Mathematics in times of internet

A few weeks more of (heavy) teaching ahead, and then I finally hope to start on a project, slumbering for way too long: to write a book for a broader audience.

Prepping for this I try to read most of the popular math-books hitting the market.

The latest two explore how the internet changed the way we discuss, learn and do mathematics. Think Math-Blogs, MathOverflow and Polymath.

‘Gina says’, Adventures in the Blogosphere String War

The ‘string wars’ started with the publication of the books by Peter Woit:

Not even wrong: the failure of string theory and the search for unity in physical law

and Lee Smolin:

The trouble with physics: the rise of string theory, the fall of a science, and what comes next.

In the summer of 2006, Gil Kalai got himself an extra gmail acount, invented the fictitious ‘Gina’ and started commenting (some would argue trolling) on blogs such as Peter Woit’s own Not Even Wring, John Baez and Co.’s the n-Category Cafe and Clifford Johnson’s Asymptotia.

Gil then copy-pasted Gina’s comments, and the replies they provoked, into a leaflet and put it on his own blog in June 2009: “Gina says”, Adventures in the Blogosphere String War.

Back then, it was fun to waste an afternoon re-reading all of this, and I wrote about it here:

Now here’s an idea (June 2009)

Gina says, continued (August 2009)

With only minor editing, and including some drawings by Gil’s daughter, these leaflets have now resurfaced as a book…?!

After more than 10 years I had hoped that Gil would have taken this test-case to say some smart things about the math-blogging scene and its potential to attract more people to mathematics, or whatever.

In 2009 I wrote:

“Having read the first 20 odd pages in full and skimmed the rest, two remarks : (1) it shouldn’t be too difficult to borrow this idea and make a much better book out of it and (2) it raises the question about copyrights on blog-comments…”

Closing the gap: the quest to understand prime numbers

I can hear you sigh, but no, this is not yet another prime number book.

In May 2013, Yitang Zhang startled the mathematical world by proving that there are infinitely many prime pairs, each no more than 70.000.000 apart.

Perhaps a small step towards the twin prime conjecture but it was the first time someone put a bound on this prime gap.

Vicky Neal‘s book tells the story of closing this gap. In less than a year the bound of 70.000.000 was brought down to 246.

If you’ve read all popular prime books, there are a handful of places in the book where you might sigh: ‘oh no, not that story again’, but by far the larger part of the book explains exciting results on prime number progressions, not found anywhere else.

Want to know about sieve methods?

Which results made Tim Gowers or Terry Tao famous?

What is Szemeredi’s theorem or the Hardy-Littlewood circle method?

Ever heard about the Elliot-Halberstam or the Erdos-Turan conjecture? The work by Tao on Erdos discrepancy problem or that of James Maynard (and Tao) on closing the prime gap?

Closing the gap is the book to read about all of this.

But it is much more.

It tells about the origins and successes of the Polymath project, and details the progress made by Polymath8 on closing the gap, it gives an insight into how mathematics is done, what role conferences, talks and research institutes a la Oberwolfach play, and more.

Looking for a gift for that niece of yours interested in maths? Look no further. Closing the gap is a great book!

The joys of running a WordPress blog

Earlier today, John Duncan (of moonshine fame) emailed he was unable to post a comment to the previous post:
“I went to post a comment but somehow couldn’t convince the website to cooperate.”

There’s little point in maintaining a self-hosted blog if people cannot comment on it. If you tried, you got this scary message:

Catchable fatal error: Object of class WP_Error could not be converted to string in /wp-includes/formatting.php on line 1031

The days I meddled with wordpress core php-files are long gone, and a quick Google search didn’t come up with anything helpful.

In despair, there’s always the database to consider.

Here’s a screenshot of this blog’s database in phpMyAdmin:

No surprise you cannot comment here, there isn’t even a wp_comments table in the database! (though surprisingly, there’s a table wp_commentmeta…)

Two weeks ago I moved this blog to a new iMac. Perhaps the database got corrupted in the process, or the quick export option of phpMyAdmin doesn’t include comments (unlikely), or whatever.

