Alexander Grothendieck passed away

Translation (from

Considered as the greatest mathematician of the 20th century, Alexander Grothendieck died, Thursday November 13, at Saint-Girons hospital, not far from Lasserre, the village where he secretly retired in the early 90s, cutting off all contact with the world. He was 86 years old. Stateless, naturalized French in 1971, known for the radicality of his pacifist and environmental activities, this singular and mythical mathematician leaves a considerable scientific legacy.

He was born on March 28, 1928, in Berlin, in an atypical family. Sascha Schapiro, his father, is a Jewish Russian, photographer and anarchist activist. Also very engaged, Hanka Grothendieck, his mother, is a journalist. In 1933, Sascha leaves Berlin for Paris, where he is soon joined by Hanka. Between 1934 and 1939, the couple leaves for Spain where it joins the Popular Front, while little Alexander is left in Germany to a family friend.


At the end of the Spanish Civil War, in the spring of 1939, Alexander meets his parents again in southern France. In October 1940, his father is taken prisoner in Vernet camp, which he leaves in 1942, for Auschwitz, where he will be assassinated. Alexander and his mother are taken elsewhere. “During my first year of high school, in 1940, I was imprisoned with my mother in Rieucros concentration camp, near Mende”, he says in Recoltes et Semailles, a monumental autobiographical text that was never published, but can be found on the Internet.

“It was war, and we were strangers – ‘undesirables’ as they said. But the camp administration closed one eye for boys, as undesirable as they were. We entered and left as we wanted. I was the eldest, and the only one to attend high school, four or five kilometers from there, regardless of whether there was snow or wind, with cheap shoes that were always soaked.


In 1944, with his high school diploma, Alexander Grothendieck had not yet been identified as the genius he was. He enrolled in math at Montpellier University, and was recommended to Laurent Schwartz and Jean Dieudonné for his thesis.

History forged his myth: the two great mathematicians gave the young student a list of fourteen problems that they viewed as a wide work program for the coming years, and asked him to pick one. A few months later, Alexander Grothendieck came back to see his supervisors: he solved them all.

In this first period of mathematical production, Grothendieck worked on functional analysis, a field of analysis that studies function spaces. His work revolutionized the field, but remains less known than the one he will conduct in the second part of his career.


In 1953, the young mathematician was quickly pressed to seek a job in academia. Stateless, he could not work in the public sector and, unwilling to serve in the military, he doesn’t want to seek french naturalization. He goes to teach in Sao Paulo (Brazil), in Lawrence (Kansas), and Chicago (U.S.)

Two years later, when he returned to France, a wealthy industrialist interested by mathematics, Léon Motchane, fascinated by the intuition and work power of the young man – Grothendieck was only 27 – decides to fund an exceptional research institute, based on the Princeton Institute for Advanced Study: l’Institut des Hautes études Scientifiques (IHES; Institue of high scientific studies), at Bures-sur-Yvette. The place was imagined as a home for the mathematician, who will begin a second career there.


Until 1970, surrounded by a multitude of international talent, he will lead his seminar on algebraic geometry, which will be published in the form of tens of thousands of pages. His new vision of geometry, inspired by his obsession of rethinking the notion of space, has shaken the very way to do mathematics. “The ideas of Alexander Grothendieck have, so to say, penetrated the subconscious of mathematicians”, says Pierre Deligne (Princeton Institute of Advanced Study), his most brilliant student, laureate of the Fields Medal in 1978 and the Abel Prize in 2013.

The notions he has introduced or developed remain today at the heart of geometrical algebra and are heavily studied. “He was unique in his way of thinking, says Mr. Deligne, very moved by the death of his ancient mentor. He had to understand things from the most general possible point of view, and once things were understood like this, the landscape became so clear proofs looked almost trivial.”


In 1966, he receives the Fields medal, but refuses it for political reasons before going to Moscow to receive it. The radicality with which he will defend his convictions will never cease. He began drifting away from the scientific community at the end of the 1960s. In 1970, with two other mathematicians – Claude Chevalley and Pierre Samuel – he founded a group called Survive and Live, pacifist, ecologist, and very touched by the hippie movement. At the same time, he discovers that IHES is partially – albeit very marginally – funded by the Ministry of Defense. He leaves the institute.

The Collège de France offers him a temporary job, which he largely uses as a political platform. He leaves the Collège soon enough. In 1973, he becomes a professor at the University of Montpellier before going to the CNRS in 1984 until his retirement in 1988. The same year, he’s awarded the Crafoord prize, which comes with a big monetary award. He refuses the distinction. In 1990, he leaves his home for a secretive lair. Bitter, not on good terms with his friends, his family, the scientific community and science, he settles in a small Pyreneean village whose name he keeps secret. He will remain there, cut off from the world, until his death.

Film and discussion: “Colours of Math”

18 November 2014, , at Pushkin House.  From an advertisement:

The independent documentary “Colours of Math” (2012) by Ekaterina Eremenko – a German-based, American-trained, Russian-born documentary producer and mathematician – has been an unlikely runaway success.  It has been translated into 12 languages, and screened around the world.

With six mathematicians from different countries and six senses that lead them in their journey of discovery, the movie gives an insight into the mystery of abstract mathematical ideas and creative thinking.

The screening (60 min) is followed by a round table discussion. What is happening in contemporary mathematics? Are there particular national schools of thought and traditions of education? Prominent mathematicians will share their views on these questions.


