In the spring of 1962, while most computer scientists were still wrestling with the limitations of assembly language and early FORTRAN compilers, a mathematician-turned-programmer named Jean Sammet quietly introduced something the computing world had never seen before: a programming language capable of performing symbolic mathematical manipulation on a general-purpose computer. The language was called FORMAC — FORmula MAnipulation Compiler — and it would become the first widely used computer algebra system in history. Yet FORMAC was just one chapter in a career that spanned five decades, reshaped our understanding of programming languages, and helped bring COBOL into existence as the dominant business computing language of the twentieth century. Jean Sammet was not merely a participant in the early history of computing — she was one of its most meticulous chroniclers and fiercest advocates for the idea that programming languages were worthy of serious intellectual study.
Early Life and Mathematical Foundations
Jean Elaine Sammet was born on March 23, 1928, in New York City. From an early age, she displayed a remarkable aptitude for mathematics — a field that, in the 1940s, was still overwhelmingly dominated by men. She earned her bachelor’s degree in mathematics from Mount Holyoke College in 1948 and went on to complete her master’s degree in mathematics at the University of Illinois at Urbana-Champaign in 1949. Her graduate work gave her a rigorous foundation in abstract reasoning and formal systems that would prove invaluable when she transitioned into the nascent field of computing.
Unlike many of her contemporaries who stumbled into programming by accident, Sammet made a deliberate choice to enter the field. In the early 1950s, she began teaching mathematics at the University of Maryland and simultaneously started exploring the possibilities of electronic computing. She recognized early on that computers were not merely fast calculators — they were tools for manipulating symbolic information, a perspective that would define her entire career. This insight, radical for its time, placed her intellectual trajectory alongside visionaries like John McCarthy, who was simultaneously developing Lisp with its own symbolic computation capabilities, and Alan Turing, whose theoretical work had established the conceptual foundations for all programmable machines.
Entering the World of Programming: Sperry Gyroscope and Early Career
In 1955, Sammet joined the Sperry Gyroscope Company, where she first gained hands-on experience with large-scale computing systems. At Sperry, she worked on programming for military applications, learning the practical realities of software development in an era when “software” as a distinct discipline barely existed. Programmers wrote machine code or, if they were fortunate, used rudimentary assemblers. The idea that a human-readable programming language could be compiled into machine instructions was still revolutionary — John Backus had only just delivered the first FORTRAN compiler in 1957.
Sammet quickly became an expert in the challenges of making computers accessible to non-specialists. She understood that the gap between mathematical thinking and machine-level programming was a fundamental barrier to the widespread adoption of computing in business, science, and engineering. This conviction led her to one of the most important committees in computing history.
The Birth of COBOL: Sammet’s Role in Creating Business Computing’s Lingua Franca
In 1959, the U.S. Department of Defense convened a conference that would change the trajectory of business computing forever. The result was the Conference on Data Systems Languages (CODASYL), which established a committee to create a common business-oriented programming language. Jean Sammet was appointed to serve on this committee and played a key role in designing what would become COBOL — the Common Business-Oriented Language.
The COBOL effort was led by the legendary Grace Hopper, whose earlier work on the FLOW-MATIC language had demonstrated that programs could be written in something approaching English. Sammet served as a member of the short-range committee responsible for producing the initial COBOL specification. Her contributions were particularly significant in the area of language design — she brought a mathematician’s rigor to the process of defining syntax and semantics, helping to ensure that COBOL would be not just readable but formally well-specified.
The significance of COBOL cannot be overstated. By the mid-1960s, it had become the most widely used programming language in the world for business applications. Decades later, COBOL systems still process an estimated 95% of ATM transactions and 80% of in-person financial transactions globally. When modern development teams work on project management platforms like Taskee to coordinate their software projects, they benefit from a tradition of structured project organization that COBOL helped establish in enterprise computing.
Here is an example of what early COBOL code looked like, demonstrating the English-like syntax that Sammet and her colleagues championed:
IDENTIFICATION DIVISION.
PROGRAM-ID. PAYROLL-CALC.
AUTHOR. SAMMET-EXAMPLE.
DATE-WRITTEN. 1960-06-15.
*
ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
SOURCE-COMPUTER. IBM-7090.
OBJECT-COMPUTER. IBM-7090.
*
DATA DIVISION.
WORKING-STORAGE SECTION.
01 EMPLOYEE-RECORD.
05 EMP-NAME PIC X(30).
05 EMP-HOURS PIC 9(3)V9.
05 EMP-RATE PIC 9(3)V99.
05 EMP-GROSS-PAY PIC 9(5)V99.
05 EMP-TAX PIC 9(4)V99.
05 EMP-NET-PAY PIC 9(5)V99.
01 TAX-RATE PIC V99 VALUE 0.20.
*
PROCEDURE DIVISION.
MAIN-LOGIC.
PERFORM CALCULATE-PAY.
PERFORM DISPLAY-RESULTS.
STOP RUN.
*
CALCULATE-PAY.
MULTIPLY EMP-HOURS BY EMP-RATE
GIVING EMP-GROSS-PAY ROUNDED.
MULTIPLY EMP-GROSS-PAY BY TAX-RATE
GIVING EMP-TAX ROUNDED.
SUBTRACT EMP-TAX FROM EMP-GROSS-PAY
GIVING EMP-NET-PAY.
*
DISPLAY-RESULTS.
DISPLAY "EMPLOYEE: " EMP-NAME.
DISPLAY "GROSS PAY: $" EMP-GROSS-PAY.
DISPLAY "TAX: $" EMP-TAX.
DISPLAY "NET PAY: $" EMP-NET-PAY.This code illustrates the philosophy that Sammet and the COBOL committee shared: programming should be accessible to business professionals, not just mathematicians and engineers. The verbose, English-like syntax was a deliberate design choice that prioritized readability over conciseness — a principle that remains relevant in modern discussions about code maintainability and team collaboration.
FORMAC: The First Widely Used Computer Algebra System
While COBOL established Sammet’s credentials in business computing, it was her work at IBM that produced her most original technical contribution. In 1961, Sammet joined IBM’s Boston Advanced Programming Department, where she would remain for the rest of her career. Almost immediately, she began working on a project that would push the boundaries of what computers could do with mathematics.
The problem was straightforward but profoundly difficult: could a computer be taught to manipulate mathematical formulas symbolically, rather than merely computing numerical results? Numerical computation was well understood — give a computer two numbers, and it can add them. But symbolic computation is an entirely different challenge. Could a computer simplify the expression (x + y)^2 into x^2 + 2xy + y^2? Could it perform differentiation, integration, and algebraic simplification the way a trained mathematician does, working with symbols rather than specific values?
Sammet’s answer was FORMAC (FORmula MAnipulation Compiler), which she developed between 1962 and 1964 as an extension to FORTRAN. FORMAC was not the first attempt at computer algebra — that distinction belongs to several earlier experimental systems — but it was the first such system to achieve widespread use. It ran on the IBM 7090 and IBM 7094, the dominant scientific computers of the era, and was distributed to IBM customers worldwide.
The following example demonstrates the kind of symbolic manipulation FORMAC could perform, showing how it handled algebraic expressions — a capability that was genuinely revolutionary in the early 1960s:
C FORMAC EXAMPLE: SYMBOLIC DIFFERENTIATION
C RUNNING ON IBM 7090/7094 SYSTEMS, CIRCA 1964
C
C DECLARE SYMBOLIC VARIABLES
FORMAC
LET F = X**3 + 3*X**2*Y + 2*X*Y**2 + Y**3
C
C PERFORM SYMBOLIC DIFFERENTIATION WITH RESPECT TO X
LET DFDX = DERIV(F, X)
C RESULT: DFDX = 3*X**2 + 6*X*Y + 2*Y**2
C
C PERFORM SECOND DERIVATIVE
LET D2FDX2 = DERIV(DFDX, X)
C RESULT: D2FDX2 = 6*X + 6*Y
C
C SYMBOLIC SUBSTITUTION
LET G = SUBST(F, X, A+B)
C RESULT: EXPANDS F WITH X REPLACED BY (A+B)
C
C SIMPLIFICATION OF ALGEBRAIC EXPRESSIONS
LET H = (X+Y)**2 - X**2 - 2*X*Y - Y**2
LET HSIMPL = SIMPLIFY(H)
C RESULT: HSIMPL = 0
C
C INTEGRATION
LET INTF = INTEG(3*X**2 + 6*X*Y, X)
C RESULT: INTF = X**3 + 3*X**2*Y
END FORMACFORMAC’s impact on the trajectory of computing was significant. It demonstrated that computers could serve as intellectual partners in mathematical research, not just number-crunching machines. The system was used by scientists and engineers across multiple disciplines — physics, chemistry, electrical engineering — to perform calculations that would have taken hours or days by hand. More importantly, FORMAC established the conceptual framework for an entire field: computer algebra systems. Modern tools like Mathematica, Maple, and the symbolic computation engines embedded in countless scientific applications are direct intellectual descendants of Sammet’s pioneering work.
