Do Not Erase: Mathematicians and Their Chalkboards

by Jessica Wynne

A photographic exploration of mathematicians' chalkboards



"A mathematician, like a painter or poet, is a maker of patterns," wrote the British mathematician G. H. Hardy. In Do Not Erase, photographer Jessica Wynne presents remarkable examples of this idea through images of mathematicians' chalkboards. While other fields have replaced chalkboards with whiteboards and digital presentations, mathematicians remain loyal to chalk for puzzling out their ideas and communicating their research. Wynne offers more than one hundred stunning photographs of these chalkboards, gathered from a diverse group of mathematicians around the world. The photographs are accompanied by essays from each mathematician, reflecting on their work and processes. Together, pictures and words provide an illuminating meditation on the unique relationships among mathematics, art, and creativity.

The mathematicians featured in this collection comprise exciting new voices alongside established figures, including Sun-Yung Alice Chang, Alain Connes, Misha Gromov, Andre Neves, Kasso Okoudjou, Peter Shor, Christina Sormani, Terence Tao, Claire Voisin, and many others. The companion essays give insights into how the chalkboard serves as a special medium for mathematical expression. The volume also includes an introduction by the author, an afterword by New Yorker writer Alec Wilkinson, and biographical information for each contributor.

Do Not Erase is a testament to the myriad ways that mathematicians use their chalkboards to reveal the conceptual and visual beauty of their discipline--shapes, figures, formulas, and conjectures created through imagination, argument, and speculation.

Genres: Mathematics, Education, Nonfiction

240 pages, Hardcover

First published June 22, 2021

Reviews

[Fernando Pestana da Costa · Rating 5 out of 5]

This beautiful book is the result of an interesting concept superbly executed. The author, a professor of photography at the Fashion Institute of Technology, is "interested in learning about the moment of discovery, the epiphany of solving a problem", and has long been fascinated by chalkboards, by their beauty and practical use, and by their symbolism. This book is the result of both these passions: in each of the odd numbered pages there is a photograph of a mathematician's chalkboard, with whatever symbols, schemes, or drawings were there at the time the photograph was taken; on the preceding (even numbered) page is the name of the mathematician, an extra-short biographical note, and, filling the bulk of the page, is a statement by the mathematician him/herself about his work (typically motivated by what is in the chalkboard in the photo), by his creative process and by the importance of discussing with students and collaborators in front of that low tech but always incredibly useful device for doing mathematics research: the chalkboard! In all there are well over one hundred mathematicians and their blackboards that are pictured and given voice in this wonderful book. Jessica Wynne has done a real service to the mathematics community in our always difficult attempt to convey what we do (and how we do it) to the general public. This is indeed a beautifully great attempt to answer the question in the quote in the book's back cover: "What does thought look like?"

[Luca Dell'Oca · Rating 5 out of 5]

Un'opera affascinante, che mi ha catturato dal momento in cui ho scoperto la sua esistenza, e che mi ha fatto compagnia per qualche mese. Ho deciso infatti di leggere una-due pagine al giorno, non di più, per poter osservare con attenzione e curiosità i vari racconti di fisici e matematici. Ognuno di loro ha raccontato il suo lavoro (che ai più, me compreso, suona totalmente incomprensibile) e il suo rapporto con la lavagna. E pur nell'unicità di ogni intervista, ci sono dei temi ricorrenti che ci insegnano - anche in quest'era moderna dominata dalla tecnologia - come l'approccio analogico di lavagna e gessetti abbia non pochi vantaggi.

Per prima cosa, la lavagna è un sistema di astrazione: non permette di raffigurare le cose come sono realmente, ma ne fa più "un fumetto", costringendo però in questo modo l'autore a semplificare, e a lasciare in vista unicamente le caratteristiche essenziali. Questo rende le spiegazioni alla lavagna molto più intuibili. I limiti di spazio inoltre non permettono di raffigurare una quantità infinita di concetti poco importanti: la lavagna richiede sintesi, e la capacità di "distillare" le informazioni nella loro forma più significativa.

C'è poi la dimensione artistica: fin dall'inizio, quando si deve decidere in quale punto della lavagna iniziare a disegnare. E tutta la creazione del disegno è un'opera paragonabile a quella di un pittore. Pennellate di vario tipo, flussi che vanno nelle varie direzioni, fino a completare una rappresentazione che spesso viene fotografata. Mentre il quadro però viene osservato solo nella sua forma finale, nella lavagna si assiste in tempo reale alla sua creazione, accompagnata dalla spiegazione dell'autore, mentre disegna.
Questo porta a un ulteriore aspetto delle rappresentazioni su lavagna: il tempo. Mentre le presentazioni su powerpoint permettono (o costringono) di osservare tantissimi grafici in poco tempo, la lavagna forza chi ci scrive a "perdere tempo" nel disegnare. Questo si rivela un vantaggio: gli utenti hanno il tempo di assimilare quanto viene detto, rendendo questo strumento di insegnamento estremamente efficace.

Altro aspetto, la collaborazione. Può capitare che più persone lavorino insieme davanti alla lavagna, aportando ognuna il proprio contributo al lavoro finale. Può capitare che l'insegnante sia anche allievo, o viceversa. E lavorando con altri ci si arricchisce, e il lavoro finale è migliore.

Infine, vi è la temporaneità. Nonostante i cartelli "Do not erase" sulle lavagne, alla fine i lavori raffigurati verranno presto o tardi cancellati. Ma i concetti che vi sono stati espressi, le amicizie che sono nate davanti ad esse, e i risultati scientifici che si no prodotti, quelli restano per sempre.

