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Tag: geometry

Grothendieck’s survival talks

Published August 6, 2009 by lieven

The Grothendieck circle is a great resource to find published as well as unpublished texts by Alexander Grothendieck.

One of the text I was unaware of is his Introduction to Functorial Algebraic Geometry, a set of notes written up by Federico Gaeta based on tape-recordings (!) of an 100-hour course given by Grothendieck in Buffalo, NY in the summer of 1973. The Grothendieck-circle page adds this funny one-line comment: “These are not based on prenotes by Grothendieck and to some extent represent Gaeta’s personal understanding of what was taught there.”.

It is a bit strange that this text is listed among Grothendieck’s unpublished texts as Gaeta writes on page 3 : “GROTHENDIECK himself does not assume any responsability for the publication of these notes”. This is just one of many ‘bracketed’ comments by Gaeta which make these notes a great read. On page 5 he adds :

“Today for many collegues, GROTHENDIECK’s Algebraic Geometry looks like one of the most abstract and unapplicable products of current mathematical thought. This prejudice caused har(‘m’ or ‘ess’, unreadable) even before the students of mathematics within the U.S. were worried about the scarcity of academic positions… . If they ever heard GROTHENDIECK deliver one of his survival talks against modern Science, research, technology, etc., … their worries might become unbearable.”

Together with Claude Chevalley and Pierre Cartier, Grothendieck was an editor of “Survivre et Vivre“, the bulletin of the ecological association of the same name which appeared at regular intervals from 1970 to 1973. Scans of all but two of these volumes can be found here. All of this has a strong 60ties feel to it, as does Gaeta’s decription of Grothendieck : “He is a very liberal man and in spite of that he allowed us to use plenty of tape recorders!” (p.5).

On page 11, Gaeta records a little Q&A exchange from one of these legendary ‘survival talks’ by Grothendieck :

Question : We understand your worries about expert knowledge,… by the way, if we try to explain to a layman what algebraic geometry is it seems to me that the title of the old book of ENRIQUES, “Geometrical theory of equations”, is still adequate. What do you think?

GROTHENDIECK : Yes, but your ‘layman’ should know what a sustem of algebraic equations is. This would cost years of study to PLATO.

Question : It should be nice to have a little faith that after two thousand years every good high school graduate can understand what an affine scheme is … What do you think?

GROTHENDIECK : …. ??

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introducing : the n-geometry cafe

Published July 17, 2009 by lieven

It all started with this comment on the noncommutative geometry blog by “gabriel” :

Even though my understanding of noncommutative geometry is limited, there are some aspects that I am able to follow.
I was wondering, since there are so few blogs here, why don’t you guys forge an alliance with neverending books, you blog about noncommutative geometry anyways. That way you have another(n-category cafe) blogspot and gives well informed views(well depending on how well defined a conversational-style blog can be).

The technology to set up a ‘conversational-style blog’, where anyone can either leave twitter-like messages or more substantial posts, is available thanks to the incredible people from Automattic.

For starters, they have the sensational p2 wordpress theme : “blogging at the speed of thought”



A group blog theme for short update messages, inspired by Twitter. Featuring: Hassle-free posting from the front page. Perfect for group blogging, or as a liveblog theme. Dynamic page updates. Threaded comment display on the front page. In-line editing for posts and comments. Live tag suggestion based on previously used tags. A show/hide feature for comments, to keep things tidy. Real-time notifications when a new comment or update is posted. Super-handy keyboard shortcuts.

Next, any lively online community is open for intense debate : “supercharge your community”



Fire up the debate with commenter profiles, reputation scores, and OpenID. With IntenseDebate you’ll tap into a whole new network of sites with avid bloggers and commenters. And that’s just the tip of the iceberg!

And finally, as we want to talk math, both in posts and comments, they provide us with the WP-LaTeX plugin.

All these ingredients make up the n-geometry cafe ((with apologies to the original cafe but I simply couldn’t resist…)) to be found at noncommutative.org (explaining the ‘n’).



Anyone can walk into a Cafe and have his/her say, that’s why you’ll get automatic author-privileges if you register.

Fill in your nick and email (please take your IntenseDebate setting and consider signing up with Gravator.com to get a nice image next to your contributions), invent your own password, show that you’re human by answering the reCapcha question and you’ll get a verification email within minutes ((if you don’t get an email within the hour, please notify me)). This will take you to your admin-page, allowing you to start blogging. For more info, check out the FAQ-pages.

I’m well aware of the obvious dangers of non-moderated sites, but also a strong believer in any Cafe’s self-regulating powers…

If you are interested in noncommutative geometry, and feel like sharing, please try it out.

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Bourbakism & the queen bee syndrome

Published July 15, 2009 by lieven

Probably the smartest move I’ve made after entering math-school was to fall in love with a feminist.

Yeah well, perhaps I’ll expand a bit on this sentence another time. For now, suffice it to say that I did pick up a few words in the process, among them : the queen bee syndrome :

women who have attained senior positions do not use their power to assist struggling young women or to change the system, thereby tacitly validating it.

A recent study by the Max Planck Institute for Human Development asserts that the QBS

likely stems from women at the top who feel threatened by other women and therefore, prefer to surround themselves with men. As a result, these Queen Bees often jeapordize the promotions of other females at their companies.

Radical feminists of the late 70-ties preferred a different ‘explanation’, clearly.

Women who fought their way to the top, they said, were convinced that overcoming all obstacles along the way made them into the strong persons they became. A variant on the ‘what doesn’t kill you, makes you stronger’-mantra, quoi. These queen bees genuinely believed it to be beneficial to the next generation of young women not to offer them any shortcuts on their journey through the glass ceiling.

But, let’s return to mathematics.

By and large, the 45+generation decides about the topics that should be (or shouldn’t be) on the current math-curriculum. They also write most of the text-books and course-notes used, and inevitably, the choices they make have an impact on the new generation of math-students.

Perhaps too little thought is given to the fact that the choices we (yes, I belong to that age group) make, the topics we deem important for new students to master, are heavily influenced by our own experiences.

In the late 60ties, early 70ties, Bourbaki-style mathematics influenced the ‘modern mathematics’ revolution in schools, certainly in Belgium through the influence of George Papy.

In kintergarten, kids learned the basics of set theory. Utensils to draw Venn diagrams were as indispensable as are pocket-calculators today. In secondary school, we had a formal axiomatic approach to geometry, we learned abstract topological spaces and other advanced topics.

Our 45+generation greatly benefitted from all of this when we started doing research. We felt comfortable with the (in retrospect, over)abstraction of the EGAs and SGAs and had little difficulties in using them or generalizing them to noncommutative levels…

Bourbakism made us into stronger mathematicians. Hence, we are convinced that new students should master it if they ever want to do ‘proper’ research.

Perhaps we pay too little attention to the fact that these new students are a lot worse prepared than we were in the old days. Every revolution inevitably provokes a counter-revolution. Secondary school mathematics sank over the last two decades to a debilitating level under the pretense of ‘usability’. Tim Gowers has an interesting Ivory tower post on this.

We may deplore this evolution, we may try to reverse it. But, until we succeed, it may not be fair to freshmen to continue stubbornly as if nothing changed since our good old days.

Perhaps, Bourbakism has become our very own queen bee syndrome…

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