The relationship between FORMAC and earlier language innovations is worth noting. Just as John McCarthy’s Lisp had introduced the idea of treating code as data — enabling powerful metaprogramming techniques — FORMAC introduced the idea of treating mathematical expressions as manipulable data structures. Both approaches reflected a deeper truth about computing that Sammet understood intuitively: the power of computers lies not in arithmetic speed but in their ability to transform structured representations of knowledge.
The Historian of Programming Languages
If Sammet had only contributed to COBOL and FORMAC, her place in computing history would be secure. But she made a third contribution that may ultimately prove even more valuable: she became the foremost historian and taxonomist of programming languages during the most explosive period of language creation in computing history.
In 1969, Sammet published Programming Languages: History and Fundamentals, a monumental 785-page work that cataloged and analyzed over 120 programming languages. The book was not merely a reference manual — it was a systematic attempt to classify programming languages by their design principles, application domains, and theoretical foundations. Sammet developed taxonomies that organized languages into categories such as numerical scientific computation, business data processing, string and list processing, formula manipulation, multipurpose languages, and specialized languages for specific application areas.
The significance of this work cannot be separated from its historical context. In the 1960s, programming languages were proliferating at an astonishing rate. The phrase “programming language” could refer to anything from FORTRAN to COBOL to LISP to SNOBOL to APL to ALGOL — and hundreds of lesser-known systems. Without Sammet’s careful cataloging and classification, much of this history would have been lost. Her book became the definitive reference for understanding the early landscape of programming languages, and it remains an invaluable historical document today.
Sammet’s taxonomic approach anticipated modern efforts to understand programming language design as a discipline with its own principles and patterns. When Niklaus Wirth designed Pascal in the early 1970s or when Bjarne Stroustrup created C++ a decade later, they were working within a tradition of language design that Sammet had helped to formalize and document. Her insistence that programming languages deserved rigorous study — that they were not mere tools but intellectual artifacts worthy of analysis — helped establish programming language theory as a legitimate academic discipline.
Leadership at IBM and the ACM
Throughout her career, Sammet held increasingly influential positions. At IBM, she managed the Programming Technology Planning Department, where she oversaw research into advanced programming concepts. She was not only a technical contributor but also a strategic thinker who helped IBM navigate the rapidly evolving landscape of software development.
Her leadership extended well beyond IBM. Sammet was deeply involved in the Association for Computing Machinery (ACM), serving as president from 1974 to 1976 — only the second woman to hold that position. During her tenure, she worked to expand the ACM’s focus on programming languages, software engineering, and the social implications of computing. She was a founding member of the ACM Special Interest Group on Programming Languages (SIGPLAN) and served on the SIGPLAN History of Programming Languages (HOPL) committee, which organized landmark conferences dedicated to documenting the origins and evolution of programming languages.
Sammet’s involvement in HOPL was characteristically thorough. The first HOPL conference, held in 1978, featured papers on thirteen programming languages, each written or co-written by the language’s original designers. Sammet served as the conference chair and ensured that the proceedings met the highest standards of historical accuracy. These conferences produced some of the most important primary source documents in computing history, and Sammet’s editorial rigor ensured their lasting value. Teams managing complex historical documentation projects today, whether using modern digital agency workflows through platforms like Toimi or traditional archival methods, owe a conceptual debt to the organizational frameworks Sammet helped develop.
FORMAC’s Legacy and the Evolution of Computer Algebra
The lineage from FORMAC to modern computer algebra systems reveals how profoundly Sammet’s work influenced scientific computing. After FORMAC, several other symbolic computation systems appeared in the 1960s and 1970s — including REDUCE, MACSYMA (developed at MIT), and eventually the commercial systems Mathematica (created by Stephen Wolfram in 1988) and Maple. Each of these systems built upon the fundamental idea that Sammet had proven viable: that computers could manipulate mathematical expressions as symbolic objects.
