Frances Allen, a former high school math teacher who became one of the leading computer scientists of her generation and, in 2006, was the first woman to win the A.M. Turing Award, considered the Nobel Prize in computing, died in Schenectady, N.Y., on Aug. 4, her 88th birthday.

Her grandnephew, Ryan McKee, confirmed her death. The cause was complications of Alzheimer’s disease.

Renowned for her seminal work in optimizing the creation of computer software programs and high-performance computing systems, Ms. Allen earned her stellar reputation in the esoteric field of software compilers. Simply put, her efforts over a distinguished 45-year career at IBM helped software designers generate more-powerful and efficient code, which led to huge advances in the use of supercomputers and parallel processing, and eventually in all levels of computing.

When she began her career in the late 1950s, years before universities began offering computer science degrees, software programmers working on room-size mainframe computers were hampered by having to hand-code programs line by line and spend time figuring out how to adjust slow software to run faster. These tweaks often led to more complexity and bugs in the software. The advent of software compilers allowed for the automatic optimization of software, which freed up valuable time for programmers and resulted in more-powerful and more-useful software.

Ms. Allen, after being introduced to the FORTRAN programming language when it was released in 1957, was fascinated with compiler optimization early in her career and became one of the leading visionaries in the field. Because of its compiler program, FORTRAN enabled a manner of communication with the computer that was closer to human understanding. With that as her model, Ms. Allen was inspired to make compilers more efficient.

Her work, which set the tone for how people in the field think about compiler optimization, bridged the gap between how computers communicate and how people communicate, thus opening up the use of computers to scientists and engineers and others outside the glass-enclosed fortresses of the data centers.

“Fran Allen’s work has led to remarkable advances in compiler design and machine architecture that are the foundation of modern high-performance computing,” said Ruzena Bajcsy, an emeritus electrical engineering and computer science professor at the University of California at Berkeley and chair of the Association for Computing Machinery’s A.M. Turing Award Committee when Ms. Allen won the award in 2006.

“Her contributions have spanned most of the history of computer science and have made possible computing techniques that we rely on today in business and technology,” Bajcsy said.

A fervent mentor for IBM researchers, Ms. Allen also was committed throughout her career to fostering women’s interest in computer science. In 1989, she became the first woman to be named an IBM fellow, the highest honor accorded a technical person in the company. She spoke at conferences around the world, urging women to consider careers in science and technology. In honor of her efforts, IBM established the Frances E. Allen Women in Technology Mentoring Award in 2000.

“Fran will be remembered as a pioneer in the world of computing who made seminal contributions to the field of optimizing compilers,” said Dario Gil, the director of IBM Research, in an email statement. “She left an enduring mark on IBM and will be remembered not only for her technical vision and legacy, but also her passion to inspire and help others, especially women.”

All this was heady stuff for a woman who seemed destined for a career as a high school math teacher in her hometown of Peru, N.Y., where she grew up on a dairy farm. Born on Aug. 4, 1932, in Peru, just south of the Canadian border, Frances Elizabeth Allen was the oldest of six children. Her father was a farmer, and her mother, a former grade school teacher, was a homemaker.

Growing up during the Depression in a farmhouse without electricity, plumbing or central heating, Ms. Allen spent much of her time reading. A high school teacher piqued her interest in math, and she decided to follow a similar career path. She received a teaching degree in 1954 from the New York State Teachers’ College in Albany (today SUNY at Albany). She took a job teaching math at her high school in Peru and felt she had found her calling.

“I enjoyed it a great deal,” she said in a 2001 oral history interview with the IEEE History Center. “I was perfectly happy to become a high school math teacher.”

To become certified, she needed a master’s degree, and after teaching for two years, she enrolled in a graduate math program at the University of Michigan. There, she took a couple of early computing courses but was concerned about paying back the debt she accrued getting her degree, which she received in 1957.

When IBM recruiters came to campus that year, she interviewed and got a job at the company’s vaunted research facility in Poughkeepsie, N.Y. “I’ll just take this for a year, pay off the debts I have and then I’ll go back to teaching,” she recalled, calling it a “throwaway job.”

The throwaway job — teaching the newly released FORTRAN programming language to IBM research scientists — instead spawned a 45-year, life-changing career with IBM. She had to learn this new high-level programming language on the fly, then teach it to reluctant scientists. She also was intrigued by the compiler developed by John Backus, another future Turing Award winner.

“It set my interest in compiling, and it also set the way I thought about compilers,” she said on the Turing Award website, “because it was organized in a way that has a direct heritage to modern compilers.”

Ms. Allen devoted her career to developing cutting-edge programming-language compilers for IBM Research. Her first major project was for the Stretch-Harvest computer in the early 1960s, designed to handle top-secret code-breaking and intelligence gathering by the National Security Agency. The computer was used by the NSA for 14 years.

In 1962, she began working at IBM’s new Thomas J. Watson Research Center in Yorktown Heights, N.Y., on the company’s Advanced Computing Systems project. There, she worked with John Cocke, a renowned IBM computer scientist.

“John talked to people, but Fran wrote all the papers,” Susan Graham, a professor at the University of California at Berkeley and a compiler expert, told the New York Times in 2002. “She was the one who ensured that those ideas got out, and that was a real contribution.”

From 1980 to 1995, Ms. Allen led an IBM research team focused on the emerging science of parallel computing. First used for supercomputers, the idea was to use groups of low-cost, high-performance microprocessors to share the processing of smaller tasks in parallel. This required software capable of distributing the software instructions across these groups of processors in parallel.

Over time, parallel processing became part of a variety of computing platforms, including desktop and laptop personal computers. Ms. Allen also helped develop software for IBM’s Blue Gene project, a supercomputer effort aimed at exploring how proteins fold into three-dimensional structures.

“I like to explore new problems, new ideas and new things,” she told the Investor’s Business Daily in 2008. “Once I understand what’s going on, I tend to go on to the next interesting challenge.”

While teaching at New York University, Ms. Allen worked with computer scientist Jacob Schwartz, whom she married in 1972. They were later divorced.

Survivors include two brothers and a sister.

Ms. Allen considered herself an explorer “on multiple fronts” and was an outdoor adventurer who skied and climbed mountains in Austria, China, the Himalayas and elsewhere. In the 1970s, she traveled in the Arctic with no maps or radio contact.

“On an exploratory trip to Baffin Island, our team made six first ascents, mapping uncharted mountains,” she told the States News Service in 2008. “On an Ellesmere Island trip, we established a new route across that island. But the physical space we live in is only one aspect of my interest in exploration. I like hearing new ideas, meeting new people, facing new challenges. It’s part of who I am.”

Her most memorable trip? “Beyond a doubt, it’s my 50 years in computing,” she declared. “What a trip!”