The Magic Word is PEMDAS

by Dr Gavin Hitchcock

WHY is this the order? Because we humans invented these tools (the symbols) to behave in a particular way, and that's the way the tools must be used, like any other tools we have invented: hammers, wheelbarrows, bicycles..... Be grateful for symbols! They are burden-bearers. Without them, sums like the one above would instead be pages and pages covered with very confusing words.

Here's the statement and solution of a quadratic equation, as the ancient Babylonians would have put it (though not in English, of course):

The area of a square is fifteen units greater than twice the side of the square; find its side and area.

Solution. Take fifteen and multiply it by four; you get sixty. Now take two and square it; you get four. Add this answer to sixty; you have sixty-four. Take the root of sixty-four; it is eight. Add this eight to two; you have ten. Divide into two parts; the answer to the question is FIVE!

Having seen that, imagine what this HORRIBLE formula would look like in words:

It is the solution of the first non-trivial quartic (4th degree equation) to be solved - by Ludovico Ferrari in the mid 16th century. Here it is, looking terribly innocent: x⁴+2x+1 = 0. Those first Italian equation-solvers actually had public equation-solving contests - the winner solved them fastest - and lots of money was won and lost! Can you see why we have them to thank for getting algebra properly symbolized?