Schoonschip was one of the first computer algebra systems, developed in 1963 by Martinus J. G. Veltman, for use in particle physics.

"Schoonschip" refers to the Dutch expression "schoon schip maken": to make a clean sweep, to clean/clear things up (literally: to make the ship clean). The name was chosen "among others to annoy everybody, who could not speak Dutch".

Veltman initially developed the program to compute the quadrupole moment of the W boson(known at the time as “intermediate vector bosons”)^[2], the computation of which involved "a monstrous expression involving in the order of 50,000 terms in intermediate stages" ^[3]

The initial version, dating to December 1963, ran on an IBM 7094 mainframe.^[4] In 1966 it was ported to the CDC 6600 mainframe, and later to most of the rest of Control Data's CDC line.^[4] In 1983 it was ported to the Motorola 68000 microprocessor, allowing its use on a number of 68000-based systems running variants of Unix.^[4]

Veltman was a recipient of the 1999 Nobel Prize in Physics along with Gerard 't Hooft for their work on gauge theories in elementary particle physics. Veltman had originally developed Schoonschip to aid in his work on the renormalizability of gauge theories. Schoonschip served as inspiration for Stephen Wolfram's Symbolic Manipulation Program (SMP), a predecessor to Mathematica. Wolfram met with Veltman in 1979, and Veltman later said:

Later, on the basis of this program [SCHOONSCHIP], the commercially successful software program Mathematica was developed by Wolfram. While most theoreticians were getting lost in all kinds of formulas, I could just get things calculated. That gave me an enormous advantage.^[5]

Wolfram wrote about Schoonschip being a specialized version of what he wanted from SMP; a computer program to solve complicated mathematical expressions without wasting time "chasing minus signs and factors of 2".^[6]

FORM can be regarded, in a sense, as the successor to Schoonschip.