Just one thought : Java was created in order to make applets/apps portable. A java application is therefore supposed to be "independent" from the hardware (beside the fact that the JVM is obviously compiled for a given architecture, but the API remains the same across architectures). You can use/call native code through the JNI interface, but this makes often your app non portable.

Beside this, I agree with Thomas. I personally wrote several traffic assignment algorithms on very large networks using parallel threads in Java. I agree that before 2002/2003 this would not have been possible, but modern JVM/HotSpot has comparable performances to C++.

This being said, did you have a look to Apache Common Math ? http://commons.apache.org/proper/commons-math/

This library is well written and supported...

I know of one JAVA project called JAS (Java Algebra system) useful for symbolic computation. There is also JAMA for doing matrix computations in JAVA and Jampack, look also in Google. For plotting I found jmathplot.

As for my personal experience, speed for scientific computations with JAVA is ok and can compete with any other high-level programming language. Only thing you have to take care is memory requirements as you would have to adjust the heap size of Java virtual machine. Otherwise, there should be same kind of obstacles in scientific computing to Java programs than also to other high-level programming languages.

Just one thought : Java was created in order to make applets/apps portable. A java application is therefore supposed to be "independent" from the hardware (beside the fact that the JVM is obviously compiled for a given architecture, but the API remains the same across architectures). You can use/call native code through the JNI interface, but this makes often your app non portable.

Beside this, I agree with Thomas. I personally wrote several traffic assignment algorithms on very large networks using parallel threads in Java. I agree that before 2002/2003 this would not have been possible, but modern JVM/HotSpot has comparable performances to C++.

This being said, did you have a look to Apache Common Math ? http://commons.apache.org/proper/commons-math/

This library is well written and supported...

1. Fist question no real solution i think

2.Many depends of the type of scientific plotting try ptplot or Jy3d. Both are free. Freechart can be used. if you want only java component you can try nebula (in eclipse). Coomon math and also Numerical recipes in java can be usefull but not on top of the Art.

Apache or google search ....

Apache commons ... I assume you will use double precision. 

depends also to your doamin. ODE? Optimization? Integration.... differents frameworksare availible

First, make sure you know what you want to do. Java was designed to be cross platform. Tying it down to native libraries makes it less portable and requires more work to maintain across multiple platforms.

Second, make sure you do an exhaustive search of what is already available. Java has countless libraries, including JNI/JNA wrapped libraries for fast math operations and working with GPUs (such as JCUDA). There's no point in reinventing the wheel; at the very least you can start with what someone else has done.

Third, never optimize first. You may be obsessed with speed, but your code has to a) actually work and b) actually be useable. As a general rule, 90% of execution time is usually spent in 10% of the code. Get it working, then go back and optimize.

Ont your questions:

1. Yes there are. I've already mention JCUDA for working with GPUs and there are a bunch of others for all sorts of mathematical operations.

2. Yes it does. But fast doesn't mean much without a description of what you're trying to plot. JFreeChart has plenty of features and graph types, but if your planning on doing a scatter plot with a billion points it might not run so fast.

3. Matplotlib.

Given all the work that has been done on python over the years to support scientific programming (scipy/numpy/matplotlib/etc.), is there any particular reason for doing this with Java?

You can find a good collection of Java numeric libraries for scientific computing in the DMelt project (http://jwork.org/dmelt). It has also many Java classes for data visualization in 2D/3D. You can find more information on the DMelt web site, or from the book "Numeric Computation and Statistical Data Analysis on the Java Platform" (http://www.springer.com/us/book/9783319285290)

It would be nice to have a streamlined uniform free computeralgebra system with good concepts an how to represent data types. For example there is maxima or Sage, but they all lack a uniformity of concepts. Especially Sage as open plattform is just a conjunction of different libraries wwhich actually is an unusable patchwork, that does not make it fitting for uniform usage. It would be nice to be able to compute in algebraic fields, rings, modules and to do actual constructions with them according to the concepts of category theory. In a certain sense such things could be considered "algebraic numerics" and involves a lot of beautiful and easy/difficult calculations. I think that there is a wide renage of libraries comprising together the basis for a mathematical computing platform encompassing almost all topics. Sage is trying to agglomerate them into a big system, competitive with Mathematica and Co.. But still i think that even those systems could be extended by considering concstruction as general as provided by category and building on the basic concepts of topology, analysis, algebra, discrete mathematics, logics. Still one uniformity of using such systems needs to be developed in order to make productive use of them ineveryday calculations and descend away from scratch paper completely. In my view a good system will need to redesign all those functions completely with a view on the generality of the overall system. If that is done, maybe it will turn out that all the functionality of different packages can be included easily and fastly by relying on elaborate concepts. For example a mathematical computing platform must also include a universal programming by its own mostly relying on the abstract data types, like finite (fields), terms. For example in such a system numerical computation could be completely defined from scratch by algebraic/categoric construction of the floats, integers, doubles in the system itself and mapping them to the native types of the machines on which they are running in predefined libraries that are encapsulated cleverly into a machine dependent basic library.

There are three problems with doing Maths on the JVM, and with Java syntax.

Firstly, the native code interface is both complicated and slow.

Secondly, if you don't use it, then your performance is decided by the JVM, with its JIT and garbage collection. It can be fast, often as fast as traditional compiled code, but it is not predictable, so optimisation of performance is hard.

Thirdly, Maths in Java is hard to read, because of the lack of operator overloading and Currying. In my opinion this is the biggest problem. Scala has good facilities for making a DSL for whichever mathematical domain you are working on. It compiles to Java bytecode, and you can call Scala classes from Java and vice versa.