Here’s what I did to get things working again. It may solve your problem if you don’t have a backup of another wordpress-blog with a functional wp_comments table.

1. Set up a new WordPress blog in the usual way, including a new database, let’s call it ‘newblog’.

2. In phpMyAdmin drop all tables in newblog except for wp_comments.

3. Export your blog’s database, say ‘oldblog’, via the ‘quick export’ option in phpMyAdmin to get a file oldblog.sql.

4. If this file is small you can use phpMyAdmin to import it into newblog. If not you need to do it with this terminal-command

mysql -h localhost -u root – p newblog < oldblog.sql

and have the patience for this to finish.

5. Change in your wp-config file the oldblog database to newblog.

Happy commenting!

Grothendieck’s gallery No. 154

Since mid May the Montpellier part of Grothendieck’s gribouillis are online and for everyone available at the Archives Grothendieck.

The story is well-known.

End of June 1990, Grothendieck phoned Jean Malgoire warning him to come asap if he wanted to safeguard the better part of G’s mathematical archive, for he was making a bonfire…

A second handover apparently took place on July 28th 1995.

Malgoire kept these notes (in huge Pampers boxes!) until 2010 when he got cold feet as a result of Grothendieck’s letter. He then donated the boxes to the University of Montpellier in 2012.

After Grothendieck’s death in 2014, Montpellier started a project to scan each and every page and put them online, with the backing of Grothendieck’s children (and generous financial support from the local authorities).

So here we are now, and… nobody seems to care.

I’m aware only of this post on MathOverflow by someone who wants to LaTex some of the material on motives.

Perhaps this is due to the less than optimal presentation of the material, or more likely, Grothendieck’s terrible handwriting. Perhaps the University of Montpellier should partner up with the (older generation of) French pharmacists.

But then, there’s this artistic gem in the archive: cote 154 systemes the pseudo-droites written in 1983-84.

It is written on ancient matrix-plotter page. Here’s a typical example

Which mathematical department wouldn’t want to acquire a framed version of one of these original pages?

That’s the point I wanted to make early may in this G+-post, hoping to raise money to safeguard the Lasserre part of Grothendieck’s gribouillis.

When in need for a header picture, I’ll use a page of Grothendieck’s gallery No 154 from now on.

Here’s evidence that Grothendieck was working on GUTS! (literally).

Ulysses and LaTeX

If you’re a mathematician chances are that your text-editor of choice will be TeXShop, the perfect environment for writing papers. Even when writing a massive textbook, most of us stick to this or a similar LaTeX-frontend. The order of chapters in such a book is usually self-evident, and it is enough to use one TeX-file per chapter.

If you’re a blogger, chances are you spend a lot of writing time within the WordPress-editor. If you have a math-blog, there’s no longer the issue of including TeX-output images in some laborious way, thanks to MathJax. Even for a longer series of blog-posts there’s no problem staying within the WordPress-environment.

However, if you’re reckless enough to want to write a novel, or a math-book for a larger audience, you may need different equipment.

You will have to be able to follow story-lines, to follow your main characters throughout the plot, get word counts on scenes and chapters, jot down ideas and results from research, but most of all: you will have to be able to remain focussed just on your writing, as far away as possible from all bells and whistles and thrills of internet and preview-on-the-go editors.

In short, you may consider moving all of your writing to Ulysses.

I’ve been an early adopter from the days their iPad-app was called Daedalus, which I found cute, being a pathetic Joyce-fan. However, the app’s iCloud syncing sucked, but it is now replaced by the which works like magic, syncing every keystroke between iPad, iPhone and whatever Mac you use as your workhorse.

But, what if you want to write about math and are unwilling to ban all LaTeX-formulas from your text.

Well, I’ve tried everything, including the approach below (in a faulty way), and figured it was impossible due to the fact that Ulysses is a MarkDown editor in which underscores are entirely different from indices.

Fortunately, yesterday Eline Steffens posted “Writing Mathematical Equations in Ulysses” showing me what I did wrong.

