On This Day in Math - August 11

 

Boy observing Mural along the flood wall in Paducah, Ky

So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.
~Albert Einstein

223 is the 48th prime number, formed from three consecutive prime digits, and the sum of three consecutive primes (71 + 73 + 79), 223 and also the sum of seven consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43)

Every number can be formed with no more than 36 fifth powers, except one, 223 is the only number that requires 37 fifth powers. This is related to Waring'a problem. In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of at most s natural numbers to the power of k. For example, every natural number is the sum of at most 4 squares, 9 cubes, or 19 fourth powers. Waring's problem was proposed in 1770 by Edward Waring, after whom it is named. Its affirmative answer, known as the Hilbert–Waring theorem, was provided by Hilbert in 1909.

Fans of Star Wars may know that this is sometimes called the Star Wars Droid Prime because it uses only the numbers in the names of R2-D2 and C3PO

An interesting note, if you take a prime number less than 223 and reverse it, some are prime, some have two factors, but 223 is the smallest prime whose reversal has three factors (322 = 2 * 7 * 23)

223 is the difference of consecutive squares, 112^2 - 111^2

The number of primes and the number of composites that cannot be written as the sum of two primes, up to 223, are equal.*Prime Curios

The prime preceding 223 The sums of the nth powers of its digits are prime for all n between 1 and 6 inclusive: sum of digits = 7, sum of squares of digits = 17, sum of cubes of digits = 43, sum of fourth powers = 113, sum of fifth powers = 307 and sum of sixth powers = 857. *Prime Curios

If you take the tens compliment of the digits of 223, you get 887, another prime. The same is true for the next three primes following 223.

If you take the square of 223 which is 49729 observe that the last three digits, 729 are prime. Try any of the next dozen primes following 223 and you will observe the same result. *Prime Curios

223 sets a new high for the distance between the two nearest primes surrounding it, they are 16 units apart.

Fans of Star Wars may know that this is sometimes called the Star Wars Droid Prime because it uses only the numbers in the names of R2-D2 and C3PO

An interesting note, if you take a prime number less than 223 and reverse it, some are prime, some have two factors, but 223 is the smallest prime whose reversal has three factors (322 = 2 * 7 * 23)

See More Math Facts for every Year Day here.

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EVENTS

1124 "In the month of August on the 11th day, before the evening service, the Sun began to diminish and perished completely. Great fright and darkness everywhere. And the stars appeared and the Moon (sic). And the Sun began to augment and became full again and everyone in the town was very glad." Refers to a total solar eclipse in Novgorod, Russia, of 11 August 1124. From: Novorodskaya I Letopic. Quoted in Historical Eclipses and Earth's Rotation, by F Richard Stephenson, Cambridge University Press, 1997, page 391. *NSEC

Night Sky Map view of totality over the US city of Dallas—during the solar eclipse of April 8, 2024—the Sun is shown to be in front of the constellation Pisces. It forms a nearly straight line with the bright planets Venus (right) and Jupiter (left) in the sky, revealing the path of the ecliptic.

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1591 Kepler received his master’s degree from Tübingen and thereupon entered the process of practical preparation for either teaching or being a Protestant pastor. Halfway through his third year, however, an event occurred that completely altered the direction of his life. Georgius Stadius, teacher of mathematics at the Lutheran school in Graz, died; and the local authorities asked Tübingen for a replacement. Kepler was chosen; and although he protested abandoning his intention to became a clergyman, he set out on the career destined to immortalize his name. *www.encyclopedia.com *Thony Christie

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In 1835, George B Airy began his 46-year reign as England's seventh Astronomer Royal. He was appointed in June of that year but seems to have assumed duty on August 11. At Greenwich he designed and installed the famous transit circle now named after him, used for timing the passage of stars across the meridian. It is the position of the Airy transit circle that defines the Greenwich meridian and since 1884 that meridian has been the basis of the world’s timekeeping and navigation. Hence Airy can be said to have brought the world’s clocks into step. *assorted sources

Airy's Transit Circle in the Transit Circle Room of the Royal Greenwich Observatory; for a hundred years from 1884 to 1984, it marked the Prime meridian of the world

