Vorgetragen habe ich mit Folien (am Beamer), es dauerte etwa 90 Minuten und ging am Ende ein bisschen zu schnell. Ich habe auch noch ca. 90 Backup-Folien mit deutlich mehr Informationen vorbereitet, bevor ich den konkreten Vortrag daraus destilliert habe. Die Folien sind mit der Latex-Beamer-class erstellt.

Die Folien zum Vortrag (ca. 35, zum Vortragen optimiert) gibt es hier, und
die deutlich umfangreichere Version (ca. 90, mit Text vollgestopft) gibt es hier.

Beides gibt es natürlich ohne Gewähr, allerdings habe ich (meines Wissens nach) alle (2) Fehler korrigiert, die das Publikum gefunden hat.

Quellen waren die Paper von Shannon und Weaver, das Buch von Brillouin (Science and Information Theory) und meine alten Notizen zur Stochastik aus dem Vordiplom (zusammen mit dem einführenden Buch von Hans-Otto Georgii, das ich immer noch gern zum Nachschlagen verwende). Einzelne Grafiken stammen von Wikipedia, andere habe ich gezeichnet (und auch als public domain in Wikipedia eingebracht). Meine Zeichnungen habe ich mit Inkscape erstellt.

Viel Spaß damit!

The ICTP

• The concept of the ICTP, founded 1964 by Nobel laureate Abdus Salam, seems to be, very broadly said, to give researchers in physics and mathematics from third-world-countries opportunities (including money) for research and learning with scientists from developed countries. To accomplish this goal, they have short-time visiting scientists (for about 6 months) and host a lot of summer schools, conferences and workshops in many different areas. Participants from not-that-much-developed countries get funding for housing and food, in the ICTP Guest Houses and restaurants. In my opinion, this works well, since I met several mathematicians from developing countries (like India or the USA ).
• The buildings I’ve heard of are: Leonardo Da Vinci Building, Enrico Fermi Building, Adriatico Guest House, Galileo Galilei Guest House. Just some small hints for anyone who intends to go to the ICTP:
  • In the Leonardo Building main lecture hall, there is only one point in the whole room where you can find outlets. So, if you intend to use a laptop the whole day, find this spot (above, in the centre) and stick to it
  • The coffee machine in the Leonardo Building (near the toilets, ground floor) isn’t that bad, if you choose the sugar level to be less than the default value of 6/8 points (more than 1/8 is already too sweet for me, and I like sweet coffee).
  • The library in the Leonardo Building is a very nice place to hang out and wander off.
  • In the Adriatico Guest House, there is a vending machine for beer. It costs only 60 cent and isn’t that bad. The problem is: if you come late, it’s empty.
• The food in the Leonardo restaurant at the ICTP was not as good as you might expect from Italy. Especially in the evening, you get exactly the same as for lunch – but now it’s probably cold and you have less choice. Therefore, a lot of people went to the next city to have dinner (which is, of course, more expensive).

Sightseeing around Miramare, Trieste and Venice

• Miramare: there is the famous Miramare castle, surrounded by an artificial (yet beautiful) park, which is a must-see (i.e. exotic birds, fishes, turtles, palm trees, small pathways etc.).
• Trieste: I have no idea what I saw, I just walked across the city randomly. It is a nice, small city with a lot of restaurants. The sea side is not that beautiful but the buildings often look like imported from Vienna. I totally recommend eating ice cream all the time.
• Walking from Miramare to Trieste: Probably a bad idea. I did it three times, but I have to admit that the last third of the way, which is about 30 minutes long, is not beautiful at all. If you don’t know where to go, you’ll end up walking down a big street with high walls to the left and the right side for the whole 30 minutes. It is impossible to walk this last part along the sea. The first part, speaking of the hour it takes to walk from Miramare to Barcola, is nice, although the way along the sea is also the way along a big street. Anyway, there is a bus.
• Grotta Gigante, a huge cave, probably (at least officially) the largest cave that you can visit as ordinary tourist, in the world. And it is really gigantic! I’ve never been to any cave before and it was impressive.
• Venezia – only 2 hours and 10 EUR away, very nice (I guess there is no need to say more).

