FORTRAN, MATLAB, and the First Scientific Languages

The first decade of computational science was written in machine code, with each instruction painstakingly wired in by hand or punched on cards. By the mid-1950s the volume of code being written for scientific problems had grown beyond what could be hand-coded, and a new idea took hold: scientists should write the formula they meant, and a translator program should figure out the rest.

That translator was FORTRAN — the FORmula TRANslator — and it is the single most influential programming language in scientific history. Almost every numerical idea you will meet in this course was first implemented in FORTRAN, and a remarkable amount of production scientific code still is.

FORTRAN: scientists' first compiler

John Backus's team at IBM started work on FORTRAN in 1954 and released the first compiler in 1957 for the IBM 704. Their goal was simple but radical: a scientist should be able to write

DO 10 I = 1, N
   Y(I) = A * X(I) + B
10 CONTINUE

and the compiler should generate machine code as efficient as hand-written assembly. Backus famously said that without that efficiency goal, "no one would have used the language."

It worked. By the early 1960s, programs that previously took weeks to hand-code in machine language could be written in an afternoon in FORTRAN. The productivity unlock was so large that nearly every scientific lab in the world adopted it within five years.

You can see this in action right now. NumPy's @ operator dispatches to a routine called DGEMM in BLAS, which is FORTRAN code from the 1970s that has been re-tuned for every generation of CPU since.

The number of GFLOPS your browser reports is delivered by a stack that is roughly: NumPy (Python) → BLAS (C wrapper) → LAPACK (FORTRAN) → CPU vector instructions. Sixty years of optimization, hidden behind a single @.

FORTRAN's lasting design ideas

Three FORTRAN ideas survive almost unchanged into modern scientific Python:

1. Arrays are the primary data type. FORTRAN was the first language with built-in multidimensional arrays. NumPy's ndarray is a direct intellectual descendant.
2. The numerical inner loop must be fast. FORTRAN compilers were tuned to vectorize loops over arrays. Today the same job is done by SIMD instructions and BLAS libraries.
3. Standard numerical libraries are shared. BLAS (1979), LAPACK (1992), FFTPACK, ODEPACK, MINPACK — these FORTRAN libraries are still the workhorses inside SciPy. Most of the algorithms in scipy.linalg, scipy.optimize, and scipy.integrate are thin Python wrappers over decades-old FORTRAN.

MATLAB: a calculator that thought in matrices

In the late 1970s, Cleve Moler was teaching a numerical analysis course at the University of New Mexico. He wanted his students to use LINPACK and EISPACK — the brand-new FORTRAN libraries he had helped write — without having to learn FORTRAN. So he wrote a tiny interactive program that let students type expressions like A * x and eig(A) at a prompt. He called it MATLAB ("matrix laboratory").

By 1984 it had been rewritten in C, commercialized by MathWorks, and was on its way to becoming the lingua franca of engineering education. For nearly thirty years, "scientific computing" and "MATLAB" were near-synonyms in most engineering departments.

MATLAB introduced several ideas that scientific Python directly copied:

If you have ever wondered why matplotlib.pyplot has functions named plot, subplot, title, xlabel, and ylabel — it is because John Hunter, Matplotlib's creator, deliberately mimicked MATLAB so that engineers could switch with as little friction as possible.

What FORTRAN and MATLAB taught us — and what they lacked

The two languages between them established the intellectual core of scientific computing:

• Array-oriented thinking. Write y = A @ x + b, not three nested loops.
• Library composition. A handful of well-tested numerical primitives (solve, eig, fft, quad) can express enormous swathes of science.
• Interactivity. Type, run, inspect, refine. The REPL is part of the workflow.

But each had serious limitations that left an opening for Python. FORTRAN was a compiled, batch language with almost no support for strings, file formats, plotting, networking, or any of the gluework that surrounds real science. MATLAB was interactive and friendly but proprietary and expensive, with a weak module system, no real support for general-purpose programming, and a license cost that locked students out the moment they graduated.

That gap — general-purpose, open-source, with a serious numerical stack — is exactly the gap Python filled. That story is the next chapter.

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