If you want MathJax to parse your text you need to include the standard code in your header. What I missed was that you have to include it as a ‘Raw source block’ (under ‘Markup’ in Ulysses).

Further, I forgot to prepend dollar-signs with a tilde, which works as an escape character in Ulysses so that all underscores are safe within the LaTeX-boundaries.

But now it works like a charm.

Ulysses is able to export your text in a variety of ways. You can preview it as HTML, including all rendered LaTex, and you can export directly either to Medium (on which I should begin to cross-post stuff asap) or your own WordPress-site.

In fact, I wrote this in Ulysses, then clicked the export-icon, choose ‘Publishing’ and NeverEndingBooks, and bingo I was able to post it as a draft. I can even fill in categories and tags, even add the featured image appearing at the top of this post, check everything in WordPress-admin and hit: “Publish”.

I guess I’ll be doing all my non-paper writing from now on entirely in Ulysses.

Grothendieck’s gribouillis

A math-story well worth following in 2015.

What will happen to Grothendieck’s unpublished notes, or as he preferred, his “gribouillis” (scribbles)?

Here’s the little I know about this:

1. The Mormoiron scribbles

During the 80ties Grothendieck lived in ‘Les Aumettes’ in Mormoiron

In 1991, just before he moved to the Pyrenees he burned almost all of his personal notes in the garden. He phoned Jean Malgoire:

“Si tu ne viens pas chercher mon bordel mathématique, il va brûler avec le reste.”

Malgoire sped to Mormoiron and rescued 5 boxes containing about 20.000 pages. The next 20 years he kept them in his office, not exactly knowing what to do with them.

On january 3rd 2010, Grothendieck wrote his (in)famous letter forbidding others to share or publish any of his writings. (Picture via the SecretBloggingSeminar)

Malgoire feared that Grothendieck would soon ask him to destroy the Mormoiron-gribouillis and decided to donate them to the University of Montpellier.

They are kept somewhere in their archives, the exact location known only to Jean Malgoire, Luc Gomel (who is in charge of the patrimonium of the University of Montpellier) and the person who put the boxes away.

After Grothendieck’s death on november 13th, FranceTV3 did broadcast a short news-item.

If Grothendieck’s children agree, the University of Montpellier intends to make an inventory of the 5 boxes and will make them available, at least to researchers.

2. The Lasserre scribbles

The final 23 years of his life, Grothendieck lived in the small village of Lasserre in the French Pyrenees.

Here he could be glimpsed blurrily through the window as he wrote for hours during the night.(Picture via the GrohendieckCircle)

Leila Schneps and her husband Pierre Lochak did visit the house and met with Grothendieck’s family the week after his death.

Before she went, she was optimistic about the outcome as she emailed:

“I have already started modifying the Grothendieck circle website and it will of course eventually return completely. Plus many things will be added, as we will now have access to Grothendieck’s correspondence and many other papers.”

Her latest comment, from december 16th, left on the Grothendieck-circle bulletin board, is more pessimistic:

“Il a ecrit a Lasserre sans cesse pendant plus de 20 ans. Je n’ai pu que jeter un rapide coup d’oeil sur tout ce qu’il a laisse. Il y a de tout: des maths, des reflexions sur lui-meme, et des reflexions sur la nature humaine et sur l’univers. Rien n’est disponible pour le moment. Ces manuscrits finiront dans une bibliotheque et seront peut-etre un jour consultables.”

The good news is that there appears to be some mathematics among the Lassere-gribouillis. The sad news being that none of this is available at the moment, and perhaps never will.

So, what happened? Here’s my best guess:

Grothendieck’s children were pretty upset a private letter from one of them turned up in the French press, a couple of years ago.

Perhaps, they first want to make sure family related material is recovered, before they’ll consider donating the rest (hopefully to the University of Montpellier to be reunited with Grothendieck’s Mormoiron-notes).

This may take some time.

Further reading (in French):

Grothendieck, mon tresor (nationale)

Un génie mystérieux, un secret bien gardé