Miramare park main gate, near the ICTP

View Larger Map

Summer School

The summer school took two and a half week, where the first week was devoted to (recall?) very basic material: the first lectures defined manifolds and varieties and rushed over to de Rham cohomology, Kähler forms, sheaves, schemes and by the end of the first week the lectures about variations of Hodge structures and mixed Hodge structures reached the limit of what I knew already before (since I used my train ride to skim through Voisin’s book).
Now seems to be a good time to thank Andreas Höring for having teached classical geometry of Kähler manifolds in Paris so well.
Since the lectures of Migliorini and de Cataldo on the Hodge theory of maps assumed knowledge of Abelian categories and spectral sequences, I still don’t understand why the summer school started with these basic courses. I can not imagine that anyone who understood any of the lectures in the second week, could have possibly needed to learn what a manifold or a variety is. Maybe there are some hidden motives behind this, I haven’t asked the organisers.
The organisation was very good, all course material was printed out in sufficient quantity, the lectures didn’t take more time than expected, there was coffee & cookies in sufficient quantity twice a day and the overall working and learning atmosphere was fine. I missed problem sessions a little bit, but the intended problem sessions might have just turned out to be example sessions instead because of people requesting this. I was impressed that the organisers found a quick replacement for Claire Voisin, who couldn’t come to Trieste. The replacement talks given by C. Schnell, F. Charles and M. Kerr were very good and understandable.
For the participants I recommend having a look at Charles Siegel’s blog and website for lecture notes he has taken.

(photo licensed from Mike Scoltock under a Creative Commons Attribution-NonCommercial 2.0 Generic License)

Conference

• D. Arapura: Beilinson-Hodge cycles on semiabelian varieties; his joint paper with Kumar on the Beilinson-Hodge-Conjecture is related. This was my favourite talk! (By the way, see also his (unrelated) exposition of D-Modules and related Hodge Theory which I didn’t know about before (thanks to Charles Siegel for pointing me to it)).
• L. Illusie: Semistable reduction and vanishing theorems, after Lan and Suh.
• P. Griffiths: Hodge domains and automorphic cohomology; there are some talk notes available. For the necessary background on Mumford-Tate groups, see Griffiths’ lecture notes from the summer school.
• M. Green: Vanishing of Chern Polynomials for Hodge Domains. He introduced his talk with a joke along the lines of “It’s my seventh talk since I came to the ICTP, and in many cultures, the number seven is special. After six days you should rest”. The talk was about his SIGMA joint paper with Carlson and Griffiths.
• C. Schnell: Néron models and Poincaré bundles. It wasn’t so much about Poincaré bundles than about mixed Hodge modules, Néron models and admissible normal functions.
• G. Pearlstein: The locus of the Hodge classes in admissible variations of mixed Hodge structure (joint work with Brosnan and Schnell).
• H. Movasati: Automorphic functions for moduli of polarized Hodge structures. He gave some intuition on modular forms as generating functions, then looked at the Hodge theory of elliptic curves, explained the notion of quasi/differential modular forms (the terminology seems to be unstable) and discussed some examples from physics.

• Doran: Normal forms for lattice polarized K3 surfaces and Siegel modular forms (I had to skip this talk in favour of sleep – but I was told that it was good).
• S. Usui: Neron Models in log mixed Hodge theory by weak fans; slightly related preprint.
• J. Carlson: Further speculation and progress on Hodge theory for cubic surfaces (joint work with D. Toledo); related preprints. He introduced the talk with a story which concluded by “if you’re confused, just keep going”.
• F. Charles: Remarks on the Lefschetz standard conjecture and hyperkähler varieties, see his preprint on the topic.
• L. Maxim: Characteristic classes of complex hypersurfaces, see related paper. He introduced the virtual tangent bundle of a (possibly singular) hypersurface in a smooth manifold (the difference between tangent and normal bundle in K-Theory) and functorial homology characteristic classes (like Todd, L, Chern, but on homology); the general case are Hirzebruch-type invariants. He proceeded to express the (complicated) Brasselet-Schürmann-Yokura “Milnor-Hirzebruch”-classes in terms of virtual Milnor-Hirzebruch classes and invariants of the singularities.
• M. Kerr: Mumford-Tate groups and the classification of Hodge structures (more accurately, classification of Mumford-Tate subdomains, joint work with Griffiths and Green).
• C. Siegel: The Schottky Problem. He explained the well-known genus 3 and 4 cases and his approach to genus 5.
• P. Dalakov: Deformations of the Hitchin section and DGLA’s.