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1859 Bernhard Riemann was made a corresponding member of the Berlin Academy based on his 1857 paper on Abelian Functions. It was the practice that newly selected members would submit an example of their recent research. Riemann submitted, "On the Number of Prime Numbers Less Than a Given Quantity." The paper contained his now famous Riemann Hypothesis that the non-trivial zeros of the Zeta function all have a real part of 1/2. It is the only paper he ever published on number theory.*John Derbyshire, Prime Obsession

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1877  Deimos /ˈdaɪməs/ (systematic designation: Mars II) is the smaller and outermost of the two natural satellites of Mars, the other being Phobos. Deimos has a mean radius of 6.2 km (3.9 mi) and takes 30.3 hours to orbit Mars. Deimos is 23,460 km (14,580 mi) from Mars, much farther than Mars' other moon, Phobos. It is named after Deimos, the Ancient Greek god and personification of dread and terror

Deimos was discovered by Asaph Hall III at the United States Naval Observatory in Washington, D.C., on 12 August 1877, at about 07:48 UTC.[a] Hall, who also discovered Phobos shortly afterwards, had been specifically searching for Martian moons at the time.

*Planets Education

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1909 First SOS, The first well documented use of the SOS distress call is by the Arapahoe on August 11, 1909, when it suffered a broken shaft in the Atlantic Ocean, near Cape Hatteras, North Carolina. However, an article titled "Notable Achievements of Wireless" in the September, 1910 Modern Electrics suggests that an earlier SOS distress call was transmitted by the Cunard liner Slavonia, on June 10, 1909.

[The wireless operator aboard S.S. Arapahoe, T. D. Haubner, radioed for help. A few months later, Haubner on the S.S. Arapahoe received an SOS from the SS Iroquois, the second use of SOS in America.(*TIS)]
The first radio distress call to be adopted appears to have been "CQD", by the Marconi International Marine Communication Company​, for Marconi-operated shipboard stations. It was announced on January 7, 1904 by the company's "Circular 57" that "...on and after the 1st February, 1904, the call to be given by ships in distress or in any way requiring assistance shall be 'C.Q.D.'." ("CQ" was a general call to all stations; amateur or "ham" radio operators still use it today when soliciting a contact with any station that hears the call.)

An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

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In 1999, the last total eclipse of the millennium occurred. Because it traveled across many populated areas, it was perhaps the most-watched eclipse of all time, seen by possibly 350 million people. Totality occurred first over the mid-Atlantic Ocean. The first land crossed by the moon's shadow was the Isles of Scilly, then the far south-west of England, (The first total solar eclipse visible from the United Kingdom mainland for more than 70 years) in Cornwall. Although the sun was obscured by clouds there, a dramatic darkness fell, and the temperature dropped, during the totality lasting 1-min 30-sec. From there the path of totality tracked across Europe, India and Iran. In Egypt, Muslims were ordered by clerics to shut themselves away, but Jordan and Syria declared a national holiday.*TIS 

Total Solar Eclipse Aug 11th 1999 France Le Havre

Total Solar Eclipse Aug 11th 1999 France Le Havre 

 

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BIRTHS

1730 Charles Bossut(11 August 1730 – 14 January 1814) was a French mathematician who was famed for his textbooks which were widely used throughout France.*SAU

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1829 Norman Macleod Ferrers; (11 August 1829 – 31 January 1903) John Venn wrote of him,

.. the Master, Dr Edwin Guest, invited Ferrers, who was by far the best mathematician amongst the fellows, to supply the place. His career was thus determined for the rest of his life. For many years head mathematical lecturer, he was one of the two tutors of the college from 1865. As lecturer he was extremely successful. Besides great natural powers in mathematics, he possessed an unusual capacity for vivid exposition. He was probably the best lecturer, in his subject, in the university of his day.

