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There are a variety of TiddlyWiki descendants that are good for online storage of notes while still allowing some of the TiddlyWiki goodness (disclaimer: some of these were written, at least in part, by me): TiddlyWeb, TiddlySpace, Tank and TiddlySpot.

Tank is the newest one, but probably least featureful. It distinguishes itself from the others by preferring Markdown over TiddlyWiki text.

What's left that doesn't run in a browser?

• music player? With the HTML5 audio tag, ogg playback plus MP3 in Chrome, it's doable
• editor? Bespin, Firefox extensions for simple text editing, FCKedit for local WYSIWYG are good enough
• todo list? TiddlyWiki is a complete editable wiki that runs from a single HTML file (impressive!); I use the mGSD version with action items and projects

I've run Linux for years and besides vim and zsh, the only native app that has impressed me as much as the best browser-based apps is Inkscape.

I'd love to run even more stuff in the browser. I hate that I access most resources through bookmarks and the browser's smart location field, but other resources I have to go through the GUI toolkit's file "browser", and then launch external apps that usually lack all the browser's niceties (View Source, Ctrl-+ to zoom, bookmarks/back/forward/history, tabs, etc.). Browser-based doesn't mean using the cloud for all my files; browsers don't care if they load resources from http or file:/// URLs. ChromeOS has a Content View to show you local files, supposedly integrated with the Open/Save dialog; I wish Firefox Places had a directory view along with its bookmarks and history view. I don't want Firefox to integrate with my Linux desktop toolkit's crappy file handling and half-hearted semantic efforts, I want Firefox to subsume them.

Tiddlywiki is quietly mind-blowing. An entire wiki that lives in a web page that's just a single HTML file (which you can archive or commit in git or whatever). That makes it a great note-taker that runs in your browser, that hyperlinks to itself and the rest of the web, but it's a local "app" that doesn't require a connection.

Even better for some, mGSD "is a Getting Things Done® system powered by TiddlyWiki and [some add-ons]" It's also just an HTML file. I know nothing about GTD, but I keep my To Do items in various areas it and with a double-click I'm editing their notes as wiki text.

Load either in a tab, use Firefox 4's "Pin as App Tab", and smile.

I'd still like something that unobtrusively makes sense of what I've done for when it's important. My computer's got my e-mails and browsing history, it should magically hand me what's relevant. How do I rate the book I ordered from Amazon? Which is the best picture of my friend out of my e-mails? Give me the e-mail confirmations and web pages related to an upcoming trip. I can use tagging in e-mail and the browser's bookmarking, but that's helping me do the work instead of doing the work for me.

I use mGSD (formerly known as MonkeyGTD) for my to-do lists. It lets me keep track of tasks and organize them by projects and by action. It even has some support for dependencies. I can keep it on USB and it's portable between systems. It does take just a bit of effort to understand how to get into it, but once you do, it's pretty intuitive.

For organizing notes, I use Tiddlywiki, the platform on which mGSD is built on.

For keeping track of web sites, I mostly rely on Google Reader.

And for the stuff that I want to remember, I blog. Yeah, I know, blogging, especially the personal kind, doesn't get a whole lot of respect anymore, but I've been able to look back into entries five years ago and say, "Whoa, I did that."

I'm still looking for a good solution for keeping track of files and documents.

If you're going to use GTD to manage your commitments (which I am a big fan of), there are a number of free tools you can use do the GTD methodology. Some of the tools I looked at are:

• ThinkingRock (http://www.trgtd.com.au/)
• MoneyGTD(http://monkeygtd.tiddlyspot.com/#MonkeyGTD)
• GTD Free (http://gtd-free.sourceforge.net/)

Plus there is the ever present use of hosted online solutions, such as:

• Remember The Milk (http://www.rememberthemilk.com)
• Toodledo (http://www.toodledo.com)

And the ever popular pen and paper method

In order for this claim to be true (...) one would at a minimum need to be able to efficiently write existing proofs in the formal language

I don't quite follow your reasoning. In order to convince you that some proof languages are readable I would need to be able to write formal proofs efficiently? Ease of writing formal proofs is not much related to readability. As I mentioned, languages that are designed to make writing the proofs easier tend to be less readable. For some examples of machine verified proofs that I consider readable you can look at the Tiddly Formal Math site (disclaimer: I am the author of that site). As for what will be formalized in someone's lifetime it's a moving target. People used to say that the prime number theorem will not be formalized in their lifetimes and many were wrong. I am happy that the proofs being mentioned in this type of argument now are much more recent. I think formalizing large areas of mathematics will advance the development of new mathematics in about the same extent as development of modern foundations of mathematics at the end of XIX century. It was not obvious to see at that time as well why there was even a need, and how it would help.

Actually I know of or have been involved in developing some off-line web apps as some experimental programming projects. Tiddlywiki is a good example of off-line capable web applications, and there are many other based on this sort of technology. I recommend you have a look at http://tiddlyspot.com or http://www.yourformbuilder.com or http://yourtimesheets.com/ if you are looking for some examples that are out there already.

Have you taken a look at TiddlyWiki? I cannot tell a lie: Somebody posted abut it here on Slashdot, and I've become a confirmed convert. By means of TiddlySpot if you are so inclined, you can open-source whatever aspects of yourself you'd like people to know about, while keeping the rest of it (like your naked pictures) under wraps. There are also numerous php implementations that allow you to upload your TiddlyWiki to your own server. TiddlyWiki ranks right up there with sliced bread, in my opinion.