• sadly, I missed the conference talks of E. Cattani, S. Cautis and L. Migliorini because I travelled back to Germany on Friday morning.

Again, Charles Siegel took notes for some of the conference talks, see here and here.

Conclusion

I would be happy to go to the ICTP again in this life. Also, Hodge theory seems to be nice (at least parts of it).

small remark: I heard some rumour about a conference last year where they decided about the pronounciation of “Hartshorne”. Clearly, the person is called Harts-horne, as several Australian mathematicians told me, but now the books name was decided to be Hart-shorne. Hilarious!

I wrote a JabRef export filter that takes a BibTex file with file links (so, BibTex fields of the form file={somefile.pdf}) and writes a linux shell script to rename the files systematically according to the scheme [bibtexkey] – [authors] – [title].[extension]. Then JabRef can find the file again via its automatic file association mechanism. I use lower-case bibtexkeys but the export filter is easily adaptable, read about it on the JabRef custom export filter documentation page.

Just create (or download) a file named “renamer.layout” and fill in this line:
\begin{file}mv "\format[FileLink]{\file}" "\format[ToLowerCase,FormatChars]{\bibtexkey} - \format[AuthorNatBib,ToLowerCase,FormatChars,RemoveBrackets]{\author} - \format[FormatChars,RemoveBrackets,ToLowerCase]{\title}.\format[Replace(.*:,),ToLowerCase]{\file}"\end{file}
then open JabRef and go to the menu entry Options->Manage custom exports->Add new where you enter (for example) “renamer” as Export name, the full path to your renamer.layout file in the Main layout file field and “sh” as File extension.

Then open your BibTex file (.bib) with JabRef and then select the menu entry File->Export and select in the drop-down-menu Files of Type your newly created export filter renamer (*.sh). This gives you a shell script which, if executed, renames all files linked from the BibTex document into a standardised format (and moves all into the directory from where you execute the script).

This is only useful if you have files linked from your BibTex file, so you might need to do this first. If you already have filenames that contain some metadata, like author names or document titles, you might be very happy with JabRef’s RegEx-capable automatic file finder, which can be configured in the menu entry Options->Preferences->External Programs->External file links.

Even if you don’t use JabRef, you can use this process as described by exploiting the export-as-BibTex-capabilities of your favourite reference management system.

You might ask “why”, and I respond: my files are all organised in a way from which I can easily extract metadata using only the tools some operating system provides, so in case I don’t have access to my BibTex file, I can still find the desired files using the GNU/Linux command locate. Of course, I also have included the BibTex information in XMP into the PDF files (which is another feature of JabRef that I like a lot), so nothing is lost if I ever switch the reference management system.

Another lesson learned from this blogpost: writing specific JabRef export filters is very easy. Another one I wrote is able to download automagically entries from the arXiv when the URL is supplied in the url BibTex field. I won’t post it here because you need to disguise wget as “Mozilla 5.0″, otherwise the arXiv won’t let you download stuff (robot protection). I hope those who are able to figure out the details are also responsible enough to not download huge amounts of papers from the arXiv.

Putting it together, this provided a convenient approach to get arXiv papers with full metadata included in filename, PDF and BibTex on my computer. The still-not-perfect part is the first, getting the metadata from arXiv in BibTex format – I use CiteULike as proxy (and would be happy to hear about better solutions with JabRef).

You might also ask why I keep copies of my references on my computer (or why they have to be linked from my reference management system). I just find it very convenient to use my laptop as eReader, even when no internet is available, and given that I have 100+ references in the system, it is good to have metadata such as keywords, abstract, reviews, annotations and so on.

I learned about JabRef export filters somehow by accident because of another project related to reference management, which you might hear about soon (not yet).

