Ada Lovelace Day is an occasion to celebrate women in mathematics, science, and technology, especially those whose contributions have not received the recognition they deserve. Today I want to remember Fatima Fenaroli Lawvere, who recently passed away, and a class of women whose contributions are too often overlooked: those who work tirelessly to support and preserve the mathematical work of their husbands.
I learned of Fatima's death through a moving message sent by Posina to the Categories mailing list. I am grateful to him for writing it, and for reminding us how much we owe her. I also want to thank Anders Kock, who provided the only photograph of Fatima that I could find, and whose presentation at the 2023 meeting dedicated to Bill Lawvere offers some wonderful testimony about her contributions.
I had some personal experience of Fatima's work behind the scenes. On several occasions when I tried to contact Bill Lawvere, it was Fatima who replied to my messages. At the time, this seemed simply the way things worked. Looking back, I realize how much she did to sustain Bill's mathematical life and his connections with the community.
Fatima Lawvere was much more than the wife of F. William Lawvere, one of the forefathers of category theory. Posina describes her as "a pedagogical revolution personified." She attended Bill's lectures, asked questions, and contributed to the development of the approach that eventually became Conceptual Mathematics: A First Introduction to Categories, by Lawvere and Stephen Schanuel.
Anders Kock quotes Bill Lawvere's recollections of working with Schanuel late into the night, sometimes laughing at the discovery of unexpectedly simple proofs. Bill remembered that Fatima could hear them laughing, and that the following morning she would type the notes he had left on her table. There is something both delightful and revealing about this image: the mathematicians laughing over their discoveries, and Fatima making sure those discoveries became written mathematics.
But her role went much further. Their son Danilo recalls that she ensured that Bill went to conferences with notes or drafts, that deadlines were met, letters answered, and extensive lecture notes preserved. He also says that Conceptual Mathematics was partly conceived by Fatima and that she was the driving force behind its completion and publication. Throughout the years, Fatima worked to preserve Bill's mathematical legacy. The Lawvere Archives are an extraordinary resource, making lectures, manuscripts, articles, and ideas spanning decades of research available to future generations.
This kind of work is rarely counted as a mathematical contribution. It doesn't produce theorems with one's name attached, or necessarily lead to papers, citations, or prizes. But without it, important parts of our mathematical history simply disappear. There is a long history of women whose intellectual and practical work has sustained the careers of celebrated men: collaborators, editors, translators, organizers, guardians of archives. Their contributions are difficult to measure, and consequently easy to forget.
I don't want to suggest that this is the role women should play in mathematics. Quite the contrary. We have fought for generations for women to have mathematical careers of their own and receive recognition for their discoveries. But that struggle should not make us forget the women whose contributions took other forms.
Making mathematics accessible and preserving mathematical knowledge are themselves valuable intellectual achievements.
Fatima Lawvere deserves to be remembered for what she did. On this Ada Lovelace Day, I want to thank her for her work, her persistence, and her generosity to the mathematical community.
The Lawvere Archives: https://lawverearchives.com/
F. William Lawvere and Stephen H. Schanuel, Conceptual Mathematics: A First Introduction to Categories.
Anders Kock, presentation at the 2023 meeting dedicated to F. William Lawvere, quoting Lawvere's 2014 obituary for Stephen Schanuel and recollections by Danilo Lawvere.
