Newsletter #91     An Almost Visit by Ray Johnson

I have known for a long time what the content of this newsletter was going to be. In fact, I cleared the boards specifically for it. I wanted to have lots of space for discussing the two day visit in which Ray Johnson of the University of Maryland was going to discuss with us ways in which we might encourage the presence of women and members of underrepresented minorities in the mathematical community in general and the UW mathematical community in specific. Alas, all the wonders of high-tech communication cannot eliminate the possibility of plain old misunderstandings, and the dates got scrambled. So instead I will give you a few snippets to show why I was excited about his planned visit and what sort of thing I was looking forward to hearing him say.

The first snippets are from his autobiography, found on his home page at His page is entitled "You can get there even from Alice, Texas (if you're lucky and you know where there is)", after which it is not too surprising to find that the story makes very good reading. His underlying theme is that "I would describe my life, including my entry into the profession, as being characterized by my coming of age on the right side of several transition points from the totally segregated society in which I grew up to the quasi-open society in which we now live." One such transition point was Brown vs the Board of Education, which happened after he finished elementary school in a two-room school that may well have served him better than the classy all-white one he had to walk past every day, but before he was bussed out of town for high school. Another transition resulted from the mad scramble to beef up mathematics and science education after Sputnik was launched -- one of his teachers attended institutes at the University of Texas. This resulted not only in Ray's getting some really good high school classes, but in Ray's introduction to a professor who served him as a mentor throughout his undergraduate career at UT. Under his wing Ray went on to do his graduate work at Rice, which was in the not-too-smooth process of becoming integrated. Ray was the first African-American to receive a degree from Rice. From there, by a process which from today's vantage point looks stunningly casual, he got a position at the University of Maryland. And went on to be "promoted though the ranks at Maryland, surviving long enough to become the African American faculty member with the longest tenure at College Park. As a reward for this, they made me Chair of the Mathematics Department; frankly, I think I deserved better, but I survived the term with some wits intact."

It was while he was chairman that he instituted some programs whose results have caused universities all over the country to sit up and take notice. The most spectacular (and widely reported) result was the granting of Ph.D.'s to three African America women simultaneously. The programs themselves are described in the Chronicle of Higher Education at I will leave that for you to follow up, because I was even more taken with an article in "Colloquy Live", also in the Chronicle of Higher Education, at This one is a transcript of a phone-in talk show with Ray as the guest, and it has some comments of his that I really like. For instance, his response to the moderator's opening question of " What are some of the best practices that your department has developed or identified in its efforts to attract more underrepresented minorities and women?"

Ray replied: "Attracting students is the easy part. Getting them through to the degree despite the obstacles provided by life is the hardest part. The practices are 1.) recruit where the minority students are (frequently at historically black universities, but know which produce students who can succeed in your program), 2.) get a critical mass of students to whom you have given a good experience (I don't think that necessarily means that they succeeded; that they feel well treated and that the program is fair is often enough), and 3.) stay involved in the students' lives (so that you can tell their undergraduate mentors how they are doing when you see them). "

And later: "Do you think the needs of women and minorities in mathematics overlap? Are they different than those of white or Asian students given that they are not underrepresented in the field?"

Ray's reply: "No, their needs do overlap. I believe that the policies that have been practiced by the math community have been detrimental to all students, but they have had a particular impact on minorities and women, as they are such a small part of that community. My experience is that when improvements are made on the practices that detrimentally effect women and minorities, these improvements also have a significant impact on the entire mathematics population."

On the issue of blaming the situation on K-12 education: "I agree that the problem has many roots that must be attacked before it is solved. For example, I think that the education some minority students receive in college can cause them to be underprepared in graduate school. However, I think that each of us has the responsibility to deal with this issue at our level. We can't wait for the other levels to solve the problem. Otherwise, we may get stuck in the "paralysis of analysis."

I see two roles for college faculty in dealing with the K-12 educational issues. First, we must recognize the difference between training and ability. Students come to us with different levels of training. Minority students are frequently characterized as not having ABILITY when what they they lack is in fact training.

.... Second, I think we should try to prepare future math and science teachers well. The mathematics community had a high level committee prepare a report that attempts to guide mathematics departments as to how they can do a better job of preparing future teachers. So my approach is to try to improve things that are in my province. The people in K-12 should be working on things in their province and the University should help them where possible."

Enough snippeting. I think it is clear why it was so disappointing that our plans struck out, and why I very much hope to revive the plans, glitch-free, another year.

One thing did go through. Our biggest single event was a forum entitled "Changing the Seen: Mathematics and Diversity" The subtitle was "Conversations with three who have made a difference", and by a lightening calculation you will note that that still left two. Joaquin Bustoz of Arizona State University and Donna Smith of Sierra College launched a lively discussion amongst a considerable bunch of people. Unfortunately I was too jolted by Ray's absence to do a decent report on it. One of the nice aspects was that the entire shebang was done as a three-way partnership among the math departments of Seattle University, Seattle Central Community College and U.W. That's a partnership that got launched with the earliest version of the PFF project, and has been growing and thriving ever since.

I'm approaching my newsword limit, but today had an event that was too good to let slide by. Manya Raman, a job candidate in the College of Education, gave a talk entitled "What is Proof? And for whom?" She has spent the past couple of years doing research on the similarities and differences among the reactions and responses of undergraduates, graduate students and faculty members to exactly that question. Her general style can be deduced from the fact that her first action was to write up the sentence "Prove that the derivative of an even function is odd" and then have us write out name tags color-coded by whether seeing that caused us to grin and reach for a pencil or to shrink under the desk (the latter category also included those who said "Eh?") It turned out to be the question which has been her research handle. She has watched a batch of people solve it, teach it, grade proofs and quasi-proofs of it as if it were on an exam and generally cogitate about it. A number of them she has also interviewed, which produced a lovely batch of quotations. A central issue is the contrast (sometimes rather a stark one) between what produces conviction and what constitutes an acceptable proof. Her conclusion at the current stage is that for mathematicians there is an overlap between the "private domain" -- the region of intuitive understanding -- and the "public domain" -- the region of formal proof -- and in that overlap lies the key idea that makes the proof function. For students the domains tend not merely to be non-overlapping, but to have a good wide breezeway between. She finished by astounding the (numerous) mathematicians present with a quotation -- not for its content: "Indeed every mathematician knows that a proof has not been 'understood' if one has done nothing more than verify step by step the correctness of the deductions of which it is composed and has not tried to gain a clear insight into the ideas which have led to the construction of this particular chain of deductions in preference to every other one." -- but for its source. It came from Bourbaki!

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