The first posts (from Feb 2010 to June 2010):

• Grand opening
• Schreier theory
• Jordan type of a modular representation
• Bundles for adults
• Primes and probability
• On an isomorphism from G_T to G_1
• Adversarial Statistics
• Devinatz-Hopkins-Smith, I, II, III
• Complex orientations and the Steenrod algebra
• Eilenberg-Mac Lane spaces in the chromatic picture

Enjoy reading!

By the way: the ICTP Summer School on Hodge Theory is still teaching the basics needed to start doing Hodge theory – I’m looking forward to see Migliorini’s lecture on the Hodge theory of maps this afternoon! See also the short lecture notes from Charles Siegel at Rigorous Trivialities (and the notes from day 2 here), he will post something every day.

Bayes (English mathematician, 1702-1761) proved a theorem about conditional probabilities, nowadays called “Bayes’ theorem“. Suppose there are two statements A and B, which might overlap (e.g. A=”it’s raining today” and B=”it’s raining the whole week”¹, where the truth of B implies the truth of A). Now imagine these statements are more or less likely, so you attach some probability to these statements, p(A) and p(B), with values in 0-100% (or, for the mathematically oriented readers: let p be a probability measure on some discrete -algebra containing A and B). It’s not only the probability of A and B we might be interested in, but also the conditional probability “How likely is A when B is true?”, which we write p(A|B). Bayes’ theorem now reads:
, and this means in words, that the probability of A under the condition that B is true, multiplied by the probability of B, is the same as the probability of B under the condition that A is true, multiplied by the probability of A.

Let me put this in context. Let A be the statement “There will be a big volcano eruption in 2010″ and let B be the statement “Someone predicted that there will be a big volcano eruption in 2010″. Then we can talk about the probabilities of A and B (although we don’t know them exactly) and about the conditional probabilities, how likely the volcano eruption is, under the condition that someone predicted it, and the conditional probability how likely it it that someone predicted it, under the condition that it happens. If we believe that predicting volcano eruptions is possible, then we think that the conditional probability that it happens if someone predicted it, is higher than the probability that it happens with or without someone predicting it. Looking at Bayes’ formula, we see
, which tells us in words, that the probability of a volcano eruption under the condition that someone predicted it, is proportional to the probability of a volcano eruption and anti-proportional to the probability of someone predicting it. We see also, that the probability of a volcano eruption under the condition that someone predicted it is greater than the probability of a volcano eruption only if , that means, only if the probability of someone predicting the eruption is strictly smaller than the probability of someone predicting it under the condition that it happens.

Now you might know that there are some ways to predict volcano eruptions (I’m no expert). So the probability that someone predicts it under the condition that it happens is relatively high, but since there is someone claiming to forecast volcano eruptions every year (whether it happens or not), the absolute probability of someone predicting a volcano eruption for this year is 100%. So we can’t infer that volcano eruptions are likely just because someone predicted volcano eruptions.

Substitute volcano eruptions with your favourite Doomsday scenario and choose some arbitrary probability for this. The probability of someone predicting this scenario is close to 100% and therefore you can’t infer that it’s likely to happen just because someone told you so.

Substitute volcano eruptions with a war in Middle East and someone predicting it with an oil company doing business there after the war. If we realise that oil companies are pretty likely to do business in oil-rich countries, even more likely if there is no war going on, then we see (via Bayes’ theorem), that it’s not likely that the war was started just because of the oil business.

I don’t want to say that conspiracies don’t exist or that there are no wars about resources (like oil). I just want to point out that in each case, one has to find more evidence and stronger arguments than just coincidence of events. Test your argument against Bayes’ theorem!
If someone tells you his latest conspiracy theory, you might have been thinking “it might be true or false but I can’t prove him wrong and the probability that he’s right is not zero”. This is not a good response. Instead, you should always ask: “and why don’t you think it’s all just coincidence and happened by chance?”². This hypothesis will save you from the Bayesian fallacy.

You can use Bayes’ theorem to strengthen your arguments: If for two events A and B the conditional probability P(B|A) is really greater than the absolute probability P(B), then the probability P(A|B) is strictly greater than the probability P(A), which means that from measuring B you can infer that A is much more likely now. This is called “Bayesian inference” and it’s really important, for example, to find out which medicinal treatments cause more good than harm.

