Early computers were excellent at numbers.
Jean Sammet helped teach them to work with algebra.
Not just calculate that 7 × 8 = 56.
But manipulate expressions containing symbols:
x.
y.
Powers.
Derivatives.
Equations that were not yet reduced to numbers.
At IBM in the early 1960s, Sammet directed the development of FORMAC — one of the first widely used systems for symbolic mathematics.
It was an early step toward treating mathematics as structure a computer could transform, not just arithmetic it could evaluate.
For a long time, “computer” mostly meant numerical computation
The earliest high-level languages reflected the work computers were being asked to do.
FORTRAN was designed for scientific and engineering calculations.
COBOL targeted business data processing.
Machines were becoming very good at processing numbers and records.
But symbolic mathematics is different.
Consider:
(x + y)²
A numerical program expects values for x and y.
A symbolic system can manipulate the expression itself:
x² + 2xy + y²
No values required.
The symbols themselves become the data.
Sammet had already helped shape programming languages before IBM
Jean Sammet was trained as a mathematician.
She entered computing in the 1950s, when experienced programmers were scarce and the field was still inventing its own vocabulary.
At Sylvania, she managed basic software development for MOBIDIC, a computer built for the U.S. Army Signal Corps.
She also served as a key member of the committee that developed COBOL.
By the time she joined IBM in 1961, she was not simply learning how programming languages worked.
She was already helping define the field.
FORMAC asked computers to manipulate meaning, not just values
At IBM, Sammet directed the development of FORMAC.
The name came from FORmula MAnipulation Compiler.
It extended ideas familiar to FORTRAN programmers into symbolic mathematics.
Instead of only evaluating a formula numerically, a program could work with algebraic expressions as objects.
Expand them.
Simplify them.
Differentiate them.
Transform one symbolic form into another.
Computer History Museum describes FORMAC as the first commonly used language for manipulating nonnumeric algebraic expressions.
This changed what “data” could mean
Symbolic computation matters because many problems are not naturally expressed as rows of numbers.
A mathematical expression has structure.
Operators.
Variables.
Relationships.
Nested subexpressions.
A symbolic system must preserve that structure while transforming it according to mathematical rules.
That requires a different mindset from ordinary numerical calculation.
The computer is not only performing arithmetic.
It is manipulating representations of mathematical ideas.
The pattern now looks familiar because software absorbed it everywhere
Modern programmers routinely treat structured expressions as data.
Compilers transform syntax trees.
Computer algebra systems manipulate equations.
Query engines rewrite database expressions.
Symbolic AI systems manipulate logical formulas.
Libraries such as SymPy let Python programmers differentiate, factor and simplify equations without assigning numerical values first.
These modern systems do not descend from FORMAC in one simple straight line.
But they operate in a world where the underlying idea feels natural:
A program can reason over the structure of an expression.
In the early 1960s, that was still a frontier.
Sammet did something unusual after helping create languages: she documented them
Programming languages were multiplying quickly.
FORTRAN.
COBOL.
ALGOL.
LISP.
SNOBOL.
APL.
And dozens more.
Someone needed to make sense of what the field had become.
Sammet did not only participate in language development.
She became one of its most important historians.
Her 1969 book Programming Languages: History and Fundamentals discussed roughly 120 languages and became a foundational reference.
That combination — builder and historian — is rare
Builders usually focus on the next system.
Historians usually look backward.
Sammet did both.
She helped create COBOL and FORMAC.
Then she cataloged, compared and classified the broader language landscape.
That mattered because a field becomes more mature when it develops not only new tools, but a memory of why earlier tools were built.
Without history, engineers keep reinventing old ideas under new names.
Programming languages were becoming a discipline of their own
In the 1950s, a language could look like a convenient notation attached to a particular computer.
By the late 1960s, languages had become a distinct field with concepts, families, design tradeoffs and history.
Sammet’s career sits directly inside that transition.
She worked on practical compilers.
She participated in standardization.
She managed language technology at IBM.
She later served as president of ACM.
The field was no longer merely asking:
“How do we program this machine?”
It was asking:
“What kinds of languages should exist?”
The important abstraction often starts by redefining what counts as an object
FORMAC is useful as a product lesson because its core move was conceptual.
Do not treat an algebraic expression as text.
Do not require it to become a number immediately.
Treat the expression itself as something the system can understand and transform.
That is a recurring pattern in software.
A document becomes structured blocks.
A workflow becomes a graph.
A conversation becomes searchable memory.
A formula becomes an object.
Once the representation changes, a new class of operations becomes possible.
The question is not always “how do we calculate this faster?”
Sometimes the breakthrough is:
“What if we stop reducing this thing too early?”
Keep the structure.
Keep the relationships.
Let the computer operate on the richer representation.
Jean Sammet helped push computing in that direction before symbolic software became ordinary.
What are you currently flattening into text or numbers that would become much more powerful if your software preserved its structure?
Sources
- Computer History Museum — Jean Sammet
- Computer History Museum — Computer Pioneer Jean Sammet Born
- ACM Selects — Jean Sammet and FORMAC
- Jean E. Sammet — History of IBM’s Technical Contributions to High Level Programming Languages
- Computer History Museum — Core 2012, Jean Sammet Fellow profile
- Featured-image portrait — Jean Sammet at the University of Maryland in 1979, photo by Ben Shneiderman, CC BY-SA 4.0 via Wikimedia Commons. Minimal FORMAC formula and editorial layout are original; derivative remains under CC BY-SA 4.0.
SIGNAL TITANS
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