Does anyone have any links to studies that show how noise affects the productivity of programmers? Specifically I would like to see how/if productivity rises when noise levels decrease.

As pointed in comments, the nature of the programming workflow is such that you go in and out of focus all the time -- so it's likely to be affected by noise differently than other lines of work.

The reason I think that this is programmer specific is that I am also interested in mathematics. In a noisy place, if I start thinking about maths, the noise goes away and I find myself lost in a world of pictures. In fact my favourite place to do maths was always The Copper Kettle cafe, a busy tourist place.

For programming it's completely different. While programming I'm usually thinking verbally, and any talking whatsoever destroys my train of thought. I'm literally incapable of programming anywhere where there is audible conversation.

I've talked to other programmers who don't even notice noise that disables me, and they say that they think mainly in pictures. Which is why I'm wondering whether there are any actual academic studies into whether programming is particularly noise-affected compared to say maths or lawyering.

The book Peopleware has several chapters that cover the subject. You can read a decent summary here.

Studies led by Tom DeMarco & Timothy Lister showed statistically significant results about the correlation between noise and defects.

Here is an interesting part of the summary:


  Workplace Quality and Product Quality - Companies that provide small and noisy workplaces explain away complaints as workers campaigning for the added status of bigger, more private space. To determine whether noise level had any correlation to work, we divided our sample into those who found the workplace acceptably quiet and those who didn't. Then, looking at workers within each group who completed the entire exercise without a single defect:


> Workers who reported that their workplace was acceptably quiet before
the exercise were 1/3 more likely to deliver zero-defect work.



  As the noise level gets worse, this trend gets stronger:
  
  
  Zero-defect workers:    => 66% reported noise level OK
  1-or-more-defect workers: => 8% reported noise level OK
  
  
  A Discovery of Nobel Prize Significance - On February 3, 1984, in a study of 32,346 companies worldwide, the authors confirmed a virtually perfect inverse relationship between people density and dedicated floor space per person. If you're having trouble seeing why this matters, you're not thinking about noise. Noise is directly proportional to density, so halving the allotment of space per person can be expected to double the noise. Even if you managed to prove conclusively that a programmer could work in 30 sq. ft. without being hopelessly space-bound, you still wouldn't be able to conclude that 30 sq. ft. is adequate space. The noise in a 30 sq. ft matrix is more than triple the noise in a 100 sq. ft. matrix, which could make the difference between a plague of product defects and none at all.


Check the summary, really, noise is one of the recurring subject in Peopleware.
