Anthology
Selected writings of Mary Boole
- on mathematical education
Compiled by D. G. Tahta
Dick Tahta was my maths tutor at St Luke's College Exeter. A brilliant and often quite unorthodox thinker in the field of mathematics education. He put together this anthology in a small booklet, now long out of print, and as a tribute to him, I am posting it up here.
Introduction
The collected works of Mary Boole amount to more than fifteen hundred pages. Among them is found a regular and passionate, insistence on the real—but widely ignored—significance of her husband's work, and a vision of mathematical education that is powerfully relevant, but still unrealised, today.
This selection sets out to provide a brief introduction to her writings in order to stimulate a wider awareness of her thought. The numbers in brackets at the end of each extract are page number references to the collected works in the now out-of-print 1931 edition.
Mary Everest, later the wife of the mathematician George Boole, was born in 1832. Her father, a rector, was a friend of Babbage and Herschel who as students had initiated various reforms in mathematics at Cambridge. Her mother was the sister of a classics professor at a college in Cork, where Boole was to hold the chair of mathematics. When Mary was five her father became seriously ill and the family moved to France, so that he could be treated by Hahnemann, the founder of homeopathic medicine. Mary grew up bilingual. An early interest in mathematics was aroused by a teacher who gave her private lessons in arithmetic; many years later she wrote a charming account of this inspiration. Her father's health improved and the family returned to England when Mary was eleven.
Mary first met George Boole on a visit to her uncle in Cork. After the hard struggle of the early years, Boole was just beginning his great work. His masterpiece, An investigation of the laws of thought, was published in 1854 and was dedicated to Mary's uncle. Her father died the following year, and they married soon after. It was a successful marriage; though Boole was seventeen years her senior they were close companions, and Mary was able to share her husband's interests—she became a devoted disciple.
They had five daughters. The youngest was only six months old when Boole died of an attack of pneumonia in 1864. Mary was then 32 years old.
In the following year she took a post at Queen's College, London. Opened in 1847, this was the first college of higher education for women. Though unable to award degrees, it gave something more valuable, at least to some of the pupils; one of Mary's was to write later, "I thought we were being amused not taught. But after I left I found you had given us a power. We can think for ourselves, and find out what we want to know."
After a few years Mary left the college to become for a brief time the secretary of James Hinton, a writer on ethics and evolution as well as a skilful ear-surgeon, who had been a friend of her father. She was interested in the aspect of his work that most of his friends found unimportant, namely 'the art of thinking itself, which he, as well as George Boole, believed to be the true key to the physical and moral regeneration of mankind'.
In the twenty years after her husband's death Mary Boole supported and raised a family and read, corresponded and discussed over a wide range of themes and with a large circle of friends (some of whom are mentioned briefly in an appendix—see p. 75).
Selected writings of Mary Boole
- on mathematical education
Compiled by D. G. Tahta
Dick Tahta was my maths tutor at St Luke's College Exeter. A brilliant and often quite unorthodox thinker in the field of mathematics education. He put together this anthology in a small booklet, now long out of print, and as a tribute to him, I am posting it up here.
Introduction
The collected works of Mary Boole amount to more than fifteen hundred pages. Among them is found a regular and passionate, insistence on the real—but widely ignored—significance of her husband's work, and a vision of mathematical education that is powerfully relevant, but still unrealised, today.
This selection sets out to provide a brief introduction to her writings in order to stimulate a wider awareness of her thought. The numbers in brackets at the end of each extract are page number references to the collected works in the now out-of-print 1931 edition.
Mary Everest, later the wife of the mathematician George Boole, was born in 1832. Her father, a rector, was a friend of Babbage and Herschel who as students had initiated various reforms in mathematics at Cambridge. Her mother was the sister of a classics professor at a college in Cork, where Boole was to hold the chair of mathematics. When Mary was five her father became seriously ill and the family moved to France, so that he could be treated by Hahnemann, the founder of homeopathic medicine. Mary grew up bilingual. An early interest in mathematics was aroused by a teacher who gave her private lessons in arithmetic; many years later she wrote a charming account of this inspiration. Her father's health improved and the family returned to England when Mary was eleven.
Mary first met George Boole on a visit to her uncle in Cork. After the hard struggle of the early years, Boole was just beginning his great work. His masterpiece, An investigation of the laws of thought, was published in 1854 and was dedicated to Mary's uncle. Her father died the following year, and they married soon after. It was a successful marriage; though Boole was seventeen years her senior they were close companions, and Mary was able to share her husband's interests—she became a devoted disciple.
They had five daughters. The youngest was only six months old when Boole died of an attack of pneumonia in 1864. Mary was then 32 years old.
In the following year she took a post at Queen's College, London. Opened in 1847, this was the first college of higher education for women. Though unable to award degrees, it gave something more valuable, at least to some of the pupils; one of Mary's was to write later, "I thought we were being amused not taught. But after I left I found you had given us a power. We can think for ourselves, and find out what we want to know."
After a few years Mary left the college to become for a brief time the secretary of James Hinton, a writer on ethics and evolution as well as a skilful ear-surgeon, who had been a friend of her father. She was interested in the aspect of his work that most of his friends found unimportant, namely 'the art of thinking itself, which he, as well as George Boole, believed to be the true key to the physical and moral regeneration of mankind'.
In the twenty years after her husband's death Mary Boole supported and raised a family and read, corresponded and discussed over a wide range of themes and with a large circle of friends (some of whom are mentioned briefly in an appendix—see p. 75).
Committed to spreading her husband's ideas about mathematics she also developed her own thoughts on education. She studied the works of Thomas Wedgwood, the son of the famous potter, and a friend of Darwin. She developed the ideas of the French logician and mystic, Gratry, and related them to those of her husband. At the same time she became more and more involved in spiritualism and theosophy with a curious amalgam of ideas from Hebrew ritual, Indian mysticism and Western science. At the age of 50 she embarked on a series of books and articles, publishing regularly up to the time of her death in 1916 at the age of 84.
Much of her writing has not been to twentieth century tastes though many contemporary young people have been rediscovering her themes. She was interested in the occult, homeopathy, vegetarianism, anti-vivisection - and love. But the practical common sense of her lesson notes, Lectures on the logic of arithmetic (1903, when she was 71), and the pioneering insights of The preparation of the child for science (1904) had their impact on progressive schools in England and the U.S.A. in the first decade of the 20th century.
Much of her writing has not been to twentieth century tastes though many contemporary young people have been rediscovering her themes. She was interested in the occult, homeopathy, vegetarianism, anti-vivisection - and love. But the practical common sense of her lesson notes, Lectures on the logic of arithmetic (1903, when she was 71), and the pioneering insights of The preparation of the child for science (1904) had their impact on progressive schools in England and the U.S.A. in the first decade of the 20th century.
She invented curve-stitching and for many years cards marked for this purpose were known as Boole cards (see p. 35). Her first book, published in 1883 but written in the sixties, was a pioneer work on mental hygiene. In the mathematical psychology of Gratry and Boole (1897) and one of her last books, The forging of passion into power (1910), she showed an understanding of the unconscious far ahead of her time.
Most educationists today appear to have other things to write about than dowsing rods and so on. Certainly other things than love. Few achieve the clarity, the vision and the highly relevant insights of Mary Boole.
Most educationists today appear to have other things to write about than dowsing rods and so on. Certainly other things than love. Few achieve the clarity, the vision and the highly relevant insights of Mary Boole.
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