[ChrisRackauckas]

The iterative linear solvers from IterativeSolvers.jl along with the preconditioner ecosystem is more expansive and uses genericness to have a lot more functionality (it's all able to be used with matrix-free operators, GPUs and Xeon Phis, arbitrary precision number choices along with complex, quaternions, etc.). The differential equations solvers from DifferentialEquations.jl covers a lot more domains than the stuff you'll find in SciPy+PyDSTool (SDEs, DAEs, DAEs, semi-linear ODEs via exponential integrators, IMEX, etc.). The dynamical systems library DynamicalSystems.jl is one of a kind. QuantumOptics.jl is not only faster than QuTIP but it also covers more areas like stochastic Schrodinger. And JuMP for mathematical programming (optimization) is also very good in comparison to Pyomo. Scientific computing's core is linear algebra, optimization, and diffeqs and right there you have the basics plus some widespread applications.

I agree that Python has a library advantage in data science + ML. R has a library advantage in the area of statistics. But Julia has quite a few advantages in the core math areas of scientific computing and algorithm development. There is headway being made into DS+ML as well. Julia's pandas/dataframe equivalent is JuliaDB which adds out-of-core and online stats functionality, so it's more at the level of pandas+dask. Flux.jl is still in its early stages but it's quite a unique ML framework which can directly incorporate any Julia function at any level, and then has some working experiments with compiling to things like JS and XLA.

But in the broad view of things, every language has SciPy+NumPy pretty satisfactory (ex: Julia's Base library has most of it, the top 20 packages cover the rest), but from there all have tradeoffs in what areas the community is specializing in.

[joshuamorton]

Cool! To be clear, I realize that could have come across as an accusatory "prove it!", it wasn't meant that way. I've just never really needed anything not available in the scipy ecosystem, except for some obscure statistical methods (or not that obscure, but with a non-terrible api) that I don't think are available in julia either.

[ChrisRackauckas]

You'd have to go to R for those esoteric stats packages :). Yeah, I think that what's available in each of the languages is kind of unknown until people need it. It would be hard to catalog it all too in a way that's both accessible and comprehensive.