[tialaramex]

Definitely if your interest is World War II, or the Intelligence process, the human side, any of that - the Bletchley Park exhibits are key and TNMOC is at most a side visit, whereas if your interest is computing, TNMOC is key and there's no reason to do more than pencil in the rest of the Bletchley Park site as a possible extra.

I don't know about Science. There's a lot of math and logic puzzle solving at Bletchley, but the other crash projects of WWII have a lot more science, Los Alamos obviously, translating from "In principle nuclear fission is a more powerful bomb than anything previously made" to an actual weapon you can use to destroy a Japanese city. But also the invention of the Cavity Magnetron - a little box can make enough radio waves to make a radar for your night fighter so you can figure out where the enemy planes are relative to you - or it can use those waves to heat a delicious baked potato in a few minutes...

[currymj]

it does seem like working on the Bombe got Alan Turing really deep into thinking about hardware. he'd previously played around with building some logic circuits but seems like he didn't go deep into it before Bletchley, before that he was mostly a very pure mathematician.

[tialaramex]

Turing was interested in lots of things. As a coincidence one of the small jobs I did many years ago was to develop the Turing Archive's web site, which I'm glad to see has since been substantially renovated: https://turingarchive.kings.cam.ac.uk/ - For that work we had a lot of high resolution images of non-Computing stuff Turing cared about, including Morphogensis (basically, why things are the shapes they are, for example why is a rose petal shaped that way? Why stripes on giraffes but spots on dalmations?).

So mathematics yes, Turing was always interested in that, but always applicability was on Turing's mind. In the early twentieth century Turing's "machine" in a paper he wrote at Princeton (before the war) was just an idea, but er, obviously with the exception of the need for an "infinite" paper tape you can realise Turing's machine, it's a computer, familiar to everybody today.

Even after Bletchley Turing wasn't a Software Engineer. The meta-applicability isn't something which would occur to a mathematician. That took Grace Hopper. Grace understood that the problem her people were tasked with (mechanically convert instructions to the code for the actual machine) is exactly the same sort of task the machine is doing anyway, and she invents the Compiler.

[Yeul]

The code breaking was more important to WW2 than Los Alamos which simply came too late to be of any effect.

The nuclear bomb was more of a backup plan for if the Germans actually managed to defeat Stalin.