https://docs.julialang.org/en/latest/stdlib/linalg/
It looks like Julia uses a combination of LAPACK and SuiteSparse. These are good choices, but it's not Julia code and these routines are callable from all sorts of other languages like Python, MATLAB, and Octave. As such, it still appears as though Julia is operating more like a glue language rather than a write all of your numerical libraries in Julia language, which is fine, but I don't feel like that's what it's being sold as.
The benefit comes from user code, which in many dynamic languages is interpreted and is much slower than built-in C libraries. For example, look at the Julia `sum`. It is written in Julia. Or that we are in the process of replacing openlibm (based on freebsd libm) with a pure julia implementation. Or any of the fused array kernels (arithmetic, indexing, etc.). Our entire sparse matrix implementation (except for the solvers) is in pure Julia.
Alright, so I write numerical codes professionally. Though it's not quite fair, I tend to bulk things into glue languages and computation languages. In a glue language, we combine all of our numerical drivers and produce an application. For example, optimization solvers don't really need to be written in a low-level language since their parallelism and computation is primarily governed by the function evaluations, derivatives, and linear system solvers. As long as these are fast, we can use something like like Python to code it and it runs about the same speed, and in parallel, as a C or C++ code. On the other hand, we have the computation languages where we code the low level and parallel routines like linear algebra solvers. Typically, this is done is C/C++/Fortran, but I'm curious to see how Rust can fit in with these language. For me, the primary focus of a computation language is one that it's fast and two that it's really, really easy to hook into glue languages. Since just about every language has a c-api, that's our pathway forward.
Alright, so now we have Julia. Is it a glue language? Is it a computation language? Maybe it's designed to be both. However, at the end of the day, most of the examples I see of Julia on HN are using Julia as a glue language. To me, we have lots of glue languages that already hook into whatever other stuff we care about be it plotting tools or database readers or whatever. If Julia is designed to be a computation language, great. However, that means we should be seeing people writing the next generation of things like parallel factorizations and then hooking them into a more popular glue language like Python or MATLAB or whatever. Maybe these examples exist and I haven't seen them. However, until this is more clear, I personally stay away from Julia and I advise my clients to as well.
And, to be clear, Julia may be wonderfully suited for these things. Mostly, I wanted to express my frustration of what I see as an ambiguity in the marketing.
I haven't been following very closely recently but there has been some active native implementation work such as: https://github.com/JuliaDiffEq/DifferentialEquations.jl