The
advent of computers allowed us to use algorithms to rapidly work out
solutions to maths problems. E.g. working out square roots of numbers or
finding roots of equations (where a graph of the equation crosses the
x-axis). The solutions are often approximate to a desired level of
accuracy, rather than an exact analytical solution. This area of maths,
using algorithms to solve problems is called numerical analysis.
If you've ever wondered how a scientific calculator works out e.g. the
sine of an angle, it just uses an infinite series or other technique and
does lots of simple arithmetic to add each element of the series
together. The most basic microprocessors can only do simple arithmetic
such as addition and subtraction of integers (whole numbers), so
anything more complex such as multiplication, division and the handling
of decimal numbers must be done using algorithms. For example,
multiplication can be thought of as adding numbers multiple times (e.g. 4
x 3 = 4 + 4 + 4). In the 80s, math coprocessors became common as
separate integrated circuits (ICs) or "chips", dedicated to doing faster
maths calculations in hardware rather than software. These could be
bought as an upgrade for PCs. Eventually the functionality of these
chips was built into the main processor.
This article from Medium shows how the square root of a number can be calculated using the Newton Raphson algorithm: