The best new feature in v10 is multiple-undo for the front end (kernel undo is still not available).
- Multiple Undo
- Improvements to Evaluation Abortion
- Associations & Dataset
- Computational Geometry
- Basic Machine Learning
- Unit Testing
Mathematica 10 brings a new powerful data type to the language, Associations. These are analogous to dictionaries in Python or Julia since they consist of key-value pairs but more robust, allowing for valuable MapReduce patterns. Dataset will be very useful once it can handle importing database tables with foreign keys, until then, not so much.
Version 10 also adds broad support for geometric computation, with the key element being that of geometric regions. Geometric regions can be created by using special regions such as circles, using formulas, using meshes containing collections of simple regions, or combining other regions through Boolean combinations and transformations. Several standard properties can be directly computed for every region, such as membership tests, measure (e.g. length, area, volume), centroid, nearest points, etc. Regions can also be used as specifications for many high-level solvers, including optimization, algebraic equation solving, integration, and partial differential equation solving.
- No support for some key modern OSX features (ehem, scrollbars?)
- Remaining lack of stability in the Frond End
- Cloud Deploy API Functions are weak, restrictive, and brittle
- Still no full implementation Risch Integration
- Classifier and Predictor functions not exportable
- No updates to RLink
- No updates to parallel programming or CUDA/OpenCL functions
- No updates to Compile or C code generation
- Social Networking Data and FinancialData are both broken
- "Mathematica > Wolfram Language" rebranding (a global search & replace)
One of Mathematica’s competitors, Maple, had a new release recently which saw the inclusion of a set of fractal exploration functions. Version 10 parrots this, but functions that plot standard fractals are not high on anyone's feature request list.
My concerns center around the data and Stephen Wolfram’s comment ‘basic versions of Mathematica 10 are just set up for small-scale data access.’ What does this mean? What are the limitations and will this lead to serious users having to purchase add-ons that would effectively be data-toolboxes, and what exactly is the Data Science Platform and how much will it cost?
Background - For four years I worked with Stephen Wolfram, the youngest Ph.D. that Caltech ever produced, building a Computable Knowledge Engine (the first of its kind) at the Harvard-based Special Projects group of Wolfram Research. If you are interested in Wolfram, I suggest you check out the Wolfram Science Summer School and the Mathematica Summer Camps. I was an instructor at both in past years and I highly recommend them for students of all fields.