Come dice uno degli intervistati: tecnicamente, la lavagna non è altro che una lastra scura su cui è possibile fare segni usando la polvere di gesso. Ma detto così è sterile, perchè manca totalmente l'aspetto umano di questo strumento senz'età. Si, è solo un contenitore nero: ma la profondità dei suoi contenuti può essere sconfinata, avendo come unico limite il pensiero di chi ci scrive sopra. La traccia dell'essere umano si vede nei segni, in "come" i segni sono stati fatti, "quando" sono stati fatti, rendendo unica ogni rappresentazione. Sono come le impronte di una mente al lavoro, lasciate come polvere bianca sulla lavagna.

[Ietrio · Rating 1 out of 5]

contorted, handicapped souls of bureaucrats thinking they are some sort of poet or philosopher. sad. much too sad. it's like visiting a museum of medical errors.

[WiseB · Rating 4 out of 5]

As someone who taught mathematics using a chalkboard, I can appreciate the author quoting the mathematicians of their memory and stickiness to the chalkboard in their words and also snapshots of their work on the chalkboard. I still recall working on problems brought up by students with the piece of chalk in my hand while thoughts flew through the brain with outputs on the board including occasional rubbing and rewriting.

[Mohammed omran · Rating 3 out of 5]

تتصدر سبورة مُكتَظة بمعادلات رياضية كَتبَها ألبرت أينشتاين أحد المتاحف في مدينة أكسفورد بالمملكة المتحدة. والمفارَقة في الأمر أن أينشتاين نفسه عارَض الإبقاء على هذه السبورة، في حين رحَّب 111 عالِمًا من علماء الرياضيات بالتقاط جيسيكا وين صورًا لسبوراتهم شديدة التنوع. كانت الأبسط من بين هذه الصور

"عالم الرياضيات، مثل الرسام أو الشاعر، هو صانع الأنماط"، كتب عالم الرياضيات البريطاني جي إتش هاردي. في "لا تمحو"، تقدم المصورة جيسيكا وين أمثلة رائعة على هذه الفكرة من خلال صور السبورات لعلماء الرياضيات. في حين حلت مجالات أخرى محل السبورات بفضل السبورات البيضاء والعروض التقديمية الرقمية، يظل علماء الرياضيات مخلصين للطباشير لإرباك أفكارهم وتوصيل أبحاثهم. يقدم وين أكثر من مائة صورة مذهلة لهذه السبورات، تم جمعها من مجموعة متنوعة من علماء الرياضيات حول العالم. الصور مصحوبة بمقالات من كل عالم رياضيات، يعكس عملهم وعملياتهم. توفر الصور والكلمات معًا تأملًا مضيءًا حول العلاقات الفريدة بين الرياضيات والفن والإبداع. يضم علماء الرياضيات الموجودون في هذه المجموعة أصواتًا جديدة مثيرة جنبًا إلى جنب مع شخصيات معروفة، بما في ذلك سان يونج أليس تشانغ، آلان كونيس، ميشا جروموف، أندريه نيفيس، كاسو أوكودجو، بيتر شور، كريستينا سورماني، تيرينس تاو، كلير فويسن، وغيرهم الكثير. تقدم المقالات المصاحبة نظرة ثاقبة حول كيفية عمل السبورة كوسيلة خاصة للتعبير الرياضي. يتضمن المجلد أيضًا مقدمة من المؤلف، وخاتمة كتبها كاتب نيويوركر أليك ويلكنسون، ومعلومات عن السيرة الذاتية لكل مساهم. لا تمحو هو شهادة على الطرق التي لا تعد ولا تحصى التي يستخدمها علماء الرياضيات السبورات الخاصة بهم للكشف عن الجمال المفاهيمي والبصري لانضباطهم - الأشكال والأشكال والصيغ والتخمينات التي تم إنشاؤها من خلال الخيال والحجة والتكهنات.
، صورة لسبورة تاداشي توكييدا. تَظهَر في الصورة دائرة، رُسِم إطارها باللون الأبيض على خلفية السبورة السوداء، وكُتِبت تحتها كلمة "أبيض". وفي نفس



الصورة، تظهر دائرة ثانية، مُظلَّلة بالأبيض، وكُتِبت تحتها كلمة "أسود". يُشَبِّه توكييدا مشاهَدة سبورة أثناء الكتابة عليها بالطباشير بالاستماع إلى مقطوعة موسيقية، "كل نوتة منها على حدة". إنّ هذا الكتاب يتميز بالبساطة والإبداع، وإنْ كان مربكًا بعض الشيء.

[Renz Ogena]

Most of the essay entries in this book have two parts: 1) freestyle writing about anything the contributing mathematician wishes to write about and 2) a sentence or two about how chalkboards are important to them. Almost never did the transition between these two topics go smooth. It was always abrupt, staggered, and at times gross. The effort to preserve the theme about the importance of chalkboards to mathematicians produced a collection of bipartite essays that could have been cleaner if everything was just split into two separate books with different albeit related topics. If the contributing authors were just left to write freestyle about the scribblings on their boards, the original intention of the book being about chalkboards would not have been abandoned.

[T.]

“We mathematicians like to watch 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 plus experience. Our age is addicted to transmitting more and more information, blaring climax (result) after climax. For us, that’s not enough: we also want to experience, indeed to relive personally, how the result has come to be. Only in this way can we create science – and on the side, experience joy.”

Review by Roy Peachey here: https://www.plough.com/en/topics/life...

[Isaac Lambert · Rating 4 out of 5]

4.5 stars

almost made me want to go back and pursue a PhD. I do miss the chalkboard and such a pure search for beauty.

my proudest moment was recognizing one mathematician just by looking at the math 🤣

[Sireesh · Rating 2 out of 5]

made a tour through the midwest and missed Prof. Goins :(