# Author Archives: Alexandre Borovik

# Yagmur Denizhan: Performance-based control of learning agents and self-fulfilling reductionism.

Yagmur Denizhan: Performance-based control of learning agents and self-fulfilling reductionism. Systema 2 no. 2 (2014) 61-70. ISSN 2305-6991. The article licensed under the Attribution-NonCommercial-NoDerivatives 4.0 International License. A **PDF file is here.**

Abstract:This paper presents a systemic analysis made in an attempt to explain why half a century after the prime years of cybernetics students started behaving as the reductionist cybernetic model of the mind would predict. It reveals that self-adaptation of human agents can constitute a longer-term feedback effect that vitiates the efficiency and operability of the performance-based control approach.

**From the Introduction:**

What led me to the line of thought underlying this article was a strange situation I encountered sometime in 2007 or 2008. It was a new attitude in my sophomore class that I never observed before during my (by then) 18 years’ career. During the lectures whenever I asked some conceptual question in order to check the state of comprehension of the class, many students were returning rather incomprehensible bulks of concepts, not even in the form of a proper sentence; a behaviour one could expect from an inattentive school child who is all of a sudden asked to summarise what the teacher was talking about, but with the important difference that –as I could clearly see– my students were listening to me and I was not even forcing them to answer. After observing several examples of such responses I deciphered the underlying algorithm. Instead of trying to understand the meaning of my question, searching for a proper answer within their newly acquired body of knowledge and then expressing the outcome in a grammatically correct sentence, they were identifying some concepts in my question as keywords, scanning my sentences within the last few minutes for other concepts with high statistical correlation with these keywords, and then throwing the outcome back at me in a rather unordered form: a rather poorly packaged piece of Artificial Intelligence.

It was a strange experience to witness my students as the embodied proof of the hypothesis of cognitive reductionism that “thinking is a form of computation”. Stranger, though, was the question why all of a sudden half a century after the prime years of cybernetic reductionism we were seemingly having its central thesis1 actualised.

# Ivor Grattan-Guinness obituary

From The Guardian, by Tony Crilly

**Energetic historian of mathematics and logic**

When Ivor Grattan-Guinness, who has died aged 73 of heart failure, became interested in the history of mathematics in the 1960s, it was an area of study widely considered to be irrelevant to mathematics proper, or something that older mathematicians did on retirement. As an undergraduate at Oxford, he found that mathematics was presented drily, with no inkling of the original motivations behind its development. So Ivor set himself the task of asking “What happened in the past?” – as opposed, he said, to taking the heritage viewpoint of asking “How did we get here?”

Ivor Owen Grattan-Guinness, historian of mathematics and logic, born 23 June 1941; died 12 December 2014

# MBE to a maths clubs volunteer

From BBC:

A man who runs free maths classes for primary age children has been recognised in the New Year Honours list with an MBE.

Gbolahan Bright has been running the Bright Academy maths clubs for primary age children in London and Essex for the past 20 years.

“I have gained a lot from this society. I have been blessed and it would have been ungrateful of me if I did not give back,” he said.

Of the 500 or so children who have taken the classes, about 50 gained their GCSE while still at primary school.

# Retraining 15,000 teachers?

Philip Nye writes in a paper Cameron needs to rethink maths and science plan (12 Dec 2014) that

Under No 10’s plan, 15,000 teachers of other subjects will also retrain as maths or physics teachers, as part of a “major push” to boost maths, science and technology skills.

However, Professor Alan Smithers, director of the Centre for Education and Employment Research at the University of Buckingham says: “It’s really easy to say ‘well, physics is science, so therefore there’ll be people teaching biology, or who have done medicine or engineering [degrees] that we can retrain as physics teachers’. But biology is really as different from physics as, say, history is.”

Perhaps the same skepticism can be applied to mathematics.

# Mathematics Resilience – making it happen

**The Shard Symposium**

**16th January 2015 10am – 4pm**

Evidence is accruing that Mathematical Resilience is fundamental to developing a numerate, empower society. You are cordially invited to attend a symposium designed to explore the next steps to be taken in enabling learners to become Mathematically Resilient.

The symposium is convened to bring together practitioners, funders and researchers to discuss what is happening in enabling learners to develop Mathematical Resilience. It is a precursor to an international conference that will be held jointly by University of Warwick and Open University in November 2015.

The symposium will be held at the Warwick University Business School Offices in The Shard, 32 London Bridge Street, London, SE1 9SG, nearest underground station London Bridge.

A small charge of £20 is payable for registration, this will be made to cover refreshments throughout the day. You can register for the event here.

# Hamid Naderi Yeganeh: Mathematical drawings made from segments

**This image shows 1,000 line segments. For each \(i=1,2,3,\cdots,1000\) the endpoints of the \(i\)-th line segment are:**

**\[\left(\cos\left(\frac{2\pi i}{1000}\right), \sin\left(\frac{2\pi i}{1000}\right)\right)\]**

**and**

**\[\left(\cos\left(\frac{4\pi i}{1000}\right), \sin\left(\frac{4\pi i}{1000}\right)\right).\]**

**See other images at:**

**mathematics.culturalspot.org &**

**Mathematical Concepts Illustrated by Hamid Naderi Yeganeh.**

# 4th International Conference on Tools for Teaching Logic

June 9-12, 2015, Rennes, France; http://ttl2015.irisa.fr/

**Call for Papers**

Tools for Teaching Logic seeks for original papers with a clear significance in the following topics (but are not limited to): teaching logic in sciences and humanities; teaching logic at different levels of instruction (secondary education, university level, and postgraduate); didactic software; facing some difficulties concerning what to teach; international postgraduate programs; resources and challenges for eLearning Logic; teaching Argumentation Theory, Critical Thinking and Informal Logic; teaching specific topics, such as Modal Logic, Algebraic Logic, Knowledge Representation, Model Theory, Philosophy of Logic, and others; dissemination of logic courseware and logic textbooks; teaching Logic Thinking.

* INSTRUCTIONS FOR AUTHORS

Submitted papers in PDF format should not be longer than 8 pages and must be submitted electronically using the EasyChair system. A demonstration is expected to accompany papers describing software tools. At least one author of each accepted paper must be registered and attend TTL 2015 to present the paper or the tool.

* PUBLICATIONS

All accepted papers will be published electronically in the LIPICS style by University of Rennes 1 with an ISBN (a USB key will be provided to the conference participants). After the conference, a special issue containing extended versions of the best accepted papers is going to be published in the IfCoLog Journal of Logics and their Applications.

* CONFERENCE FORMAT

Papers presentations will be presented in parallel sessions along the week. Half-a-day slot will be dedicated to demo tools.

* IMPORTANT DATES

Paper submission: 30 January 2015;

Notification: 1 March 2015;

Final cameraready due: 29 March 2015

Conference: 9-12 June 2015

# Pierre Cartier on Alexander Grothendieck

# Alexander Grothendieck passed away

Translation (from https://www.reddit.com/r/math/comments/2m82zw/reports_are_coming_in_of_the_death_of_alexandre/cm1wt6u):

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.

**HIS FATHER DIES IN AUSCHWITZ**

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.

**THE MYTH OF SCHWARTZ’S AND DIEUDONNÉ’S 14 PROBLEMS**

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.

**AN INSTITUTE FUNDED FOR HIM**

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.

**A NEW GEOMETRY**

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.”

**HE LEAVES THE SCIENTIFIC COMMUNITY**

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.