These web pages are a new version and re-write of pages I wrote around 2006-7. In 2007 these pages looked rather good, but web standards and web software has changed since then and the old pages stopped working due to changes in software issued by the big "players" - mainly Google and Microsoft. The amount of effort getting the pages to work in an adequate way with on the current browsers was substantial. (Admittedly I didn't do most of the work - it wasn't until MathJax became available in a reasonably mature state that this became possible at all.) Thus it was that the pages lay unchanged for a number of years.

Like the previous version of these pages, the new pages are written using a combination of HTML and MathML. (More specifically, presentation MathML is used here exclusively.) Unlike the old set of pages I have used HTML5 throughout rather than XHTML. Provided your web browser is reasonably modern and set up in the usualy way you should not have to do anything at all to be able to view these pages properly as intended.

The HTML and MathML in these pages are authored using my own text based authoring program, Gloss, which has been completely re-writtten recently - these pages are testbeds for the new version which has not yet gone "public". The actual source code for the web pages has not been modified so much from its original form of 2006-7, though Gloss itself has. I have noted that it is not always perfect MathML (in particular more mrow elements are required throughout) and will try to address that matter, but my time is limited. If you use a non-visual browser your browser may not work so well on these pages, sorry.

Instead of rendering MathML directly, the MathML in these pages is now rendered by MathJax in its MathML mode. MathJax is a suite of javascript programs that converts MathML to something that is viewable when the page you want to look at is loaded. It seems to work well within a number of limitations which are all due to the nature of current browsers and how JavaScript works in them, and not to do with MathJax itself. MathJax can be heartily recommended. The main disadvantage of MathJax is that it is slow: it takes an extra second or two to render each page on my computers. I have noticed a small number of issues to do with MathJax and the way CSS dictates a web page should be viewed. Necessarily, it seems, MathJax does not fully comply with the CSS stylesheet on a page, nor do I see how it could be expected to.

Ideally, it would be better to view MathML using a web browser that understands MathML natively. In 2007 there was real hope that soon all browsers would be able to do this, Firefox and Mozilla based bowsers could, there was experimental support for Safari which in principle could be applied to Google Chrome (though the Google people didn't use it) and there was an excellent plug-in available for Internet Explorer. Currently (as of 2015) Firefox and other Mozilla browsers are still able to render MathML natively but Safari, Google Chrome and others have publicly announced that they have no plans to support Mathmematics and the current version of Internet Explorer is now designed in such a way that a MathML plug-in is impossile. So, for simplicity, I have not produced files that view in Firefox only, however. I understand that MathJax works with the Firefox browser if it finds it to make the rendering faster or better. (I am not sure of the details.) Therefore I suspect these pages will look better with Firefox and I would recommend that you at least try these pages using that browser. In any case, if like me, you think mathematics is important you should be supporting Mozilla and not one of the companies that reject the importantce of Mathematics.

Currently, the two biggest players in the browser market, Microsoft and Google, have both publicly announced that they will not support MathML in their web browsers. In my opinion this is nothing short of scandalous, not least because both pushed hard for MathML in a new version of HTML (HTML5) rather than the superior XHTHML platform that was preferred by the main web standards. My guess concerning this is that neither party were prepared to modify their existing code to support XHTML. Tht Microsoft's Intenet Explorer did not and still cannot properly display XHTML is common knowledge. Less well-known is how poor Google's search engine supported it. Lack of correct indexing by Google for XHTML pages was the main headache behind the previous version of these pages, and this was a much more severe problem than providing support for Intenet Explorer. Opera does not have MathML support either, but CSS/javascript implementations such as MathJax should work in Opera too.

Unfortunately, mathematicians themselves are not completely without blame. They are used to Knuth's TeX and Lamport's LaTeX, and while these can produced excellent quality printed output they are not ideal for the web. In particular the fonts used are not compatible with unicode standards (copy and paste rarely works between TeX and non-TeX programs, let alone searching) and almost always, PDF, is required to render the output on-screen. Less obviously, TeX was designed for low power computers of the 1970s and 1980s, and there should be and are much better options now.

So, the world-wide situation seems to be that the only people who will continue to work for mathematics in web browsers are a small number of unpaid enthusiasts, and Microsoft and Google both say that the whole of mathematics is too small and unimportant to consider any effect needed. That is what I think is scandalous. It is not helped by the vast majority of mathemematicians (who are not IT professionals and do not in general really understand these matters) who, if pressed, think TeX is "good enough".