Professor Sergey Foss, Heriot Watt University

Professor Leonid Parnovski, University College London

Professor Eugene Shargorodsky, Kings College London

Dr June Barrow-Green, Open University

Understanding Emotions in Mathematical Thinking and Learning

Call for book chapters on:

Understanding Emotions in Mathematical Thinking and Learning

To be published by Elsevier Academic Press, 2016

Editor: Ulises Xolocotzin (UNAM, Mexico)

The last 25 years have seen an increasing interest in the ways in which emotions might influence the learning, instruction, and practice of mathematics. The relevant research covers an ever-expanding breadth, reflecting the diversity of the academic and cultural backgrounds of those scholars who are actively studying the connections between mathematics and emotions.

There has been an important progress in understanding the interplay between emotions and mathematical activity. However, resources integrating the current state of knowledge are lacking and much needed. Researchers and students working in this subject are often unaware of the contributions made by colleagues in other fields, presumably because they publish in different journals and attend different conferences. This book will contribute to support the coordination of perspectives across disciplines.

This book aims to attract an international cadre of authors from different disciplines, in order to offer a comprehensive coverage of research concerning emotions and their relation to different aspects of learning, teaching, and practicing mathematics.

The chapters in this book will draw on the advances made by researchers from different fields, such as mathematics, education, mathematics education, cognitive psychology, educational psychology, neuroscience, learning sciences, affective sciences, as well as K-12 mathematics teachers. Readers can expect to see chapters based on diverse epistemological traditions and research methodologies, such as self-reports, interviews, ethnography, brain imaging, behavioral experiments, or automatic emotional expression analysis. However, the focus of the book will be to identify and highlight overarching theoretical concepts and methodological alternatives that might be relevant across disciplines.

The areas covered by the book include, but are not limited to:

Numerical cognition

• Emotions and number sense
• The influence of emotions in the processing of symbolic and non-symbolic representations of number
• Neuroscience perspectives on the relationship between emotions and numerical cognition

Mathematical activity

• The influence of emotions on mathematical activities such as calculation, problem solving, argumentation and probing
• The relationship between emotions and performance in specific mathematical domains such as arithmetic, algebra, or geometry.
• Positive emotions in relation to mathematics, e.g., interest, enjoyment, curiosity, wonder, or aesthetic experiences

Individual differences

• Emotional experiences of children with disabilities, individuals with mathematics difficulties, or high achievers in mathematics
• Recent advances in mathematics anxiety and performance under stress
• The influence of emotions in individuals’ attitudes and beliefs towards mathematics

Teaching and learning mathematics

• Mathematics teachers’ emotions and their influence in students’ learning
• Teachers’ understanding of their students’ emotions
• The emotions experienced whilst learning mathematics in the school and in informal settings
• The role of emotions in the use and design of mathematics learning technology

Social and cultural factors

• Cross-cultural studies on emotions and mathematics
• Emotional experiences related to mathematics amongst individuals in challenging social settings, for instance in contexts of political tension and immigration.
• Stereotype threat and performance in mathematics

Theoretical frameworks and methodologies

• Theoretical views integrating cognition and emotion in relation to mathematical activity
• Chapters addressing methodological issues in the study of the intersection between emotions and mathematics.


Submission procedure:

Those interested in submitting chapters on the above suggested topics or on other related topics in their particular area of interest should submit a 2-4 paragraphs manuscript proposal to outlining the proposed chapter by January 16, 2015.

You will be notified about your proposal by January 30 2015.

Upon acceptance of your proposal, you will have until May 1st to prepare a chapter of 5000-8000 words.

Revised chapters due: July 1st 2015

Ulises Xolocotzin

Job opportunity at the Cambridge Mathematics Education Project

From Julian Gilbey:

We are currently looking for somebody to join our team at the Cambridge Mathematics Education Project.  The appointee will be working with us to develop Educational Resources for our website which is aimed at 16+ mathematics.

More information about the project is available from

Details of the job are available here:

The beginning of the end?

Is this beginning of the end of the traditional model of mathematics education?

This advert for PhotoMath gone viral:  and enjoys an enthusiastic welcome.

Mathematical capabilities of PhotoMath, judging by the product website, are still relatively modest. However, if the scanning and OCR modules (“OCR” here refers to “Optical Character Recognition”, not to the well–known examination board). of PhotoMath are combined with the full version of Yuri Matiasevich‘s “Universal Math Solver“, it will solve at once any mathematical equation or inequality,  or evaluate any integral, or check convergence of any series appearing in the British school and undergraduate mathematics. Moreover, it will produce, at a level of detail that can be chosen by a user, a complete write-up of a solution, with all its cases, sub-cases, and necessary explanations (with slight Russian accent, but that can be easily fixed).

In short, smart phones can do exams better, and the system of mathematics education based on standard written examinations is dead. Perhaps, we have to wait a few years for a formal coroner’s report, but we cannot pretend that nothing has happened.

In my opinion, a system of mathematics education which focuses on deep understanding of mathematics and treats mathematics as a discipline and art of those aspects of formal reasoning which cannot be entrusted to a computer is feasible. But such alternative system cannot be set-up and developed quickly, it is expensive and raises a number of uncomfortable political issues. I can give an example of a relatively benign issue: in the new system, it is desirable to have oral examinations in place of written ones. But can you imagine all the complications that would follow?

PhotoMath gives a plenty of food for thought.