Hall and Knight<\/a>, something like:\u00a0 “Insert three arithmetic means between 11 and 23.”\u00a0 I loved formulas.\u00a0 I could do this.\u00a0 David was sitting next to me, drawing some organic molecule he had been reading about.<\/p>\n“C’mon!\u00a0 Let’s do this!\u00a0 This is interesting!” I urged him.\u00a0 Anything that is fun to do is more fun to do with others.<\/p>\n
But David wasn’t particularly interested:\u00a0 “Oh, I did that.\u00a0 It’s 11, 14, 17, 20, 23.”\u00a0 And he went back to drawing his molecule.\u00a0 It was at that moment, from my friend David’s answer, that I realized that algebraic formulas were invented to capture intuitions\u2014here, that the numbers we seek are evenly spaced.\u00a0 It is unlikely that David had used the formula.\u00a0 Rather, he knew what he was looking for, the numbers were easy, and he found them without bothering with formulas.\u00a0 This astonished me.<\/p>\n
For the purists among my readers: yes, intuitive methods are not general.\u00a0 David would probably not have inserted four arithmetic means as easily.\u00a0 But intuition drives formalization, seeds discovery, lends meaning to what we have discovered.\u00a0 And intellectually\u2014putting aside the personal and emotional\u2014it was through his lightning intuition that David taught me the most.<\/p>\n
And not just me.\u00a0 His death has occasioned an outpouring of sympathy and recollection by lawyers and public figures who had been his students in law school.\u00a0 The same value of intuition, of making ‘obvious’ the meaning behind formalities, seems to have marked his teaching of the law as well.<\/p>\n
And it is for students\u2014David’s, mine, and yours, Dear Reader, for whom I write these thoughts.\u00a0 We all know that the year 2020 was an annus horribilis<\/em>, a year of loss for all of us.\u00a0 As we plan our first ever Virtual, and last ever Joint, Mathematics Meeting, my wish is that 2021 be a year of renewal.\u00a0 For education is about renewal:\u00a0 e-ducare<\/em>, to lead out.\u00a0 Out of darkness and grief, towards hope for the future.\u00a0 To renewal, to a passing of the torch to our students.<\/p>\nSomehow, sometime, whatever the cause, we all come to the Same End.\u00a0 As researchers, we advance knowledge in the present.\u00a0 As teachers, we build the knowledge of the future.<\/p>\n
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