... 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.

There was no possibility of education in the ordinary sense, but Mrs Boole's friendship with James Hinton attracted to the house a continual stream of social crusaders and cranks.

Anything which the teacher intends to prove should never be stated; children should be led up to find it out for themselves by successive questions.

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.

As soon as the hands can hold steadily compasses and set-square the child should be encouraged both in copying diagrams ... and in inventing others for himself. It is desirable that, before any systematic teaching of mathematics begins, the compass, set-square, and ruler marked in fractions of an inch should be as familiar implements as the fork and spoon.

Between the time when a child handles an actual cube, cuts sections etc., and the time when he comes, among his ordinary geometrical exercises, to problems requiring him to draw the elevation of a cube cut in some particular way, there is a period when he finds it useful, and very delightful, to go through a set of processes in imagination and to express them in his own words.

[James] Hinton's son Howard, brought a lot of small wooden cubes, and set the youngest three girls the task of memorising the arbitrary list of Latin words by which he named them, and piling them into shapes. To Ethel, and possibly Lucy too, this was a meaningless bore; but it inspired Alice (at the age of about eighteen) to an extraordinarily intimate grasp of four-dimensional geometry.

She found that there were exactly six regular polytopes on four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections. ...

Alice's method of discovery was typically that of an amateur. She started by noticing that a corner in a regular four-dimensional figure bounded by tetrahedra, for instance, can only have either 4, 8 or 20 of them meeting at a point because a section of three-dimensional space close to the corner in a symmetrical position could only be a tetrahedron, an octahedron, or an icosahedron. She then traced, using only Euclid's construction, the progress of the section as the four-dimensional figure passed through our three-dimensional space. In this way Alice, employing only Euclid's constructions, produced sections of all the six regular polytopes.

... I have not done anything more interesting than staining very shabby floors and such like homehold things for some time; but last night I received by post a M.S. of 70 very closely written pages containing an analytical counterpart of my last geometrical paper. Of course I must read it. It is the second attempt and was only written because I did not like the first but I am such a duffer at analytical work anyhow that I don't suppose I shall like this very much better.

From these papers, one infers a very special gift for seeing the position and forms in a space of four dimensions. Three of these papers are written jointly with late Professor Dr P H Schoute connected during so many years to the University of Groningen; And this fruitful cooperation with the professor that she lost, is the reason for the Faculty of Mathematics and Physics to propose Mrs A Boole Stott for the doctorate honoris causa in Mathematics and Physics, to confer on the occasion of the coming festive commemoration of the 300th birthday of the University.

Coxeter's alliance with Aunt Alice was a great source of joy. "The strength and simplicity of her character," he said, "combined with the diversity of her interests to make her an inspiring friend." They conducted an ongoing conversation about polytopes, by letter and with visits back and forth.

When Coxeter's turn came up for another session at Baker's tea party, he invited his "Aunt Alice" to deliver a joint lecture. ... When Aunt Alice made her appearance as Coxeter's guest at Baker's tea party, she brought her models and donated them to the department for permanent exhibit.

My dear! I don't know how to write to you - words seem so futile beside so great a separation! But indeed one can rejoice, for your sake, that it happened so ... While I have been writing my mind has gone back to the lovely world we have visited together, and which you have made so much your own. I wonder where you will get to in it! How I wish I could follow.