Mark Saul, Editor
Mathematics and mathematicians rarely make press. So it was a bit sweet, but mostly bitter, to read in the New Yorker of the deaths of John Conway, Ronald Graham, and Freeman Dyson, three great losses to our profession. (Yes, Virginia, Dyson published in ‘pure’ mathematics as well as in physics.)
And of course as soon as this article appeared, friends and colleagues wrote about others we have lost who were not mentioned in the press. It is likely that each of us has suffered some loss, some grief. I write here of my own, and what we can learn from it about our work.
My old and dear friend David Dolinko passed away last week, a final stab-in-the-back from the year 2020. His career can tell us something about our field. Mathematics is the heavy industry of the sciences, but also of other intellectual endeavors. The tools of thought that we develop are not apparent when a vaccine is tested, when an election is contested–or when a legal precedent is set. Mathematics is largely unseen by the public, and even sometimes by the people who are using it.
David started his intellectual life as a mathematics major, but became interested in logic, and earned his Ph.D. in philosophy. From there his interest ‘drifted’ (or progressed) to a law degree. He spent his career teaching the philosophy of law at UCLA until his recent retirement. He will be mourned by his students as well as friends and family.
David had a roving intellect, from the music of Mahler to the poetry of Eliot, from the history of Fascism to molecular biology. He became a prominent writer about punishment and the death penalty. In all of this, I think, his early training in mathematics betrayed itself. He had an uncanny ability to make intuitively clear ideas that were too often cloaked in formality.
Indeed, it was he who was responsible for my own initial epiphany in mathematics, a moment to which I can trace my love affair with the field. We were thirteen years old, in ninth grade. Our enlightened math teacher, Ms. Funke, spent her lunch period (and ours) meeting with interested students to form a math team. (At the time, competition was the only extra-curricular activity available for students interested in mathematics.)
Ms. Funke defined an arithmetic progression, providing us with the usual formulas for the nth term and the sum of n terms. Then she gave us a problem, straight from Hall and Knight, something like: “Insert three arithmetic means between 11 and 23.” I loved formulas. I could do this. David was sitting next to me, drawing some organic molecule he had been reading about.
“C’mon! Let’s do this! This is interesting!” I urged him. Anything that is fun to do is more fun to do with others.
But David wasn’t particularly interested: “Oh, I did that. It’s 11, 14, 17, 20, 23.” And he went back to drawing his molecule. It was at that moment, from my friend David’s answer, that I realized that algebraic formulas were invented to capture intuitions—here, that the numbers we seek are evenly spaced. It is unlikely that David had used the formula. Rather, he knew what he was looking for, the numbers were easy, and he found them without bothering with formulas. This astonished me.
For the purists among my readers: yes, intuitive methods are not general. David would probably not have inserted four arithmetic means as easily. But intuition drives formalization, seeds discovery, lends meaning to what we have discovered. And intellectually—putting aside the personal and emotional—it was through his lightning intuition that David taught me the most.
And not just me. His death has occasioned an outpouring of sympathy and recollection by lawyers and public figures who had been his students in law school. The same value of intuition, of making ‘obvious’ the meaning behind formalities, seems to have marked his teaching of the law as well.
And it is for students—David’s, mine, and yours, Dear Reader, for whom I write these thoughts. We all know that the year 2020 was an annus horribilis, a year of loss for all of us. As we plan our first ever Virtual, and last ever Joint, Mathematics Meeting, my wish is that 2021 be a year of renewal. For education is about renewal: e-ducare, to lead out. Out of darkness and grief, towards hope for the future. To renewal, to a passing of the torch to our students.
Somehow, sometime, whatever the cause, we all come to the Same End. As researchers, we advance knowledge in the present. As teachers, we build the knowledge of the future.
Lovely, Mark.
Al