I look upon Mathematics as distinct from "Science", and "Poetry and Mathematics" as a mix that provokes issues distinct from those of the more commonly discussed "Poetry and Science" mix, so it's interesting to see how real poets handle maths. However, as an integration of the 2 disciplines I find poems like Wislawa Szymborska's Pi rather disappointing. It focusses on one feature of pi, namely that its digits go on forever without repeating. But the vast majority of numbers' digits go on forever. The poem's allusions aren't pi-related - e and the golden mean might have been more appropriate choices, or the square root of 2 - though it's not a transcendental number, it's an irrational one. If she'd written a poem called "Hamlet" or "Childbirth" with this amount of empathy with the subject I could imagine readers being unhappy, but poets get an easy ride when they use Mathematics. That said, the outsider's viewpoint is one perspective, and at least this name-dropping ensures that the poetry audience isn't alienated.
A photo of a test-tube isn't a fusion of Art and Science in the way that opera combines Music and Drama. I think many poems about maths are like that photo rather than like opera - if they're good (and they may well be) it's not because of their understanding of the subject matter. However, if I'm accusing Szymborska of being in some sense shallow what do I mean by "deep"? Mathematically important, characteristic, fundamental? Can a mathematician's notion of beauty or depth be tranferred into poetry? The Greeks were allegedly upset when the square root of 2 was shown to be irrational - the proof's short and elegant too. Godel's results shook the foundations of maths. The Continuum Hypothesis underpins many other results. All of these are perhaps worthy topics. For style, perhaps Tractatus or some of Spinosa's texts offer a model. I've seen some contemporary attempts to bring more balance to the poetry/maths mix
Ted Chiang's prize-winning short story Division by Zero is serious about maths too, and Alice's Adventures in Wonderland has many allusions - "Wonderland's madness reflects Carroll's views on the dangers of the new symbolic algebra" (Melanie Bayley in New Scientist, 16 December 2009)
Of course, there's more to mathematics than numbers. Perhaps in these other topics (topology, combinatorics, the Mobius Strip, Godel's theorems, etc) there are more fertile possibilities. Fractals excite some - "Fractals may be the most complex and the most subtle examples of patterns found in both mathematics and poetry ... When poets borrowed ideas from fractal geometry and applied them to the reading and writing of poetry, they made a remarkable intellectual leap" (M. Birken and A.C.Coon, "Discovering Patterns in Mathematics and Poetry", Rodopi, 2008, p.167)
Or perhaps I'm looking too hard for deep similarities. Poetry and maths are activities that humans do, so they're bound to share features just as Cookery and Woodwork do: both require good ingredients, careful preparation, a balance between function and beauty, between the parts and the whole. With Poetry and Maths
In Mathematics influences poetry by JoAnne Growney there's a reasonable list of points of contact
In A Mindful Beauty: What Poetry and Applied Mathematics Have in Common ("The American Scholar", Autumn 2009) Joel E. Cohen writes
I think it's over-ambitious to take matters further than that. All the same, I think mathematical allusions deserve to be followed-up as assiduously as literary ones.
Computing though is a rather different issue. There are many computing languages to choose from, and they needn't be used merely to describe and prove. Some poems (particularly kinetic Concrete poems or those involving procedural poetics) are already programs. In addition
Many online poems exist, written in Flash, etc. I've only recent found The periodic table as assembled by Dr. Zhivago, oculist which a collaboration between a writer and a computer programmer showing how chemistry terms can be translated into literary ones by a computer program.