It was as a mathematician that Ferrers acquired fame outside the university. He made many contributions of importance to mathematical literature. His first book was "Solutions of the Cambridge Senate House Problems, 1848 - 51". In 1861 he published a treatise on "Trilinear Co-ordinates," of which subsequent editions appeared in 1866 and 1876. One of his early memoirs was on Sylvester's development of Poinsot's representation of the motion of a rigid body about a fixed point. The paper was read before the Royal Society in 1869, and published in their Transactions. In 1871 he edited at the request of the college the "Mathematical Writings of George Green" ... Ferrers's treatise on "Spherical Harmonics," published in 1877, presented many original features. His contributions to the "Quarterly Journal of Mathematics," of which he was an editor from 1855 to 1891, were numerous ... They range over such subjects as quadriplanar co-ordinates, Lagrange's equations and hydrodynamics. In 1881 he applied himself to study Kelvin's investigation of the law of distribution of electricity in equilibrium on an uninfluenced spherical bowl. In this he made the important addition of finding the potential at any point of space in zonal harmonics (1881).

Ferrers proved the proposition by Adams that "The number of modes of partitioning (n) into (m) parts is equal to the number of modes of partitioning (n) into parts, one of which is always m, and the others (m) or less than (m). " with a graphic transformation that is named for him. *SAU

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1842 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.
Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.
D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU

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1895 Egon Sharpe Pearson, (Hampstead, 11 August 1895 – Midhurst, 12 June 1980) was the only son of Karl Pearson, and like his father, a leading British statistician.
He went to Winchester School and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika.
Pearson is best known for development of the Neyman-Pearson lemma of statistical hypothesis testing.
He was President of the Royal Statistical Society in 1955–56, and was awarded its Guy Medal in Gold in 1955. He was awarded a CBE in 1946.
He was elected a Fellow of the Royal Society in Mar 1966. His candidacy citation read: "Known throughout the world as co-author of the Neyman-Pearson theory of testing statistical hypotheses, and responsible for many important contributions to problems of statistical inference and methodology, especially in the development and use of the likelihood ratio criterion. Has played a leading role in furthering the applications of statistical methods - for example, in industry, and also during and since the war, in the assessment and testing of weapons." *Wik

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1912 Norman Levinson (August 11, 1912, Lynn, Massachusetts – October 10, 1975, Boston) set out to become an electrical engineer. Here he describes the events that led to his change of major:

I became acquainted with Wiener in September 1933, while still a student of electrical engineering, when I enrolled in his graduate course. It was at that time really a seminar course. At that level he was a most stimulating teacher. He would actually carry on his research at the blackboard. As soon as I displayed a slight comprehension of what he was doing, he handed me the manuscript of Paley-Wiener for revision. I found a gap in a proof and proved a lemma to set it right. Wiener thereupon sat down at his typewriter, typed my lemma, affixed my name and sent it off to a journal. A prominent professor does not often act as secretary for a young student. He convinced me to change my course from electrical engineering to mathematics.

Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey.*SAU

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1921 Tom Kilburn (11 August 1921 – 17 January 2001) British electrical engineer who wrote the computer program used to test the first stored-program computer, the Small-Scale Experimental Machine, SSEM, also known as "The Baby." First tested on 21 Jun 1948, the program took 52 minutes to run. The tiny experimental computer had no keyboard or printer, but it successfully tested a memory system developed at Manchester University in England. This system, based on a cathode-ray tube, was the first that could store programs, whereas previous electronic computers had to be rewired to execute each new problem.*TIS

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1950 Steve Wozniak, (August 11, 1950; ) Apple inventor, is born
Wozniak and Jobs entered into business after Wozniak designed a single-board personal computer known as the Apple I. In 1976, with specifications in hand and an order for 100 machines at $500 each from the Byte Shop, he and Jobs founded the business.
While still studying at the University of California-Berkeley in 1972, Wozniak had shown his electronics skill as well as his sense of humor in building his blue box, a tone generator used to make free phone calls, which he sold in dormitories
Wozniak now teaches computer science to school children in his home town of Los Gatos, California. *CHM

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1956 Pierre-Louis Lions (August 11, 1956, ) French mathematician who was awarded the Fields Medal in 1994 for his work since the 1980's on partial differential equations. The sources of such equations are many - for example, physical, probabilistic or geometric and other diverse subareas - each studying different phenomena for different nonlinear partial differential equations by utterly different methods. Pierre-Louis Lions has been called unique in his ability to transcend these boundaries and to solve pressing problems throughout the field.*TIS

