Ever since the days of Charles Babbage, who conceived of a giant mechanical calculator called the Analytical Engine in the 1830s, the engineering of computer hardware has been dominated by men. The pioneers of software, however, were often women, beginning with Babbage’s friend and muse Ada, Countess of Lovelace. Daughter of the Romantic poet Lord Byron and a mother who loved math, Ada combined both fields into what she called “poetical science.” When she saw some mechanical looms that used punched cards to direct the weaving of beautiful patterns, it reminded her of how Babbage’s engine used punched cards to make calculations, and she developed the historic insight that a calculator could be instructed to handle not just numbers but anything that could be notated in logical symbols, such as music or words or graphics or textile patterns. In other words, she envisioned the modern computer. She also drew up a step-by-step sequence of operations for programming Babbage’s engine to generate a complex series known as Bernoulli numbers. It included subroutines, recursive loops, and a table showing how it would feed into the computer, all of which would be familiar to any C++ coder today. It became the first published software program, earning Ada the title of “the world’s first computer programmer.”

A century later, when the first electronic computers were being invented, the men were still focusing on the hardware, and many women followed in Ada’s footsteps. One was Lt. Grace Hopper, who helped program the Harvard Mark I computer in the early 1940s. Less heralded by history was a group of six women who worked in wartime secrecy at the University of Pennsylvania, where John Mauchly and Presper Eckert led a team that was building ENIAC, the world’s first programmable, all-electronic, general-purpose computer. Here is an except from Walter Isaacson’s The Innovators telling their story:

To listen to this excerpt as an audio book, press the “play” button below:

Walter Isaacson's "The Innovators"

As ENIAC was being constructed at Penn in 1945, it was thought that it would perform a specific set of calculations over and over, such as determining a missile’s trajectory using different variables. But the end of the war meant that the machine was needed for many other types of calculations—sonic waves, weather patterns, and the explosive power of atom bombs—that would require it to be reprogrammed often.

This entailed switching around by hand ENIAC’s rat’s nest of cables and resetting its switches. At first the programming seemed to be a routine, perhaps even menial task, which may have been why it was relegated to women, who back then were not encouraged to become engineers. But what the women of ENIAC soon showed, and the men later came to understand, was that the programming of a computer could be just as significant as the design of its hardware.

ENIACOne of the control boards used to program ENIAC.Photo: Bettmann/Corbis

The tale of Jean Jennings is illustrative of the early women computer programmers. She was born on a farm on the outskirts of Alanthus Grove, Mo. (pop. 104), into a family that had almost no money and deeply valued education. Her father taught in a one-room schoolhouse, where Jean became the star pitcher and lone girl on the softball team. Her mother, though she had dropped out of school in eighth grade, helped tutor algebra and geometry. Jean was the sixth of seven children, all of whom went to college. She attended Northwest Missouri State Teachers College in Maryville, where the tuition was $76 per year. She started out majoring in journalism, but she hated her adviser so switched to math, which she loved.

When she finished in January 1945, her calculus teacher showed her a flier soliciting women mathematicians to work at the University of Pennsylvania, where women were working as “computers”—humans who performed routinized math tasks—mainly calculating artillery trajectory tables for the Army. As one of the ads put it:

Wanted: Women With Degrees in Mathematics…Women are being offered scientific and engineering jobs where formerly men were preferred. Now is the time to consider your job in science and engineering…You will find that the slogan there as elsewhere is WOMEN WANTED!

Jennings, who had never been out of Missouri, applied. When she received a telegram of acceptance, she boarded the midnight Wabash train heading east and arrived at Penn 40 hours later. “Needless to say, they were shocked that I had gotten there so quickly,” she recalled.

ENIACJennings, left, Wescoff, center and Lichterman, work on portable function tables programming trigonometric functions into the room size computer.Photo: Corbis

When Jennings showed up in March 1945, at age 20, there were approximately 70 women at Penn working on desktop adding machines and scribbling numbers on huge sheets of paper. Adele Goldstine, a mathematician who was married to the Army’s liaison with the ENIAC team, was in charge of recruiting and training. “I’ll never forget the first time I saw Adele,” Jennings said. “She ambled into class with a cigarette dangling from the corner of her mouth, walked over to a table, threw one leg over its corner, and began to lecture in her slightly cleaned up Brooklyn accent.” For Jennings, who had grown up as a spirited tomboy bristling at the countless instances of sexism she faced, it was a transforming experience. “I knew I was a long way from Maryville, where women had to sneak down to the greenhouse to grab a smoke.”