If you want to know more about argumentational fallacies of a similar kind, take a look at this paper (Khalil 2008) I found googling for “Bayesian fallacy”, although the author uses these words (completely) differently.

¹ – by the way, it has been raining the whole week here in Freiburg…

² – If people don’t like the thought that something happens “by chance”, they might not understand how order arises from chaos. This is another problem (which causes a lot of confusion), which I want to discuss separately (later).

1. Easy video recording – let the user take videos with every webcam within seconds, then upload to YouTube or similar. A similar proposal (a simple video editor) is on the lifehacker.com five feature request list.
2. Stream capturing – saving streamed video data doesn’t work so easily with all those different streaming formats. For some, you need a RTSP stream catcher, then maybe a RTMP stream catcher and for some you seem to be able to use just mplayer. And then there are many cases where all fails. Technically, what can be played can also be saved. But then there is the big Flash Player obstacle – some Flash videos are well-protected. Gnash may help there.
3. PDF reader&editor – one tool that allows for reading PDFs, annotating them, publishing&sharing the comments, manipulating the PDF itself, adding additional layers, manipulating PDF metadata, etc. Just like the Adobe Acrobat Reader in its more expensive variant – but as open source tool with the ability to write plug-ins and integration into Gnome or KDE (or any) desktop. Okular is already on the right track! See also my article about editing PDF metadata.
4. Centralised instant messenger and (video)telephony – unite Pidgin, Skype and other Videochat and IM apps in one UI. Maybe put this together with microblogging tools, since people use their IM status messages like microblogging anyway. Skype has announced to open-source parts of their Linux client, so this is not totally out of reach. Open source alternatives to TweetDeck are also there, for example Gwibber. See also my article on microblogging and news.
5. Metadata in file browser – make the file explorer a metadata editor, paving the road for a semantic desktop. Even the Windows Explorer can do better than Nautilus for now! But then I haven’t tried KDE’s Dolphin for a while and this might be the right thing to do… See also my article on music metadata as well as my article on photo metadata.
6. Asset manager – even one step further, make the file browser a pluggable asset manager, that can take the shape of a photo collection manager, a scientific paper organiser or a website bookmark manager. So far I know only of commercial asset managers and haven’t yet investigated which one runs on Linux and might be useful for me. Do you have any recommendations?
7. Annotation everywhere – a note-taking application that can annotate every single file or item on the desktop. This way you can relate a specific email to a task, to a note, to a website, to an application and a specific file – thus documenting entire work-flow states for later continuation. Well, there is Tomboy for now. See also my article on note-taking.
8. Private browsing – create for Firefox or any other browser a CSS/Javascript security model that avoids CSS privacy hacks by not letting any information about how the HTML rendered leak into the Web. That would include creating an open source Flash plug-in that doesn’t publish all Font and SuperCookie information. See EFF’s PanoptiClick for more information about this. The SuperCookie issues can be softened with the BetterPrivacy Add-On for Firefox.
9. Easy emulation – integrate a Dalvik VM naturally into the desktop, so that it’s very easy to install&run Android apps from the applications menu. Maybe the project to implement a Dalvik VM in Java is the right way to do this. Of course, the same would be nice for Wine but I don’t consider this an option because Dalvik is open and Windows isn’t.
10. Synchronise data with external sources – I want to backup all configuration and some data files with a variety of places: external hard-disks and remote storage services in the Web (encryption is necessary here). Ubuntu One is already a big step forward but I really want to backup all configuration so I could crash my computer, buy a new one, hit the “reinstall the software that was there before” button and then everything is back to normal. This is (almost) technically possible. Another road is, that I want to backup the data stored elsewhere (Delicious bookmarks, Google Reader Shared news, Facebook comments, etc.) to my home computer so I’m not stuck with one provider forever (so I can quit Facebook some day). This seems to be impossible for now, but the problem lies in coding “adapters” that take data from one service and move it to the other one.

