# What is this type of math notation called? (+ 4 5)

So I've been looking for a general name of this type of mathematics notation (google hasn't been very useful) so that I can learn more about it. Basically, the symbols are in the form of functions and the numbers are the inputs to the function. + is the function taking 4 and 5, outputting 9 so, (+4 5) = 9. Formulaic (* a b ) = a * b. Where ' * ' can be any basic math symbol. More complicated forms are: (+ 4 (+ 5 1)) = 4 + (5+1) = 10. 4 being input for 'a' and (5+1) being 'b' in (* a b ).

Hope it makes sense.

• AFAIK this is looks like the LISP programming language. – user258700 Apr 4 '16 at 19:15
• Looks like arithmetics in Polish Notation, except the Polish Notation does not need - and does not use - parentheses. – CiaPan Apr 4 '16 at 19:19
• @JeanMarie I know what Lisp is (some time ago I knew some dialect of Lisp), but the question was 'for a general name of this type of mathematics', not about the name of a programming language which uses this type of maths. – CiaPan Apr 4 '16 at 20:07
• It's not a "type of mathematics". It's just a trivial variation on notation. Good notations are important in mathematics, but a different notation does not make a different mathematics. – Michael Kay Apr 4 '16 at 21:44
• Lisp uses parentheses because (among other reasons) + and * are actually sum and product functions on an arbitrary number of operands, rather than binary operators. – Random832 Apr 5 '16 at 4:35

• And because nobody noted it yet, 4 5 + 6 7 * - (like Forth) is known as Postfix notation or Reverse Polish Notation. – cat Apr 4 '16 at 22:41