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DEATHS

1464 Nicholas von Cusa died (1401 – August 11, 1464). We know his work in mathematics primarily because a home for the aged in Kues, which he generously endowed, has survived the ravages of time and war. Luckily his own manuscripts were housed there.*VFR
Nicholas is also considered by many to be a genius ahead of his time in the field of science. Nicolaus Copernicus, Galileo Galilei and Giordano Bruno were all aware of the writings of Cusanus as was Johannes Kepler (who called Cusanus 'divinely inspired' in the first paragraph of his first published work). Predating Kepler, Cusanus said that no perfect circle can exist in the universe (opposing the Aristotelean model, and also Copernicus' later assumption of circular orbits), thus opening the possibility for Kepler's model featuring elliptical orbits of the planets around the Sun. He also influenced Giordano Bruno by denying the finiteness of the universe and the Earth's exceptional position in it (being not the center of the universe, and in that regard equal in rank with the other stars). He was not, however, describing a scientifically verifiable theory of the universe: his beliefs (which proved uncannily accurate) were based almost entirely on his own personal numerological calculations and metaphysics.
Cusanus made important contributions to the field of mathematics by developing the concepts of the infinitesimal and of relative motion. He was the first to use concave lenses to correct myopia. His writings were essential for Leibniz's discovery of calculus as well as Cantor's later work on infinity. *Wik

Tomb in San Pietro in Vincoli, Rome, with the relief "Cardinal Nicholas before St Peter" by Andrea Bregno

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1578 Pedro Nunes or Nunez (1502 – August 11, 1578) was a Portuguese scholar who worked in geometry, spherical trigonometry, algebra as well as geography, physics, and cosmology. *SAU He was the first to propose the idea of a loxodrome and was also the inventor of several measuring devices, including the nonius, named after his Latin surname. *Wik

The nonius is a system of concentric circles etched on instruments like astrolabes or quadrants. Each circle has one fewer division than the previous, e.g., 90°, 89°, 88°, and so on 

When measuring an angle, the observer notes exactly which division on which circle the alidade aligns with. By consulting a table, they can deduce the precise angle with accuracy beyond whole degrees 

 This system enhanced angular precision to within a few arc minutes—crucial for maritime navigation, where a small angular error could translate into many kilometers off course . *Wik

Tycho Brahe used Nunes’ nonius in his astronomical instruments but found it cumbersome. Christopher Clavius and Jacob Curtius refined the idea further and in 1631, Pierre Vernier perfected it, reducing it to the familiar sliding dual-scale system known today as the vernier scale 

.Until the 19th century, many places still referred to the vernier as the nonius in Nunes’ honor.

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1854 Macedonio Melloni, (11 April 1798 – 11 August 1854) Italian physicist who was the first to extensively research infrared radiation. Sir William Frederick Herschel discovered infrared radiation in 1800, but research stalled until the invention of a thermopile in 1830. That instrument was a series of strips of two different metals that produced electric current when one end was heated. Melloni improved the thermopile and used it to detect infrared radiation. In 1846, from an observation point high on Mount Vesuvius, he measured the slight heating effect of moonlight. He showed also that rock salt, being transparent to infrared, made suitable lenses and prisms to demonstrate the reflection, refraction, polarization and interference of infrared in the same manner as visible light.*TIS

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1880 Ramchundra (Ramachandra Lal) (Devanagari,रामचन्द्र लाल) (c. 1821– 11 August,1880) was a British Indian mathematician. His book, Treatise on Problems of Maxima and Minima, was promoted by mathematician Augustus De Morgan.

Writing in his preface to the treatise, De Morgan states that Ramchundra was born in about 1821 in Panipat to Sunder Lal, a Kayasth of Delhi. He came to De Morgan’s attention when, in 1850, a friend sent him Ramchundra’s work on maxima and minima. The 29-year-old self-taught mathematician had published the book at his own expense in Calcutta in that year. De Morgan was so impressed that he arranged for the book to be republished in London under his own supervision, and in general undertook to bring Ramchundra's work to the notice of the broader European scientific community. Quoting De Morgan, from the preface of the treatise:

On examining this work I saw in it, not merely merit worthy of encouragement, but merit of a peculiar kind, the encouragement of which, as it appeared to me, was likely to promote native effort towards the restoration of the native mind in India.