Am I the only one who wants these features? Are they that hard to implement? (Yes) Hey, for most of these features, I would pay some money (depending on how well it’s implemented). Oh well, and I admit that these features are not really Linux-related. It’s just that I use Ubuntu and would want to have solutions available on open platforms. I guess web-apps and Java- or .NET-based apps would be OK for me, too – but then look again at the wish-list and you’ll see that most features require desktop applications.

If you have suggestions for applications that solve one of those problems at least somehow a little bit, please leave a comment.

What is your favourite not-yet-there Desktop/Ubuntu/GNU/Linux feature?

The penguin image (Tux) is licensed from linux.org under a CC-BY-SA license

Searching for a mysterious “asdf jkl” bug is really difficult. I found about 3 different laptop keyboard problems similar to this one, although they always had problems with the “Enter” key, too. My “Enter” key worked fine. Even if those problems would have been more similar to mine, it wouldn’t have helped. Nobody who has had those strange keyboard issues has found a solution so far. First I looked for Ubuntu/Linux related problems, and looked through various log files, then I found out the keys didn’t work even on the BIOS level. Oh, it was horrible.

Then I found a solution.

The keys were dirty. Not like the yellow patina that you can see on old keyboards – I clean my keyboard regularly, so this doesn’t happen. Dust stuck deep inside, almost invisible. If it would be visible, I wouldn’t have looked for a software problem for an hour… I suppose the dust got wet from humidity in the air (sometimes I use my laptop in the kitchen).

How to repair a Lenovo Thinkpad T60 laptop keyboard that has some kind of strange some-keys-no-longer-working issue:

Turn off the computer and remove one key with your bare hands (gently). It’s most easy to begin with “g”, “h” or “b” because you can pull off the TrackPoint (the red mouse thing) first. Then you can remove all letters (or even more, at least remove the letters that don’t work).

Don’t forget your keyboard layout. It won’t be so easy to google the correct layout if you can’t type!

This is the place where you can find hidden dust. Removing this dust was crucial to get the keys working again (for me).

I wrote this, so that other Laptop users with the same problems can find the solution in google and don’t have to spend an hour of their life searching for non-existent bugs, like I did.

The words “cheese” and “wrap” are translated…

Let’s have a look at some of the best Web 1.0 math websites:

• The On-Line Encyclopedia of Integer Sequences – look up some short sequence of numbers to see in which patterns they fit.
• John Baez: This Week’s Finds in Mathematical Physics – John Baez has been writing his wonderful thoughts about mathematics, physics and the in-between for more years than I know what mathematics is. You can learn a lot from these notes. He has been posting it in sci.physics.research, sci.math.research, sci.physics and sci.math but now he also has an RSS feed, of course.
• The Mathematical Atlas – a hand-crafted tour through the various regions of mathematics, clustered along the AMS classification, spiced with many useful links. (I hope this will be relaunched as a community-based website one day. It deserves to survive).
• The Mathematics Genealogy Project – find out how half of all professors are descendants of Mersenne: 139335 mathematicians in the database, 61089 descendants of Mersenne. They have nice posters, too.

And now, before I sketch my vision of Math 2.0, for some of the best Web 2.0 math projects:

• The n-category café – a group blog about higher algebraic structures (especially n-categories) and physics. There are almost always interesting discussions going on.
• The Catsters – two mathematicians explain category theory (thus the name Catsters) in short, understandable snippets made exclusively for YouTube. Have you ever felt the need to learn what Monads are? String diagrams? Maybe you would be happy if someone would explain you limits and colimits. The Catsters do it, and they do it for free.
• The Open Problem Garden – a collectively maintained list of open problems in mathematics, ranked in difficulty. It’s still in an early phase of it’s life-time and somehow concentrated on problems with a combinatorial flavour, especially graph theory. Maybe you could enter your favourite open problem there?
• Wolfram Alpha – a mathematical data search and browse engine. You can look up statistics, perform comparisons and calculations and visualise this data. Very nice!
• Complexity Zoo – a website that collects computational complexity classes, with lots of helpful explanations and fact around them. At the moment of writing, they count over 480 complexity classes!
• Rigorous Trivialities – a group blog about algebraic geometry, with a huge series about “Algebraic Geometry from the Beginning” – which I recommend for it’s little intuitive text-snippets, where you can pick just what you need.
• The Secret Blogging Seminar – a group blog about algebraic geometry.
• The Unapologetic Mathematician – John Armstrong’s high-level educational math blog. You can pick some topic you want to learn and track back the links to the point where you’re on safe ground. This way, learning is much more efficient than using a linear book. Covers, for example, some category theory.
• What’s new – Terence Tao’s blog. He describes it with the words “Updates on my research and expository papers, discussion of open problems, and other maths-related topics”. Well said, worth a look!
• Timothy Gowers’s blog – currently obsessed with the PolyMath project (see below).