A few months after she arrived, a memo was circulated among the women about six job openings to work on the mysterious machine that was behind locked doors on the first floor of Penn’s Moore School of Engineering. “I had no idea what the job was or what the ENIAC was,” Jennings recalled. “All I knew was that I might be getting in on the ground floor of something new, and I believed I could learn and do anything as well as anyone else.” She also was looking to do something more exciting than calculating trajectories.

When she got to the meeting, Herman Goldstine, Adele’s husband, asked her what she knew about electricity. “I said that I had had a course in physics and knew that E equaled IR,” she recalled, referring to Ohm’s law. “No, no,” Goldstine replied, “I don’t care about that, but are you afraid of it?” The job involved plugging in wires and throwing a lot of switches, he explained. She said that she wasn’t afraid. While she was being interviewed, Adele Goldstine came in, looked at her, and nodded. Jennings was selected.

ENIACJean Jennings, left, and Frances Bilas operate the main control pane of the ENIAC at Moore School of Electrical Engineering in 1946Photo: US Army

In addition to Jean Jennings (later Bartik), the others were Marlyn Wescoff (later Meltzer), Ruth Lichterman (later Teitelbaum), Betty Snyder (later Holberton), Frances Bilas (later Spence), and Kay McNulty (who later married John Mauchly). They were a typical squad thrown together by the war: Wescoff and Lichterman were Jewish, Snyder a Quaker, McNulty an Irish-born Catholic, and Jennings a lapsed Church of Christ Protestant. “We had a wonderful time with each other, mainly because none of us had ever been in close contact with anyone from one of the others’ religions,” according to Jennings. “We had some great arguments about religious truths and beliefs. Despite our differences, or perhaps because of them, we really liked one another.”

In the summer of 1945, the six women were sent to Aberdeen Proving Ground to learn how to use IBM punch cards and wire up plug boards. Jennings became a ringleader: “We worked together, lived together, ate together, and sat up until all hours discussing everything.” Since they were all single and surrounded by a lot of single soldiers, there were multiple memorable romances and affairs nurtured over Tom Collins cocktails in the booths of the officers’ club. Wescoff found a Marine who was “tall and quite handsome.” Jennings paired up with an Army sergeant named Pete, who was “attractive but not really handsome.” He was from Mississippi, and Jennings was outspoken in her opposition to racial segregation: “Pete told me once that he would never take me to Biloxi because I was so outspoken in my views on discrimination that I’d be killed.”

ENIACA close up view of the components on the ENIAC at the Army’s Aberdeen proving grounds in 1947.Photo: Jerry Cooke—Corbis

After six weeks of training, the women consigned their boyfriends to memory archives and returned to Penn, where they were given poster-size diagrams and charts describing ENIAC. “Somebody gave us a whole stack of blueprints, and these were the wiring diagrams for all the panels, and they said, ‘Here, figure out how the machine works and then figure out how to program it,’” explained McNulty. That required analyzing the differential equations and then determining how to patch the cables to connect to the correct electronic circuits. “The biggest advantage of learning the ENIAC from the diagrams was that we began to understand what it could and could not do,” said Jennings. “As a result we could diagnose troubles almost down to the individual vacuum tube.” She and Snyder devised a system to figure out which of the 18,000 vacuum tubes had burned out. “Since we knew both the application and the machine, we learned to diagnose troubles as well as, if not better than, the engineers. I tell you, those engineers loved it. They could leave the debugging to us.”

Snyder described making careful diagrams and charts for each new configuration of cables and switches. “What we were doing then was the beginning of a program,” she said, though they did not yet have that word for it. They wrote out each new sequence on paper to protect themselves. “We all felt that we’d be scalped if we ruined the board,” said Jennings.

One day Jennings and Snyder were sitting in the second-floor classroom they had commandeered, staring at rolled-out sheets containing the diagrams of ENIAC’s many units, when a man came in to inspect some construction. “Hi, my name is John Mauchly,” he said. “I was just checking to see if the ceiling’s falling in.” Neither woman had met the ENIAC visionary before, but they were not the least bit shy or intimidated. “Boy, are we glad to see you,” Jennings declared. “Tell us how this blasted accumulator works.” Mauchly carefully answered the question and then others. When they finished, he told them, “Well, my office is next door. So anytime I’m in my office, you can come in and ask me questions.”

