Starting to Demo the Wolfram Language [video]

Ego Force One has taken off again :(

It would be slightly easier than coding Mathematica from scratch (you have better computers and an example to follow) but much harder to fund, since you would be re-treading old ground and wouldn't be able to competitive for a long time. The types of problems simplified by Mathematica don't include coding Mathematica. To be sure, it pioneered a few nifty techniques that you would want to take advantage of, especially regarding symbolic manipulation, but you wouldn't be able to implement them faster if you used Mathematica (vs just drawing inspiration from it).

Mathematica's huge selling points (to me) are that it's a fantastic CAS and it shatters the barriers between analytic and numeric tools. Many engineering and statistical codes involve 2/3 math and 1/3 computer science (or the other way around). Mathematica is in a completely different league for those problems because it handles the 2/3 about 50x better than your typical programming language and it handles the interface between the 2/3 and the 1/3 about 100x better than your typical programming language.

Mathematicians, engineers, and scientists regularly use a number of abstractions that your typical programmer doesn't care about: integration, differential equations, linear algebra (including infinite-dimensional and tensors), coordinate systems, statistical distributions, etc, etc. These abstractions are almost never considered during language design so you spend hours writing glue code to achieve the simplest of tasks. Unless you have a Mathematica license.

Example: you're writing a finite element code. The "meat and potatoes" of the problem involve putting a differential equation into weak form and evaluating a bunch of integrals to compute matrix elements. Mathematica can represent and display those elements using proper mathematical notation, it can find analytic AND numeric solutions, it can hold off on substituting variables until the last second (or elegantly substitute different sets of values for different problems), it can visualize all of this in a dozen different ways without worrying about indices and sampling rates, and it can generate code if you're feeling trusting that day. Now you want to evaluate convergence for a bunch of different meshing strategies. Not a problem: Mathematica can interpolate your meshed solutions to whatever order you want in whatever dimension using a single command and it can take differences between those interpolations and integrate with another. You never have to notice that the mesh points don't line up. You never have to spend a second thinking about multi-dimensional quadrature on tetrahedral meshes. Now you want to compare statistics about the mesh graph to an analytic model you found using Bayes Theorem in 3D parameter space and solve for the maximum likelihood values? Again, you don't have to worry about meshing or gradient descent or how to put least squares into matrix form. Just write the high-level math and let Mathematica worry about the rest. Now you want to use a simplified PDE model with an analytic solution and compare that to the numerical solutions? Mathematica can solve the PDE and take care of all the interpolation and quadrature needed to integrate the square difference with the numerical solutions. Then it can plot all these errors and update the plot automatically as you go back and change things. The value-addition vs a general purpose language is off the charts.

None of that translates to the process of writing another Mathematica, since the algorithms Mathematica lets you abstract away are precisely the things you would need to worry about to implement another Mathematica.

Mathematica = A + B = (1000s of algorithms that mathematicians, scientists, and engineers care about, all coded with a common interface) + (syntax that elegantly glues them together)

B is comparatively easy and interesting if you like languages -- Mathematica's language is LISP on steroids. A is the schlep, and it's a doozy.

Wolfram started a startup and put his name on the door and it has been incredibly successful. No story about Wolfram appears on HN without someone complaining about his ego. Perhaps he is the Mohammed Ali of programming.

Mathematica for handling data aggregation, recursive descent parsing, and tasks well suited for it, while the rest is an enormous codebase of compiled and JVM languages stitched together with Mathematica. Such projects are referred to as the "mud bowl", where when something breaks you just have to throw more mud at it.

So while I can't see myself using this to write applications I can certainly see it replacing / augmenting my current iPython notebooks. I can do a lot with pandas and plotly for data exploration and visualization, but I can't do many of the things he demo'ed nearly as easily.