This Scientific American article tells the tale of one of the genesis stories of complexity science, this one from 1952, describing what, until relatively recently, was known as the Fermi-Pasta-Ulam (FPU) problem (or 'paradox', though it is not in fact a paradox). It is now more commonly known as the Fermi-Pasta-Ulam-Tsingdou (FPUT) problem, in recognition of the fact that it was only discovered thanks to the extraordinary work of Mary Tsingou, who wrote the programs that revealed what, to Fermi, Pasta, and Ulam, was a very unexpected result. 

The team was attempting to simulate what happens to energy as it moves around atoms connected by chemical bonds. This is a classic non-linear problem that cannot be observed directly, and that cannot be solved by conventional reductive means (notwithstanding recent work that reveals statistical patterns in complex systems like urban travel patterns). It has to be implemented as a simulation in order to see what happens. Fermi, Pasta, and Ulam thought that, with enough iterations, it would reveal itself to be ergodic: that, given long enough, every state of a given energy of the system would be visited an equal number of times. Instead, thanks to Mary Tsingou's work, they found that it was non-ergodic. Weird stuff happened, that could not be predicted. It was chaotic.

The discovery was, in fact, accidental. Initial results had shown the expected regularities then, one day, they left the program running for longer than usual and, instead of the recurring periodic patterns seen initially, it suddenly went haywire. It wasn't a bug in the code. It was a phase transition, perhaps the first unequivocal demonstration of deterministic chaos. Though Fermi died and the paper was not actually published until nearly a decade later, it is hard to understate the importance of this 'accidental' discovery that deterministic systems are not necessarily ergodic. As Stuart Kauffman puts it, 'non-ergodicity gives us history'. Weather is non-ergodic. Evolution is non-ergodic. Learning is non-ergodic. We are non-ergodic. The universe is non-ergodic. Though there are other strands to the story that predate this work, more than anything else this marks the birth of a whole new kind of science - the science of complexity - that seeks to deal with the 90% or more of phenomena that matter to us, and that reductive science cannot begin to handle. 

Here's a bit of Tsingou's work on the program, written for the MANIAC computer:

It was not until 2008 that Tsingou's contribution was fully recognized. In the original paper she was thanked in a footnote but not acknowledged as a co-author. It is possible that, had it been published right away she might have received proper credit. However, it is at least as possible that she might not. The reasons for this are a mix of endemic sexism, and (relatedly) the low esteem accorded to computation at the time.

The relationship between these two factors runs deep.  Historically, the word 'computer' originally referred to a job title.  As scientists in the 19th Century amassed vast amounts of data that needed processing, there was far too much for an individual to handle. They figured out that tasks could be broken up into smaller pieces and farmed out in parallel to humans who could do the necessary rote arithmetic.  Because women were much cheaper to hire, and computing was seen as a relatively unskilled (albeit very gruelling and cognitively demanding) role, computing therefore became a predominantly female occupation. From the 19th Century onwards into the mid 20th Century, all-women teams worked on astronomical data, artillery trajectories, and similar tasks, often performing extremely complex mathematical calculations requiring great precision and endurance, always for far less pay than they deserved or that a man would receive. Computers were victims of systematic gender discrimination from the very beginning. 

The FPUT problem, however, is one that doesn't lend itself to chunking and parallel computation: the output of one iteration of the computation is needed before you can calculate the next. Farming it out to human computers simply wouldn't work. For work of this kind, you have to have a machine or it would take decades to come up with a solution.

In the first decade or so after digital computers were invented significant mathematical skill was needed to operate them. Because of their existing exploitation as human computers, there was, luckily enough, a large workforce of women with advanced math skills whose manual work was being obsoleted at the same time, so women played a significant role in the dawn of the industry. Mary Tsingou was not alone in making great contributions to the field.

By the 1970s that had changed a lot, not in a good way, but numbers slowly grew again until around the mid-1980s (a terrible decade in so many ways) when things abruptly changed for the worse.

Whether this was due to armies of parents buying PCs for their (male) children thanks to aggressive marketing to that sector, or highly selective media coverage, or the increasing recognition of the value of computing skills in the job market reinforcing traditional gender disparities, or something else entirely (it is in fact complex, with vast self-reinforcing feedback loops all the way down the line), the end result was a massive fall in women in the field. Today, less than 17% of students of computer science are women, while the representation of women in most other scientific and technical fields has grown considerably.

There's a weirder problem at work here, though, because (roughly - this is an educated guess) less than 1% of computer science graduates ever wind up doing any computer science, unless they choose a career in academia (in which case the figure rises to very low single figures), and very few of them ever do more mathematics than an average greengrocer. What we teach in universities has wildly diverged from the skills that are actually needed in most computing occupations at an even sharper rate than the decline of women in the trade. We continue to teach it in ways that would have made sense in the 1950s, when it could not be done without a deep understanding of mathematics and the science behind digital computation, even though neither of these skills has much if any use at all for more than a minute fraction of our students when they get out into the real world. Sure, we have broadened our curriculum to include many other aspects of the field, but we don't let students study them unless they also learn the (largely unnecessary in most occupations) science and math (a subject that suffers even lower rates of non-male participation than computing). Thinking of modern computing as a branch of mathematics is a bit like treating poetry as a branch of linguistics or grammar, and thinking of modern computing as a science is a bit like treating painting as a branch of chemistry. It's not so much that women have left computing but that computing - as a taught subject - has left women. 

Computing professionals are creative problem solvers, designers, architects, managers, musicians, writers, networkers, business people, artists, social organizers, builders, makers, teachers, or dreamers. The main thing that they share in common is that they work with computers. Some of them are programmers. A few (mostly those involved in designing machines and compilers) do real computer science. A few more do math, though rarely at more than middle school level, unless they are working on the cutting edge of a few areas like graphics, AI, or data science (in which case the libraries etc that would render it unnecessary have not yet been invented).  The vast majority of computing professionals are using the outputs of this small elite's work, not reinventing it. It it not surprising that there is enormous diversity in the field of computing because computers are universal machines, universal media, and universal environments, so they encompass the bulk of human endeavour. That's what makes them so much fun. If you are a computing professional you can work with anyone, and you can get involved in anything that involves computers, which is to say almost everything. And they are quite interesting in and of themselves, partly because they straddle so many boundaries, and ideas and tools from one area can spark ideas and spawn tools in another.

If you consider the uses of computer applications in many fields, from architecture or design to medicine or media to art or music, there is a far more equal gender distribution. Computing is embedded almost everywhere, and it mostly demands very different skills in each of its uses. There are some consistent gaps that computing students could fill or, better, that computing profs could teach in the context they are used. Better use could be made of computers across the board with just a little programming or other technical skills. Unfortunately, those who create, maintain, and manage computers and their applications tend to mainly come out of computer science programs (at least in North America and some other parts of the world) so many are ill prepared for participating in all that richness, and computing profs tend to stick with teaching in computer science programs so the rest of the world has to figure out things they could help with for themselves.

I think it is about time that we relegated computer science to a minor (not unimportant) stream and got back into the real world - the one with women in it. There's still a pressing need to bring more women into that minor stream: we need inspirations like Mary Tsingou, we could do worse than preferentially hiring more non-male professors, and we desperately need to shift the discriminatory culture surrounding (especially) mathematics but, if we can at least teach in a way that better represents the richness and diversity of the computing profession itself, it would be a good start.