Mathematica is very large and complex software which covers many many different areas.
I can only comment myself on few areas. In the area of integration, this bar chart shows the progress made. This is for integration test using 14,944 integrals of many types
(Just updated to add 12.1 after it completed building). There are 2 integrals, out of 14,943 that 12.1 did not solve compared to 12.0, this explains why 12.1 got 94.42% and 12.0 got 94.43%. Still, the overall curve is upwards, but may be the curve is flattening now. But 94.4% is good score anyway, these are hard integrals. See these-indefinite-integrals-evaluate-in-12-0-but-not-in-12-1-what-can-be-done if interested to know more.
But the quality of the anti-derivatives has improved. This chart shows the percentage of
A grade of anti-derivatives for same test over the years.
A grade means optimal anti-derivative. (Higher is better)
There are 4 grades for each integral. A,B,C and F. Where
A is best, and
F for not able to integrate it.
The leaf size also improved. Lower leaf size is better. This is the size of the anti-derivative. This chart shows good progress in this area where the average size has decreased. (Lower is better)
So overall, I would say that Integrate has been improving over the years.
DSolve for PDE
DSolve in the area of PDE's, using test suite of about 2,000 PDE's, here is the result
This shows steady and good improvement in this area.
DSolve for ODE
In the area of
DSolve and ODE's, using the famous Kamke's set of ODE's (1,940 diﬀerential equations from Kamke book), this is the result
This also shows steady and good improvement in this area.
Some of the things that WRI needs to improve on is overall quality and performance of the FE and or the kernel, to make things more robust and less prone to hangs, crashes and sudden freezes, specially when using Dynamics.
Oh, and I forgot one thing we all need and been waiting for for many many years: an easy to use debugger !!
Additional related charts on this subject are at
Differential equations, version 12.3 and improving the level of the questions