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What benefits are there to employing agile software development methodologies for quants?
While I agree that research oriented development can make it difficult to define the long term goal, I disagree that an agile-like process is impossible. Part of the benefit of the methodology is to be able to get a well defined (well defined but small) set of tasks in place before you start. Re-evaluating them afresh at the next iteration allows you to steer your development by taking into consideration what you've learned in the last iteration. The key is to make that cycle short. Regardless of the approach taken, the comments about source control are critical.
Why is C++ still a very popular language in quantitative finance?
Garbage collection is indeed a huge concern but keep in mind that you always have control over when garbage collection will happen. It's a balance between suffering from memory leaks and having to have a system that may need to be tuned.