Charles Muses, in an article in the Mathematical Intelligencer (1998) called Ramchundra "De Morgan's Ramanujan". He was mystified why, in spite of De Morgan's efforts to make this "remarkable Hindu algebraist known, he does not appear in most texts on history of mathematics. He is also known for his great ability to calculate."

Ramchundra was teacher of science in Delhi College for some time. In 1858, he was native head master in Thomason Civil Engineering College (now Indian Institute of Technology, Roorkee) at Roorkee. Later that year, he was appointed head master of a school in Delhi.

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1892 Enrico Betti (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giving early expositions of Galois theory. He also discovered Betti's theorem, a result in the theory of elasticity. *Wik

For a torus, the first Betti number is b1 = 2 , which can be intuitively thought of as the number of circular "holes"

*Wik

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1955 Robert Williams Wood (May 2, 1868 – August 11, 1955) was an American experimental physicist. He photographed the reflection of sound waves in air, and investigated the physiological effects of high-frequency sound waves. The zone plate he devised could replace the objective lens of a telescope. He invented an improved diffraction grating, did research in spectroscopy, and extended the technique of Raman spectroscopy (a method to study matter using the light scattered by it.) He made photographs showing both infrared and ultraviolet radiation and was the first to photograph ultraviolet fluorescence.

"What Wood invented was in a way even more spectacular: whereas Niépce and Daguerre (inventors of photography) merely photographed the visible, Wood was the first to photograph the invisible images obtained via illumination with ultraviolet and infrared light. In the process he invented Wood's glass, which blocks visible light while passing ultraviolet light, thereby making possible today's blacklight lamps obtainable in hobby and novelty stores and used for Halloween parties and indoor blacklit miniature golf links."

 Wood was the first to observe the phenomenon of field emission in which charged particles are emitted from conductors in an electric field. *TIS
According to a post at Greg Ross' Futility Closet:

"How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:
The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.
This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

 

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1977 Sir Frederic Williams, (26 June 1911 Stockport – 11 August 1977 Manchester) British electrical and electronics engineer who, with Tom Kilburn, invented the Williams tube, a cathode-ray tube using the persistence of the image on the phosphor screen for data storage. This made possible the random access memory that launched the digital computer age. As the Chair in Electrotechnics at Manchester University, he incorporated this invention into the Mark I computer, the world's first stored-program digital electronic computer to be commercially produced during the early 1950's. *TIS

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1995 Alonzo Church (June 14, 1903 – August 11, 1995) made important contributions to mathematical logic and theoretical computer science.*SAU He is best known for the lambda calculus, Church–Turing thesis, proving the undecidability of the Entscheidungsproblem, Frege–Church ontology, and the Church–Rosser theorem. *Wik

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2003 Armand Borel (21 May 1923 –11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. *Wik

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Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

We badly need a Hippocratic Oath for schooling:

I actually wrote this back in 2010, and every couple of years there would be a day or a week when someone found and shared it and a couple of hundred to a thousand hits roll up.... who were these people and what drove them to a blog 8 to 15 years old. It seems Daily Kos still exists but their search function didn't let me look up the 2010 version they wrote, but they have another with essentially the same name in 2025,,,, but I hated it.  So I hope you enjoy this old post and share your thoughts.  *Pat B

"Above All Else, Do No Harm"

Sunday morning... put on the coffee, turn on the feed from KSCS in Fort Worth (Ok, you got me..I'm country) and start flipping through blogs I haven't had time to read all week... and the one that most caught my eye had the quote above.

Those who have read my blog for awhile know that I occasionally set aside my blogs on math to comment on education, my grand kids, or whatever happens to catch my interest.