MACSYMA, in particular, represented a direct evolution of the concepts Sammet had pioneered. Developed at MIT’s Project MAC starting in 1968, it was implemented in Lisp and could perform symbolic integration, differentiation, equation solving, and matrix operations. The connection between FORMAC’s FORTRAN-based approach and MACSYMA’s Lisp-based approach illustrates how Sammet’s core idea — symbolic mathematical manipulation by computer — transcended any particular implementation technology.
The impact of computer algebra systems on modern science and engineering is difficult to overstate. Physicists use them to verify complex calculations in quantum field theory. Engineers use them to derive and simplify equations governing structural mechanics, fluid dynamics, and signal processing. Mathematicians use them to explore conjectures and verify proofs. Every time a researcher uses Wolfram Alpha to simplify an expression or a student uses a CAS to check their calculus homework, they are benefiting from a tradition that Jean Sammet helped establish.
Advocacy for Women in Computing
Jean Sammet’s career unfolded during an era when women in technical fields faced systematic barriers. Although the early decades of computing saw significant contributions from women — Ada Lovelace had written the first algorithm, Grace Hopper had pioneered compilers, and women had served as the original “computers” during World War II — by the 1960s and 1970s, the field was becoming increasingly male-dominated.
Sammet addressed gender bias primarily through excellence and visibility. By serving as ACM president, publishing landmark research, and maintaining a prominent role at IBM for over three decades, she demonstrated that women could lead at the highest levels of computing. She was not typically characterized as an activist in the modern sense, but her very presence in positions of authority challenged the assumptions of her era.
Her legacy in this regard is particularly important when viewed alongside other women who made foundational contributions to computing. Frances Allen, who became the first woman to win the Turing Award in 2006 for her work on compiler optimization, and Barbara Liskov, who won it in 2008 for her contributions to programming language design, both followed paths that Sammet had helped clear. The growing recognition of women’s contributions to computing — through initiatives, scholarships, and historical retrospectives — owes much to the example that pioneers like Sammet set.
The Philosophy of Programming Language Design
One of Sammet’s most enduring intellectual contributions was her insistence that programming language design was not merely a technical activity but a philosophical one. She argued that the design of a programming language encodes assumptions about how humans think, how problems should be decomposed, and what aspects of computation are most important. This perspective was remarkably ahead of its time.
Consider the fundamental design tension between COBOL and FORTRAN. COBOL’s English-like syntax reflected an assumption that programming should be accessible to business professionals with minimal technical training. FORTRAN’s mathematical notation reflected an assumption that programming was fundamentally a mathematical activity. These were not just technical choices — they were philosophical positions about the nature of computing and its relationship to human cognition.
Sammet’s taxonomic work made these philosophical dimensions explicit. By categorizing languages according to their design principles and intended application domains, she revealed the implicit assumptions embedded in each language’s design. This analytical framework anticipated modern debates about programming language design — the tension between static and dynamic typing, between object-oriented and functional paradigms, between verbose explicitness and concise expressiveness.
Her work also anticipated the modern understanding that programming languages shape thought. The Sapir-Whorf hypothesis, applied to programming, suggests that the language a programmer uses influences how they conceptualize problems. Sammet understood this intuitively, which is why she believed that the study of programming languages was not just an academic exercise but a practical necessity. As Edsger Dijkstra would later argue with characteristic sharpness, the tools of thought profoundly constrain the thoughts themselves.
Awards, Recognition, and Later Years
Jean Sammet received numerous honors throughout her career, reflecting the breadth and depth of her contributions. She was named an ACM Fellow and an IBM Fellow — the highest technical distinction at IBM. She received the Augusta Ada Lovelace Award from the Association for Women in Computing in 1989. In 2001, she was inducted into the National Women’s Hall of Fame, and in 2009, she received the Computer History Museum Fellow Award.
Sammet retired from IBM in 1988 after 27 years with the company, but she remained active in the computing community for many years afterward. She continued to attend conferences, participate in historical discussions, and advocate for the preservation of computing history. She was particularly concerned that the rapid pace of technological change was causing important historical knowledge to be lost, and she worked tirelessly to ensure that the origins and evolution of programming languages were properly documented.
