First Monday

FM reviews

 

Blackboards and chalk, to the rescue:
A review of Do not erase: Mathematicians and their chalkboards by Edward J. Valauskas

 

Do not erase Jessica Wynne.
Do not erase: Mathematicians and their chalkboards.
Princeton, N.J.: Princeton University Press, 2021.
haardback, 227 pp., ISBN 978–0–691–19922–1, $US35.00 (also available as an ebook).
Princeton University Press: https://press.princeton.edu/

 


 

An incredible, intense delight to read and study, where mathematical symbols in chalk transform into art, Do nor erase has become my favorite book to randomly explore. Composed from spectacular 111 photographs by Jessica Wynne and accompanying essays (or to be accurate, ‘reflections’) by mathematicians on their intellectual and graphic handiwork, this book is a delight to read from cover to cover, as well as a tome to explore randomly. It has become one of my favorite academic books in the ways in which it is organized, formatted, and presented.

I must confess that when I first heard of this work, in a 2019 New York Times story [1], I was excited and impatiently awaited the arrival of Do not erase. I am of that generation that became quite involved with blackboards as pedagogical tools at an early age. Blackboards initially in my Catholic parochial school terrified me, with unexpected demands to solve arithmetical problems or, even more frightening, parsing grammar.

It was not until fifth grade when I realized the ‘magic’ of blackboards [2], as an aid in explaining a concept at the speed of thought and verbal communication. I had been reading for entertainment, an old geology textbook [3] thanks to my growing youthful fascination with paleontology. I had spent some idle time memorizing the names and chronological order of geological eras, periods, and epochs, discovering as a result ‘deep time’. I had wondered how time on that scale could be measured and quite accidentally discovered Harrison Brown’s article entitled “The age of the solar system”, published in Scientific American [4]. All became clear to me, and I was ready to explode with this new information.

A lunch time session with my long-suffering teacher, a tolerant member of the congregation known as the Sisters of Christian Charity, gave me my first experience with chalk and blackboard, as I tried to explain my childish comprehension of geologic time and its accurate resolution by radioactive isotopes in minerals.

Repeatedly, in Do not erase, mathematicians refer to the speed of ‘chalk talk’, that is the time spent understanding, explaining, thinking, and communicating with chalk in hand. Chalk talk was mentioned, praised, and saluted in many different ways in this book, in contrast to the horrific more modern methods of carefully prepared slides and videos.

“We mathematicians like mathematics being done with chalk on a board for the same reason that people like to listen to music note by note, in real time. Science, at least mathematics, is made of information and experience.” — Tadashi Tokieda [5]
 
“I’ve always hated giving presentations with slides — I am a big fan of what we call ‘chalk talks’.” — Silvia Ghinassi [6]
 
“A virtue of chalk, and talks that use it, is that it checks the Icarian desire of a speaker to communicate too much, heedless of the capacity of the listeners to comprehend.” — Paul Apisa [7]
 
“The chalkboard is the glue that holds together this community and its rituals. ... My closest adult friendships have all begun through mathematical collaboration, standing in front of a chalkboard trying to understand, together, some mathematical puzzle. This experience, somehow, leads to friendship; it has been one of the great joys of my life.” — Nicholas G. Vlamis [8]
 
“The chalkboard allows us to depict abstract forms that represent the essence of mathematical ideas, and these depictions build bridges among the minds of mathematicians when they are working on a problem together. Writing on a chalkboard is a kind of special language that I use to talk to my collaborators and students. almost every new idea or project starts with a discussion on a blackboard.” — Alexei A. Mailybaev [9]
 
“When giving lectures, some people put up slides, but it is often difficult to absorb a slide since it comes and goes quickly. Much better is a chalk talk. There, the speaker covers the board at a relatively slow pace, slow enough that the audience can absorb the material.” — James H. Simons [10]
 
“I usually do not give good talks, but if the chalk is bad, then diaster is guaranteed.” — Bassam Fayad [11]
 

I must admit that my overall positive experiences have led to a lifetime addiction to the smell of chalk, the sensation of chalk dust-covered fingers, the sound of chalk pressed slowly and carefully on a blackboard, all accompanied by the slow but steady comprehension of a topic.

I rescued a blackboard to sustain this addiction, now proudly mounted in a room in my home. It is tiny, four-foot square blackboard, with a rim pf wood painted decades ago dim gray. This particular blackboard occupied a wall in the corner of a laboratory on the fourth floor of the Fermi Institute for Nuclear Studies at the University of Chicago. It was once a lab used by Harold Urey and his colleagues many decades ago; more recently, it was filled with experimental equipment for Robert N. Clayton. I had spent a summer 52 years ago in Clayton’s lab, examining stable isotopes of carbon and oxygen in fossil mollusks. With the demolition of the Institute for a new facility, Dr. Clayton invited me to help in cleaning up before the wrecking ball arrived in 2012; the blackboard was one of my rewards.

