My favorite $2,500 application that I don’t own, Mathematica, has just been bumped to version 7. New in this version is integrated Geodesy & GIS functions, brought to you with Wolfram Research’s usual obsessive attention to detail. I mean, look at this:
“Exaggerated differences between common reference ellipsoids and WGS84.”
As with every self-respecting application these days, Mathematica now also comes with geolocation-finding tools! And, yes, current & historical weather data for 17,000 weather stations worldwide, all ready for integrating into whatever mathematical analysis you have waiting for it. Country data (including a wealth of health, transportation and economic statistics) and city data is also included (since version 6), letting you easily find solutions to fun stuff like the Traveling Salesman Problem:
You can also load your own data for analysis, as Mathematica 7 supports a wide variety of geospatial file formats, including GeoTIFFs, ESRI Shape files and DEM files.
Mathematica also makes it easy for others to explore your work interactively, using the free downloadable Mathematica Player. Here are some sample country data analysis demonstrations for downloading, and here are some city analysis demonstrations. (Some more free geography demos for good measure, including the Traveling Salesman Problem as a game.)
If you have Mathematica running on a server, you can create a web interface for your users with WebMathematica, letting you create Java applets that allow interaction right from the web page. The documentation doesn’t say, however, if this Mathematica 7 is compatible with WebMathematica, so it’s not clear if you’d be able to integrate these newest GIS functions into your web apps yet. [Update: The answer is yes, as per the comment below.]
If you’ve been waiting for the right tools to build a competitor to ESRI ArcGIS from scratch, here’s your chance:-) More seriously, well-funded programmatically inclined educators should take a look at what Mathematica can offer, as should GIS professionals looking to bring the full force of mathematical analysis to their dataset, beyond what desktop GIS tools can offer.