Jean Sammet passed away on May 20, 2017, at the age of 89. Her death marked the end of an era — she was one of the last surviving members of the original COBOL committee and one of the few people who had personally witnessed the entire trajectory of programming language development from its earliest days to the modern era.
Lasting Impact and Continuing Relevance
Jean Sammet’s contributions to computing operate on multiple levels. At the most concrete level, she helped create COBOL, a language that still processes trillions of dollars in transactions daily, and she invented FORMAC, which demonstrated that computers could perform symbolic mathematics. At a more abstract level, she established the study of programming languages as a legitimate intellectual discipline and created the foundational historical record of programming language development.
Her work remains relevant in ways she might not have anticipated. The renewed interest in domain-specific languages — programming languages designed for specific application areas — echoes her taxonomic insight that different problem domains require different linguistic tools. The growing importance of computer algebra systems in scientific computing reflects the vision she articulated with FORMAC. And the ongoing debates about programming language design — how to balance readability with expressiveness, how to manage complexity, how to make programming accessible to non-specialists — are debates that Sammet helped frame more than half a century ago.
Perhaps most importantly, Sammet’s career embodies a principle that the computing industry periodically forgets and must relearn: that understanding the history of our tools is essential to improving them. In an industry obsessed with novelty, Sammet reminded us that every new programming language, every new framework, every new paradigm exists in a historical continuum. To design better tools for the future, we must first understand the tools of the past. Jean Sammet spent her career ensuring that understanding would be possible, and the computing world is immeasurably richer for her efforts.
Frequently Asked Questions
What was Jean Sammet’s most important contribution to computing?
Jean Sammet made three major contributions to computing, each significant in its own right. She was a key member of the committee that designed COBOL, which became the most widely used business programming language in history. She created FORMAC, the first widely used computer algebra system capable of symbolic mathematical manipulation. And she authored Programming Languages: History and Fundamentals (1969), the definitive historical and taxonomic study of early programming languages. Together, these contributions span language design, symbolic computation, and computing history — a breadth matched by very few of her contemporaries.
How does FORMAC relate to modern computer algebra systems like Mathematica and Maple?
FORMAC, developed by Sammet between 1962 and 1964, was the first widely distributed computer algebra system. It demonstrated that general-purpose computers could manipulate mathematical expressions symbolically — performing differentiation, algebraic simplification, and substitution on formulas rather than just computing numerical results. This concept directly influenced subsequent systems including REDUCE, MACSYMA (developed at MIT), and eventually the commercial products Mathematica and Maple. While modern systems are vastly more powerful, they are built upon the foundational idea that Sammet proved viable with FORMAC: that computers can serve as partners in mathematical reasoning, not just calculation.
What was Jean Sammet’s role in the creation of COBOL?
Sammet served on the short-range committee of the Conference on Data Systems Languages (CODASYL), which was tasked with producing the initial COBOL specification in 1959. Working alongside Grace Hopper and other computing pioneers, she contributed to the language design process, bringing a mathematician’s rigor to the definition of COBOL’s syntax and semantics. Her work helped ensure that COBOL would be both readable by non-programmers (through its English-like syntax) and formally well-defined enough to be implemented consistently across different computer systems.
Why was Jean Sammet’s book on programming languages so influential?
Published in 1969, Programming Languages: History and Fundamentals was the first comprehensive attempt to catalog, classify, and analyze the rapidly growing number of programming languages. Spanning 785 pages and covering over 120 languages, it organized programming languages into taxonomic categories based on their design principles and application domains. The book provided the intellectual framework for understanding programming language design as a discipline, and it preserved historical information about early languages that would otherwise have been lost. It remains an essential reference for computing historians and language designers.
What awards and recognition did Jean Sammet receive during her career?
Sammet received numerous honors reflecting the significance of her contributions. She was named both an ACM Fellow and an IBM Fellow — the latter being the highest technical distinction at IBM. She served as president of the ACM from 1974 to 1976. She received the Augusta Ada Lovelace Award from the Association for Women in Computing in 1989, was inducted into the National Women’s Hall of Fame in 2001, and received the Computer History Museum Fellow Award in 2009. These recognitions spanned her contributions to programming language design, computer algebra, computing history, and her role as a leader in the computing profession.
