How it began
The logician Jan Łukasiewicz invented the notation in 1924. Mathematicians had long written general function symbols before their arguments, and Leon Chwistek mentioned this to Łukasiewicz in the early 1920s as a possibility for the connectives of propositional logic. Łukasiewicz then worked out the principles, possibly by experimenting with wooden blocks to compose formulas. He was based in Warsaw, where he and his students used the notation in their work on propositional calculus.
Before it existed
In the standard notation of Peano and Russell, symbols for connectives such as implication were written between their arguments. Anything beyond the simplest formulas then needed parentheses or clusters of dots to remove ambiguity, and these were hard to follow in complex formulas. Frege's branching notation avoided parentheses but took up space and was difficult to typeset.
How it works
Every connective is written before its arguments, is represented by its own capital letter and takes a fixed number of arguments. Variables are lower-case letters. The formula for 'if p then q' becomes Cpq. A simple count tests whether a formula is well formed: start at 1, add 1 at each two-place connective, subtract 1 at each variable, and the count must reach zero for the first time at the final variable. One formula of 43 symbols, twenty of them parentheses, shrinks to 23 symbols.
Who pushed back
The Stanford Encyclopedia of Philosophy notes that the notation never became standard or even widespread in logic, although Arthur Prior and others adopted it. It is less helpful in predicate calculus, where the scope of a quantifier calls for brackets. The same source calls it a minor and incidental part of Łukasiewicz's work compared with his results in propositional and many-valued logic.
What lasted
The notation could be typed on an ordinary typewriter without special symbols, an advantage before computer typesetting. Its mirror image, reverse Polish notation, places operators after their arguments. That form was implemented in Hewlett-Packard calculators and some programming languages, though most users have since returned to conventional notation with parentheses.