My treasured memories of the Institute include many blackboards, some captured and preserved in photographic archives. There is, of course, the most famous image of Enrico Fermi, that eventually decorated a commemorative stamp in 2001 [12]. Another photograph from 1957 illustrates Harold Urey lecturing in 1957 to a small class, with a blackboard in the background and chalk in hand. That photograph was taken in the Institute for I recognize the particular walls (in reality, a sort of light, unpleasant green), and Urey’s class blackboard includes brief text on rates of radiometric decay. That blackboard remarkably resembles my rescued blackboard! [13]

I was a mathematically challenged student in grammar and high school, but discovered the power of statistics for a science project on the evolution of a genus of a Cretaceous oyster. In college, excellent math instructors, especially teaching assistants, helped me shed my mathematical reservations. I even learned to enjoy proofs, discovering that they reflected my convoluted, byzantine ways of thinking [14]. Blackboards heavily contributed to my mathematical revival as an undergraduate.

Do not erase provides incredible insights into mathematical thinking, both in words and in deeds (as illustrated on blackboards). Nearly every mathematician in this work proves Stanisław Lem’s observation that “the mathematical order of the universe is our answer to the pyramids of chaos.” [15] Indeed, many of the observations by mathematicians in this book on their chalk handiwork are understandable to non-mathematically inclined, not requiring some sort of futuristic universal translator. For that, I am quite grateful.

The sample of mathematicians in this book is certainly not random, nor representative of all mathematicians on this planet. It might not even qualify as snowball sampling. Photographer Jessica Wynne honestly explains in her introduction how the subjects of Do not erase were discovered, largely through Wynne’s Cape Cod neighbors, mathematicians Amie Wilkinson and Benson Farb of the University of Chicago. Hence, the sampling of subjects leans largely on mathematicians accessible via Wilkinson and Farb in the Chicago area, as well as mathematicians in obvious academic locales on the eastern seaboard in New York, Princeton, and Cambridge, as well as a dash of Californians. Connections are made through these individuals to mathematicians in Rio, Paris, and Switzerland, adding a welcome influx of mathematical and chalk thinking outside the U.S. It would be interesting to see a new edition of this work with a more global sampling, especially in more exotic locales.

There are repeated references to the necessity of good chalk for blackboard, which I can well understand. For many readers of Do not erase, they will be introduced to the notion of a kind of special chalk, Japanese Hagamoro, known for its smooth application on a board and reduced emissions of dust. It is praised in the very first essay in Do not erase, by Philippe Michel in Lausanne. Repeatedly, good chalk and a suitably sized blackboard (or multiple boards) seem to be catalysts for mathematical thought.

Mathematicians in turn find chalk and blackboards as catalysts for collaboration at all levels, in classrooms, in offices, outdoors (weather and locale permitting [16]) with colleagues. There is a meditative value in examining a blackboard over time, as an individual, adding or subtracting content as necessary. There is repeated reference to thinking at the speed of communication, with chalk twirling in fingers, hands ready as quick erasers.

I was pleased that a number of women graced the pages of Do not erase, far more than I expected [17]. My most significant math teachers, at all levels, were women. I found the blackboards of women in Do not erase to be far more organized, even artistic compared to their male colleagues. This impression may be just a subconscious bias in favor of women in math, correlated to their sensitive uses of colored chalk and more orderly scripts.

That said, I wondered as I examined, studied, and meditated on the text and photographs in Do not erase over the true spontaneity reflected on some of the blackboards. Were the boards really representative of the daily lives of mathematicians? Were they staged? Were the boards just random jottings reflecting mathematically inclined minds? Sometimes, the accompanying text provided clues to ‘staging’ — in so many words, ‘oh here is my famous theorem on ... [fill in the blank] with an accompanying partial proof, for which I was awarded the ... [fill in the blank] award’. In other cases, the chalky scripts and cartoons seemed ‘real’, that is, honest reflections of daily mathematical work. I could guess over the identities of artfully staged blackboards vs. ‘natural’ chalkboards, or even invoke mathematical guidelines for strict analysis, based on physicist Satosi Watanabe’s notions [18]. Certainly, a Gedankenexperiment for the reader.

This book is the first to demonstrate clearly and obviously the graphic nature of mathematics, and the beauty of its efficient symbolic language. I would hope that Do not erase starts a rush to install proper blackboards — not those devilish spawns of hell called whiteboards and their foul greasy, sloppy pens — in classrooms and offices as well as homes. I only wish that I could locate more orphaned blackboards for my home, to help me remember past science and math lessons, as well as construct new personal insights.