This Sunday it was a month old blog at the Daily Kos (I have no idea what that means) by teacher Ken. It is long, but good enough to take the time..  [[[It seems this link no longer works... my apologies, I remember it as far better than the one I mention above]]]

The title is "students should graduate with a résumé, not a transcript", and is taken from a quote by Arnold Packer, who was the principal author of the SCANS report, from the Dept of Labor. Much of the blog is based on an article by Grant Wiggins, a regular proponent of "Authentic Education." (Sort of like "Pro-life", who could be against that?)
Here is the opener from the Wiggins piece:

Imagine the following HS requirements being recommend to the School Board:
• 3 years of economics and business
• 2 courses in philosophy – one in logic, the other in ethics
• 2 years of psychology, with special emphasis on child development and family relations
• 2 years of mathematics, focusing on probability and statistics
• 4 years of Language Arts, but with a major focus on semiotics and oral proficiency
• US and World history, taught as Current Events - backwards from the present
• 1 Year of Graphics Design, Desktop Publishing, and Multimedia presentation

Outrageous? Hardly – if we do an analysis of what most graduates actually need and will use in professional, civic, and personal life. How odd it is that we do not require oral proficiency when every graduate will need the ability. How absurd it is in this day and age that students aren’t required to understand the capitalist system. How sad it is that physics is viewed as more important than psychology, as parents struggle to raise children wisely and families work hard to understand one another. Requirements based on pre-modern academic priorities and schooling predicated on the old view that few people would graduate and fewer still would go on to college make no sense. Ask any adult: how much algebra did you use this past week?

Ok, that last line struck a nerve that I come back to sometimes....... If someone took a survey in 1900 of the frequency with which people used automobiles, television, airplanes, (complete with your own examples) no organization could use it to justify research on the basis of that survey. And the adult who has NO training in algebra will have only the most superficial understanding of probability and statistics from his two years of mathematics in those areas. ...and how much do you learn in a course in semiotics in the absence of algebraic reasoning??? consider this trilogy of the elements of the subject in a online "introduction"....

* semantics: the relationship of signs to what they stand for;
* syntactics (or syntax): the formal or structural relations between signs;
* pragmatics: the relation of signs to interpreters
remember, you are teaching this to the same kids who have trouble figuring out how to add fractions, or find the area of a triangle, or explain what a polynomial is

But given that big objection I like the idea of a more student tailored curriculum. I like the idea of a student getting the education they want, getting a recognition of the level of achievement they have reached, and let business decide (and test to see) if they have the credentials that the business needs.. I had a parent recently say she would be having her kid skip a day of school to go to Cambridge and participate in the science day there... Another is missing a week to go to Crete with her father who just returned from six months being deployed in Iraq. I hate for kids to miss my class, but not much I will do in a day or a week will be as life changing as a day with world class scientists designing and explaining the future of an area of physics that one kid is interested in, or spending a week on a beautiful island with family to recover from some of the sacrifice of an extended absence (he didn't just miss seeing her spike a volley ball, he missed her first real date, falling totally in love for the very first time, and her first heartbreak six weeks later when the boy decided they should "just be friends" all of which she went through missing only a moment or two of classes for a trip to the hall when tears flowed). These kinds of events should be part of the experience of high school. I believe schools ought to have more independent explorations in subjects the student is interested in... Bright kids take calculus because it is the next course in the "college-intending" sequence, but some (many) would be much better served with a course in Statistics, and although I teach it, AP Statistics is not necessarily the best syllabus for that learning for lots of them. And I have several bright students who have accelerated right through all the pre-calculus curriculum and never saw a Moebius Strip, never played with a bent nail puzzle, and have never heard of Fibonacci, or a thousand other things that give math life and energy.

So Let's offer kids the option to tailor their own education... really empower students, and you Mr. Taxpayer, will need to cough up several more dollars each year because to do that schools will need to have lots more small classes (hence more teachers) and the technology to do more independent study .. What? oh, on second thought you don't like it as much... Yeah, let's just go back to blaming all our problems on the teachers and the unions.... Did you hear, there is a school over in Whatsit Town that let a private company take over the school system and saved thousands of dollars a semester. They can manage with just one certified teacher in each subject to design lessons and they hire aides to manage classes and the kids learn independently.... and their state test scores hardly dropped at all this year.....

Teach Like Their Lives Depended On It!!!

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 came, 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 had 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. (Conway died in 2020 after this was first written.) 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 descendants of Joan Hinton.  I have also taken liberally from a blog at A New Yorker in  Beijing .