Foundation
Mathematics

The story of mathematics

is one that begins with certain axioms, recognised as basic truths,

and takes them step by logical step

into the most extraordinary places,

many that defy imagining.

But if maths is going to take us into places that can't be pictured,

if we are to trust it we need to make sure

that each step follows the one before,

and that all of them are based on solid foundations.

It is the job of Foundation Mathematics

to test the accuracy of those claims,

considering the fundamental rules of mathematics,

and rigorously challenging and testing

mathematical logic.

This includes considerations of what we mean by by maths itself

because what we call mathematics

is often said to be less to do with numbers than with sets.

This means we have a whole area of maths dealing with Set Theory

as well as a mathematics of Category Theory

to deal with data that can be classified but not ordered.

Of course, with the ever increasing role of computers now not just for calculation

but also for instigating new mathematical thought

a Theory of Computation has been developed

to consider how they function and how much they can be trusted.

Then, as well as these considerations of

the roots and structure of mathematics itself,

Foundation Mathematics usually embraces within its remit

the history of maths

along with the biographies

of historically noteworthy mathematicians.

And just as a cherry on top of its mathematical cake,

Foundation Maths takes under its wing

the various forms of recreational mathematics.

Because of course

with mathematics, being integral to human life

it has been used as something from which to draw pleasure.

Solving a mathematical puzzle

has its own emotional reward,

and although very few have the mathematical ability

to tackle the Clay Institute Millennial Problems,

many more can enjoy a relationship with numbers

by playing with Sudoku.

Numbers are for everybody,

because

as we are told in the Qur'an

everything in creation is numbered with numbers.