As a teenager, back in the 1870s, almost by chance, Alice Boole learned basic ideas of geometry in four dimensions. From then on, she continued to think about these ideas, moved to Liverpool, married Liverpudlian Walter Stott and had two children. In 1899, the Liverpool Mathematical Society - the very one organising this talk - was founded, with Walter as secretary. In parallel, to better understand four-dimensional objects Alice built beautiful cardboard models. To her surprise, one day, in a mathematical magazine, she found a drawing that seemed to be copied from one of her models. She wrote to the author of that article, the mathematician Pieter Schoute, initiating a collaboration that would last until Pieter's death.
The three topics of this talk will be those in the title: Alice Boole, the beginnings of the Liverpool Mathematical Society and some ideas about the fourth dimension. (For example, in a four-dimensional world the inhabitants can move in such a way that the heart changes sides from left to right. We do not promise to change the heart sideways, but we will try to understand the mathematics of these and other four-dimensional adventures.)
Alicia Boole has a Wikipedia page: https://en.wikipedia.org/wiki/Alicia_Boole_Stott/.