UPDATE: For a list less biased by my personal interests, see the thread “most helpful math resources on the web” on MathOverflow

Okay, now what is Math 2.0?

Math 2.0 is mathematics done collaboratively in genuine new ways over the internet.

This means, a website qualifies as Math 2.0 if it changed the way mathematicians collaborated.

However, it seems like the school education community, more focused on children, uses the term Math 2.0 as a buzzword for “learning math over the internet”.
From the Delicious tag Math2.0 you can see that the term is also used for math blogging.

Keep in mind that all this 1.0, 2.0 buzzword terminology is just tagging some websites. It’s not important, and as Tim Berners-Lee says, the web was always about communication from person to person, it’s nothing new.

My favourite Math 2.0 projects:

• The nLab – the wiki associated to the n-category café, an attempt to structure the discussions and facilitate re-use. This way, the nLab users build an expert encyclopaedia about their subject. Since it’s a subject with intense research going on, it’s more like their secret lab book than like the consensus-based Wikipedia. The rather inclusive viewpoint instead of the encyclopaedic exclusive viewpoint of Wikipedia has already created a very helpful collection of references. The nLab personal lab wikis have already shaped how people do their mathematical research, thus it truly qualifies for Math 2.0.
• MathOverflow – the mathematical question&answer web site, intended to be used by mathematicians (so, no homework questions on this site). Without MathOverflow you would have to know the right people. With MathOverflow you can just ask them.
• PolyMath – the first massively collaborative mathematics problem solving project. It was successful, so they’ve just recently started the next PolyMath project. Gowers and Nielsen have an article in Nature about PolyMath.
• The Tricki – a wiki of problem solving tricks. It’s somehow in the spirit of Polya’s book about mathematical problem solving, but much more practical, solution-centered in concrete situations. It’s something you couldn’t get with a book and it’s perpendicular to classical literature.

Usage of the terms “Web 2.0 math” and “Math 2.0″:

I have some ideas in my mind for a future Math 2.0 project, involving creative use of LaTeX, wikis and collaborative/social websites… but it will take another few months until the idea is ready to go public, and I still need to convince some collaborators to help me with the workload.

Where they talk about Web 1.0 and Web 2.0, the Web 3.0 is not far. Clearly, somebody must fill the buzzword Math 3.0 with some nonsense! Since this post is already long enough, I will speak about the semantic web, Web 3.0 and the great potential for mathematicians another time.

(And I’m really sorry that I didn’t list all good math blogs or other math projects, not even all my favourite ones, like this wonderful blog about motivic stuff. However, if I missed a popular one, I would be happy to hear about it in the comments.)

How to manage news?

It is vital to get at least some news. You need to know about political developments, to be informed when it’s time to cast your vote (or, if you’re not living in a democracy, when it’s time to protest). You need to know about developments in your work, so you can adapt and don’t risk losing your job because you’re too old-fashioned. You need to know about economy if you’re investing money. You need to stay informed about every project you want to participate in. Maybe you even need to know what pop-stars do, because if not, you have nothing to talk about with your friends.
How to cope with this information overload?

Disclaimer: if you’re using a feed reader/aggregator and/or know about Google Reader, scroll to the bottom of this post. There’s not much new for you in here.