Princeton University Press should be congratulated for creating a physically beautiful book. Elongate, the size of small handheld blackboard, the text and illustrations are printed with detail on appropriately sturdy stock for repeated study and contemplation. My only regret is that there were not alternative editions of Do not erase in stock: a limited edition that included an actual signed print by Jessica Wynne of one of the blackboards (I have to admit a particular fancy to Amie Wilkinson’s colorful board [19]).

Wilkinson in Paris
Figure 1: Professor Wilkinson’s blackboard in Paris; Image by Jessica Wynne, from Do not erase, p. 5.

Another limited edition of Do not erase would feature a slab of slate the exact size of the book, with a few mint sticks of Hagamoro for personal experimentation. One possible alternate version of Do not erase could explore historical collections of photographs, of mathematicians and physicists with their blackboards and chalk. My own random hunting in a few archival sites, now online in special collections of online libraries, has yielded some inspirational wonders.

Do not erase is wonderful and imaginative, a most important and delightful book. Highly, highly recommended for all, even those suffering from the darkest depths of mathematical anxiety. The artistry of the blackboards in Do not erase will take your breath away, windows into other worlds — much like a Joan Miró print or a Hiroshige landscape. — Edward J. Valauskas. End of article

 

Notes

1. Dennis Overbye, 2019. “Where theory meets chalk, dust flies: A photo survey of the blackboards of mathematicians,” New York Times (23 September, updated 24 September), at https://www.nytimes.com/2019/09/23/science/mathematicians-blackboard-photographs-jessica-wynne.html.

2 “Blackboards are truly magical objects for mathematicians!” Dimitri Y. Shlakhtenko, Do not erase (Princeton University Press, 2021), p. 58. I would argue that blackboards, under certain circumstances, can be ‘magical’ for even non-mathematicians. I will avoid the obvious Hogwartian references for now.

3 If you must know, it was Joseph LeConte’s Elements of geology; a text-book for colleges and for the general reader (Fourth enlarged and revised edition; New York, D. Appleton, 1896).

4 Scientific American, volume 196, number 4 (April 1957), pp. 80–95.

5 Do not erase, p. 16.

6 Do not erase, p. 48.

7 Do not erase, p. 78.

8 Do not erase, p. 88.

9 Do not erase, p. 114.

10 Do not erase, p. 130.

11 Do not erase, p. 146.

12 Image on left, Enrico Fermi at the Institute for Nuclear Studies, undated, image number apf1-06023, University of Chicago Library, Special Collections Research Center; Town & Country Photographers; see https://photoarchive.lib.uchicago.edu. Image on right, Enrico Fermi and chalkboard on U.S. stamp, released initially in Chicago on 29 September 2001, 100th birthday of Fermi; see https://postalmuseum.si.edu/object/npm_2002.2010.8.

Enrico Fermi Enrico Fermi US stamp
Figure 2: Enrico Fermi (1901–1954) at the University of Chicago’s Institute for Nuclear Studies, undated, left; U.S. commemorative stamp, released on 29 September 2001, right. Not the prominence of a blackboard, which features a controversy (in some circles).

13 Photograph of Urey and blackboard taken on Saturday, 23 November 1957 by Archie Lieberman for the Black Star photographic agency. From the University of Chicago Library, Special Collections Research Center, image number apf1-08436.

Harold Urey teaching
Figure 3: Harold Urey (1893–1981), lecturing at a class in the University of Chicago’s Institute for Nuclear Studies, 1957.

14 Much like this review. A more concise version of this review of Do not erase would simply state: “One of greatest math books of the century. Buy this book. No, buy this book in bulk, in order to give copies as gifts to family, friends, and colleagues. You will not regret it.”

15 Stanisław Lem, The investigation. Translated by Adele Milch. New York: Seabury Press, 1974.

16 I can’t imagine Professors Wilkinson and Farb working on portable blackboards outside of Eckhart Hall on the quadrangle in some of the more inhospitable points in the Chicago academic year.

17 However, Do not erase does not reflect the significant gender gap in mathematics; see, for example, “National Mathematics Survey” at https://math.mit.edu/wim/2019/03/10/national-mathematics-survey/.

18 Satosi Watanabe. Knowing and guessing: A quantitative study of inference and information. New York: Wiley, 1969.

19 Although Jessica Wynne’s photograph of Professor Wilkinson, and her vibrant blackboards, on Wilkinson’s home page is, in some ways, a more thought-provoking image; see https://math.uchicago.edu/~wilkinso/.

Copyright © 2021, Edward J. Valauskas. All Rights Reserved.

Blackboards and chalk, to the rescue: A review of Do not erase: Mathematicians and their chalkboards
by Edward J. Valauskas.
First Monday, Volume 26, Number 9 - 6 September 2021
https://firstmonday.org/ojs/index.php/fm/article/download/12284/10221
doi: http://dx.doi.org/10.5210/fm.v26i9.12284