Almost every afternoon, they did. “He was a marvelous teacher,” according to Jennings. He pushed the women to envision the many things ENIAC might someday do, in addition to calculating artillery trajectories. He knew that in order to make it a true general-purpose computer, it would need to inspire programmers who could coax various tasks out of the hardware. “He used to always try to get us to think of other problems,” said Jennings. “He would always want us to invert a matrix or something like that.”

“The biggest advantage of learning the ENIAC from the diagrams was that we began to understand what it could and could not do. As a result we could diagnose troubles almost down to the individual vacuum tube.”

Around the same time that Grace Hopper was doing so at Harvard, the women of ENIAC were developing the use of subroutines. They were fretting that the logical circuits did not have enough capacity to compute some trajectories. It was McNulty who pushed a solution. “Oh, I know, I know, I know,” she said excitedly one day. “We can use a master programmer to repeat code.” They tried it and it worked. “We began to think about how we could have subroutines, and nested subroutines, and all that stuff,” recalled Jennings. “It was very practical in terms of doing this trajectory problem, because the idea of not having to repeat a whole program, you could just repeat pieces of it and set up the master programmer to do this. Once you’ve learned that, you learn how to design your program in modules. Modularizing and developing subroutines were really crucial in learning how to program.”

Because it was being used for atom bomb calculations and other classified tasks, ENIAC was kept secret until February 1946, when the Army and Penn scheduled a gala unveiling for the public and the press. Herman Goldstine decided that the centerpiece of the ENIAC presentation would be a demonstration of a missile trajectory calculation. So two weeks in advance, he invited Jean Jennings and Betty Snyder to his apartment and, as Adele served tea, asked them if they could program ENIAC to do this in time. “We sure could,” Jennings pledged. She was excited. It would allow them to get their hands directly on the machine, which was rare. They set to work plugging memory buses into the correct units and setting up program trays.

The men knew that the success of their demonstration was in the hands of these two women. Mauchly came by one Saturday with a bottle of apricot brandy to keep them fortified. “It was delicious,” Jennings recalled. “From that day forward, I always kept a bottle of apricot brandy in my cupboard.” A few days later, the dean of the engineering school brought them a paper bag containing a fifth of whiskey. “Keep up the good work,” he told them. Snyder and Jennings were not big drinkers, but the gifts served their purpose. “It impressed us with the importance of this demonstration,” said Jennings.

The night before the demonstration was Valentine’s Day, but despite their normally active social lives, Snyder and Jennings did not celebrate. “Instead, we were holed up with that wonderful machine, the ENIAC, busily making the last corrections and checks on the program,” Jennings recounted. There was one stubborn glitch they couldn’t figure out: The program did a wonderful job spewing out data on the trajectory of artillery shells, but it just didn’t know when to stop. Even after the shell would have hit the ground, the program kept calculating its trajectory, “like a hypothetical shell burrowing through the ground at the same rate it had traveled through the air,” as Jennings described it. “Unless we solved that problem, we knew the demonstration would be a dud, and the ENIAC’s inventors and engineers would be embarrassed.”

ENIACThe machine that prints and tabulates the answers to the problems solved by the ENIAC, 1946.Photo: Bettmann/Corbis

Jennings and Snyder worked late into the evening before the press briefing trying to fix it, but they couldn’t. They finally gave up at midnight, when Snyder needed to catch the last train to her suburban apartment. But after she went to bed, Snyder figured it out: “I woke up in the middle of the night thinking what that error was…I came in, made a special trip on the early train that morning to look at a certain wire.” The problem was that there was a setting at the end of a “do loop” that was one digit off. She flipped the requisite switch and the glitch was fixed. “Betty could do more logical reasoning while she was asleep than most people can do awake,” Jennings later marveled. “While she slept, her subconscious untangled the knot that her conscious mind had been unable to.”

