Why is fortran used for scientific computing?

I've read that Fortran is still heavily used for scientific computing. For code already heavily invested in Fortran this makes sense to me.

But is there a reason to use Fortran over other modern languages for a new project? Are there language design decisions in Fortran that makes it much more suitable for scientific computing compared to say the more popular languages (C++, Java, Python, Ruby, etc.)? For example, are there specific language features of Fortran that maybe allow numeric optimization in compilers to a much higher degree compared to other languages I mentioned?

Fortran is, for better or worse, the only major language out there specifically designed for scientific numerical computing. It's array handling is nice, with succinct array operations on both whole arrays and on slices, comparable with matlab or numpy but super fast. The language is carefully designed to make it very difficult to accidentally write slow code -- pointers are restricted in such a way that it's immediately obvious if there might be aliasing, as the standard example -- and so the optimizer can go to town on your code. Current incarnations have things like coarray fortran, and do concurrent and forall built into the language, allowing distributed memory and shared memory parallelism, and vectorization.

The downsides of Fortran are mainly the flip side of one of the upsides mentioned; Fortran has a huge long history. Upside: tonnes of great libraries. Downsides: tonnes of historical baggage.

If you have to do a lot of number crunching, Fortran remains one of the top choices, which is why many of the most sophisticated simulation codes run at supercomputing centres around the world are written in it. But of course it would be a terrible, terrible, language to write a web browser in. To each task its tool.

The main reason for me is the nice array notation, and many other design decisions that make writing and debugging scientific code easier. The fact that it is usually the best choice in terms of performance on the relevant tasks (array operations) does not hurt either :)

Honestly, I would not consider most the languages cited as real competitors for Fortran -- Java and Ruby are far, far behind in terms of both convenience and performance, while C++ is much too complex and tricky a language to recommend to anyone whose main job for the last few years has been anything other than daily programming in C++. Python with numpy could be an option though. I am personally not a huge fan of the language, but I know a number of people who use numpy regularly and seem quite happy with it.

Real competition I see is not from these, but from Matlab, R, and similar languages, that offer similar convenience, combined with many standard libraries. Luckily, it is usually possible to start a project in R or Matlab, and write performance-critical parts in Fortran later.

Few projects are completely new projects. I'm not sure it's specific to scientific computing, but at least in this field, you tend to build your applications based on existing (scientific) models, perhaps produced by other groups/people. You will always have to deal with some amount of legacy code, whether you want it or not.

Fortran is what a lot of scientists have been taught with and what a lot of the libraries they need are implemented in. A number of them might not be computer scientists or IT people, more computational scientists. Their primary goal is rarely computing, it's their science first. While a large number of programmers would have a tendency to learn a new programming language or framework whenever they get a chance (including during their spare time), most scientists would use that time exploring new ideas regarding their science.

A domain expert who's trained in Fortran (or any language) and surrounded by people who are in a similar situation will have no incentive to move away from it. It's not just that now other languages can be as good as Fortran in terms of performance, they need to be much better: there needs to be a good reason to move away from what you have and know.

It's also a "vicious" circle to a degree. I've always found comparisons between Java and Fortran a bit difficult, simply because a number of Java scientific applications are not programmed in a Java way. Some of the Java Grande benchmark applications look clearly like Fortran programs turned into C programs, copied/pasted/tweaked into Java programs (in a method, passing the length of the array as an extra parameter next to the array itself gives a clue, if I remember well). Because of this, Java (for example) hasn't got a great reputation in the scientific community, even though its performance is getting better. A consequence of that is that there is little overlap between HPC experts and Java experts, for example. Even from the hardware vendors or libraries implementors, little demand from users leads to little support offered, which in turns deters users who would potentially be interested in moving to other languages.

Note that this doesn't preclude the same (or other) scientists from using other languages for other purposes (e.g. workflow management, data management, quicker modeling with Matlab, Numpy, ...).

As I understand it, there are libraries that are some of the most efficient implementations of their algorithms available, which makes Fortran popular for this kind of work in spite of the language's limitations.

One reason is in how the arrays were constructed. They are column major, unlike most other languages. This provides faster computation for their calculations.