In Memoriam

F. William Lawvere

February 9, 1937 – January 23, 2023

With profound sorrow we inform you of the death of the renowned mathematician Dr. William Lawvere on January 23, 2023. Professor Lawvere was a good friend of the Communist Party of Canada (Marxist-Leninist), a fellow traveller who always took the high road of civilization, engaged in settling scores with the old conscience of society and removing the blocks in the way of progress and enlightenment.

Beginning in the early 1970s, he worked on several philosophical and other projects related to the Necessity for Change and dialectics with CPC(M-L)'s founder and leader Hardial Bains, a scientist and philosopher in his own right. From 1969 to 1971, he was a Killam Scholar at Dalhousie University, in Halifax, head of a prestigious international team of mathematicians who came there to study with him. But in 1971, when Professor Lawvere protested the War Measures Act and crimes committed with the suspension of civil liberties by the government of Pierre Trudeau, Dalhousie refused to renew his contract, despite the protestations of his own team of mathematicians. More than 1,000 students rallied in the lobby of the Dal Student Union Building to oppose the arbitrary dismissal of Professor Lawvere.

On many occasions, Professor Lawvere joined us in Canada to discuss important topics and contribute his thorough and extensive knowledge on them. In February 1996, he spoke at the Inter-Disciplinary Conference held at the University of Windsor on the theme The Origin of Consciousness and Social Change. Papers delivered on that occasion presented important insights into consciousness existing independent of us, the historiography of the Cold War, the emergence of the modern democratic personality and the like. Professor Lawvere presented a paper titled The History and Philosophy of Mathematic Reform which examined various aspects of a trend in pedagogy which restricted the knowledge of mathematical science showing, amongst other matters of concern, how this provided an effective basis for promoting mysticism and blind acceptance of authority.

In 1997, he attended the funeral of Comrade Bains along with scholars from various parts of the world. He also attended the 7th Congress of CPC(M-L) in 1998 where he expressed his appreciation for the work of Hardial Bains and contributed to the thesis under discussion. He attended the Party's 35th anniversary celebration in 2005 where he again expressed his appreciation for the work of the Party on theory and the need for modern definitions. He later wrote that the 35th anniversary "was a very rewarding occasion. [...] In particular, that occasion is leading to further advances in my work, especially the project to appropriately commemorate the centenary of Lenin's books on philosophy by detailing how they have been a useful guide in the study of 19th and 20th century philosophical developments, both from the point of view of natural science as well as from the point of view of the class struggle for enlightenment. Since Hardial pointed out the importance of those books 35 years ago, they have been my constant companions. [...]"

Hearing about the death of Professor Lawvere, his long-time associate Eric Hoffman had this to say in appreciation of the profound influence that both Hardial Bains and Bill Lawvere have had on his own life and work:

"Developing from their earliest seminal work done separately in the 1960s emerges the strongest evidence for a new and surprising connection. This connection forms a part of and is embedded in an ensemble of relations among humans and nature. Bill pointed out that the objectivity of this complex compels the relentless adherence to the needs of the study of space and quantity.

"In one of the interviews on his blog, Bill said, 'The core of mathematical theories is in the variation of quantity in space and in the emergence of quality within that.' Whether considerations are geometry, categories, logic, the transition of political forms, kinship relations or any other, Bill corroborated that the unity and identity of opposites, the dialectic, lives.

"Bill's work will endure as a contribution to expanding the space of enlightenment."

In the message of condolences the First Secretary of the Central Committee of CPC(M-L) sent to Professor Lawvere's family, she wrote:

"Bill contributed so much in his lifetime we have much to appreciate. His enthusiasm and dedication to the discovery of new things was always inspiring. His approach was always vigorous, dedicated, fresh in many ways. His patience as a teacher, the intelligence and coherence of his arguments, his enthusiasm for the younger generation and for their edification, and his courageous adherence to the high road of civilization were outstanding.

"Meeting with Bill was always a great pleasure. We will always treasure his friendship, generosity of spirit and dedication to our common cause for which he spoke out without trepidation. It showed he was made of special stuff."

To illustrate the quality of his work as an educator in mathematics, his straightforward approach to explaining the matter at hand and discussing with those who showed an interest in his work, we give the example of the answer he gave to a request to provide "a broad justification of why category theory may be so useful." Here is what Bill had to say:

Everyday human activities such as building a house on a hill by a stream, laying a network of telephone conduits, navigating the solar system, require plans that can work. Planning any such undertaking requires the development of thinking about space. Each development involves many steps of thought and many related geometrical constructions on spaces. Because of the necessary multistep nature of thinking about space, uniquely mathematical measures must be taken to make it reliable. Only explicit principles of thinking (logic) and explicit principles of space (geometry) can guarantee reliability. The great advance made by the theory invented 60 years ago by Eilenberg and Mac Lane permitted making the principles of logic and geometry explicit; this was accomplished by discovering the common form of logic and geometry so that the principles of the relation between the two are also explicit. They solved a problem opened 2300 years earlier by Aristotle with his initial inroads into making explicit the Categories of Concepts. In the 21st century, their solution is applicable not only to plane geometry and to medieval syllogisms, but also to infinite-dimensional spaces of transformations, to "spaces" of data, and to other conceptual tools that are applied thousands of times a day. The form of the principles of both logic and geometry was discovered by categorists to rest on "naturality" of the transformations between spaces and the transformations within.

Below we provide the obituary published on the occasion of Professor Lawvere's death. We add a facsimile of the article from the Dalhousie Gazette of January 22, 1971 on his dismissal from the Dalhousie University. We also provide the paper titled The History and Philosophy of Mathematic Reform delivered by Dr. Lawvere at the Inter-Disciplinary Conference on the Origin of Consciousness and Social Change held at the University of Windsor, February 9-11, 1996. Finally, we provide an interview with Dr. Lawvere where he explains his work in his own words.

We express our deepest condolences to Bill's life partner and collaborator, his children, grandchildren, brothers and sisters and many many friends and colleagues. May they all find solace in the memories they created together.

Central Committee
Communist Party of Canada (Marxist-Leninist)