At the demonstration, ENIAC was able to spew out in 15 seconds a set of missile trajectory calculations that would have taken human computers several weeks. Mauchly and Eckert, like good innovators, knew how to put on a show. The tips of the vacuum tubes in the ENIAC accumulators, which were arranged in 10-by-10 grids, poked through holes in the machine’s front panel. But the faint light from the neon bulbs, which served as indicator lights, was barely visible. So Eckert got Ping-Pong balls, cut them in half, wrote numbers on them, and placed them over the bulbs. As the computer began processing the data, the lights in the room were turned off so that the audience would be awed by the blinking Ping-Pong balls, a spectacle that became a staple of movies and TV shows. “As the trajectory was being calculated, numbers built up in the accumulators and were transferred from place to place, and the lights started flashing like the bulbs on the marquees in Las Vegas,” said Jennings. “We had done what we set out to do. We had programmed the ENIAC.”

ENIACCodesigners John Mauchly (left) and Presper Eckert with ENIAC in 1966. The team put Ping-Pong balls on the bulbs as the computer began processing the data, the audience would be awed by the blinking Ping-Pong balls, a spectacle that became a staple of movies and TV shows.Photo: Hulton Archive/Getty Images

The unveiling of ENIAC made the front page of the New York Times under the headline ELECTRONIC COMPUTER FLASHES ANSWERS, MAY SPEED ENGINEERING. The story began, “One of the war’s top secrets, an amazing machine which applies electronic speeds for the first time to mathematical tasks hitherto too difficult and cumbersome for solution, was announced here tonight by the War Department.” The report continued inside the Times for a full page, with pictures of Mauchly, Eckert, and the room-size ENIAC. Mauchly proclaimed that the machine would lead to better weather predictions (his original passion), airplane design, and “projectiles operating at supersonic speeds.” The Associated Press story reported an even grander vision, declaring, “The robot opened the mathematical way to better living for every man.” As an example of “better living,” Mauchly asserted that computers might one day serve to lower the cost of a loaf of bread. How that would happen he did not explain, but it and millions of other such ramifications did in fact eventually transpire.

Later Jennings complained, in the tradition of Ada Lovelace, that many of the newspaper reports overstated what ENIAC could do by calling it a “giant brain” and implying that it could think. “The ENIAC wasn’t a brain in any sense,” she insisted. “It couldn’t reason, as computers still cannot reason, but it could give people more data to use in reasoning.”

Jennings had another complaint that was more personal: “Betty and I were ignored and forgotten following the demonstration. We felt as if we had been playing parts in a fascinating movie that suddenly took a bad turn, in which we had worked like dogs for two weeks to produce something really spectacular and then were written out of the script.” That night there was a candlelit dinner at Penn’s venerable Houston Hall. It was filled with scientific luminaries, military brass, and most of the men who had worked on ENIAC. But Jean Jennings and Betty Snyder were not there, nor were any of the other women programmers. “Betty and I weren’t invited,” Jennings said, “so we were sort of horrified.” While the men and various dignitaries celebrated, Jennings and Snyder made their way home alone through a very cold February night.

Shortly before she died in 2011, Jean Jennings Bartik reflected proudly on the fact that all the programmers who created the first general-purpose computer were women: “Despite our coming of age in an era when women’s career opportunities were generally quite confined, we helped initiate the era of the computer.” It happened because a lot of women back then had studied math, and their skills were in demand. There was also an irony involved: The boys with their toys thought that assembling the hardware was the most important task, and thus a man’s job. “American science and engineering was even more sexist than it is today,” Jennings said. “If the ENIAC’s administrators had known how crucial programming would be to the functioning of the electronic computer and how complex it would prove to be, they might have been more hesitant to give such an important role to women.”

This story is from the October 6, 2014 issue of Fortune. The excerpt draws on: Jean Jennings Bartik, Pioneer Programmer (Truman State, http://tsup.truman.edu/item.asp?itemid=480); Jean Bartik oral history , conducted by Gardner Hendrie, Computer History Museum, July 1, 2008; Jean Bartik oral history, conducted by Janet Abbate, IEEE Global History Network, Aug. 3, 2001; Steve Lohr, “Jean Bartik, Software Pioneer, Dies at 86,” New York Times, Apr. 7, 2011; Jennifer Light, “When Computers were Women,” Technology and Culture, July 1999. See also LeAnn Erickson, “Top Secret Rosies: The Female Computers of WWII” (Video, PBS, 2002); Thomas Petzinger Jr., “History of Software Begins with Work of Some Brainy Woman,” Wall Street Journal, Nov. 15, 1996; Kathy Kleiman, The Computers, documentary, ENIAC Programmers Project, http://eniacprogrammers.org/.