Why information overload?
Imagine you were living in the newspaper times, without television, without internet. Then, you could read (parts of) the local newspaper every morning and that was it. No problem yet. Of course, it would have taken much longer than today, to transmit the latest information about some projects, developments in society, and so on. Since everyone has had the same conditions, it wasn’t a problem to be that uninformed.
Now imagine you were living in the television times, without internet. Then you could always get the latest “breaking news” and stock market information, and it was vital to have this information because everybody had access to this information, so you would risk a disadvantage when being uninformed. It was easy to select the information you needed, because you could just find out which channels are sending the information you want and then stick to these channels.
(Sorry for skipping the “radio” times.. here almost the same applies as for television).
What’s different with the internet? You’re no longer restricted to 100 channels sending information in a linear fashion. It’s a completely uncontrollable mess, just way to much to consume, even if you would try to do nothing else. Today, it’s not only vital to get information, it’s also absolutely unavoidable to select important information – for everyone.

Another problem that’s creeping in since the invention of radio and television is the restricted attention span: human brains are not capable of doing several things at the same time – it just looks like that because we’re able to switch very fast from one task to another. Switching tasks is a problem, sometimes. When you’re concentrating on something cognitively challenging, you will need about 5 minutes to get back to your level of concentration if you were interrupted. Another problem is, that our brain is relatively good at doing very different things in short alteration (like playing piano and drinking water and thinking about stock markets), but it’s not that good at doing very similar things in short alteration (like speaking one foreign language and then another). That means, watching TV while working does not really work for jobs that involve information processing (at least, you won’t be as good as you could).
The internet is even worse: many people have e-mail notifications, mobile phone ring tones, twitter notifications, etc., so they’re interrupted in their work very often. Since many jobs today involve information processing and getting the latest news is information processing, our brain has severe problems in doing this in short alteration.
An interesting text about the question how the internet changes the way we think can be found on the BackReaction blog.

Software can be used to control the news flood, if you use it wisely. For example, you can use an instant messenger like ICQ or Skype to let people contact you, but without an audible notification. Then you’ll only read their messages when you’re not in a state of concentration. The same applies to (mobile) phones: you should mute them for some time each day. A phone call would interrupt you immediately, while a short message is controllable by you – it’s you who decides when to digest the information.
Ask yourself: do you really need the latest latest news? Most likely it suffices to get the news some hours later, too. Instead of watching TV and hoping for not missing the breaking news, you can use feeds in the internet, so you get news immediately but are able to consume later. Feeds offer another problem solution: You don’t have to navigate to 50+ websites to know what’s going on about your favourite projects, to get your favourite opinions about politics, etc.. You just subscribe to the feed of each website and a software manages the information flow for you.

Wikipedia has a nice explanation what a web feed is. You can learn about feed aggregators/readers there, too. I’m using the Google Reader, which is a web-application, so you can use it from everywhere on any computer that has internet access. It offers collaborative features: you can select information entries to “like” them or to “share” them, if you want even with a personal comment. The software then displays on top of every entry how many people “liked” this entry, so you can use this as a guideline in the selection of important information. To “share” a news item means it’s added to a special feed, the shared items feed, which your friends or co-workers can subscribe to. This way, an organisation can effectively process the information that’s important for them and then distribute it to all members. Most aggregators offer ways to sort the various news items, so you could select some to read them later and delete some items unread.

(comic licensed from Oliver Widder under a Creative Commons Attribution-NoDerivs 2.0 License)

Feeds offer interesting ways to organise various kinds of information. If you’re a Wikipedia author, you can use feeds to watch thew pages you’ve written. If you’re using MathOverflow, you can use feeds to get the latest questions about your favourite mathematical topic (same applies to StackOverflow). Every blog in the internet has a news feed. You can avoid twitter, because each twitter account has an associated feed. Podcasts are nothing than feeds with sound- or videofiles in it.

Another software recommendation besides Google Reader is the Android software NewsRob (which works only on Android smartphones). NewsRob synchronises with your Google Reader account and is able to save the feed items (and even the websites that are behind the feed items) for later use. This is really helpful if you don’t have an internet-everywhere contract with your mobile phone provider and still want to read the news somewhere where you don’t get internet access (in a train, for example).

UPDATE: At the time I’m writing this, Google presents a new feature: Subscribe to websites that don’t even have feeds. This way you can monitor changes on any site that’s important to watch. Google creates a feed with the URL http://www.google.com/notificationservice/webchanges/webfeeds/12345.... so you can even share the feed. For those who don’t like being watched, you can exclude your site from the feature by standard methods.