Patterns
&
Sequences

You know,

lots of mathematicians say that maths

is mainly being able to see patterns in numbers and number sequences

the things that are different

and things that are the same

all related in a rhythmic dance.

And some numbers may belong to groups that are common,

like the evens and the odds,

and some are rare and precious,

like the fibonaccis and the primes.

And you can even see the patterns

when you take away the numbers underneath them,

when you replace them with symbols

different shapes,

perhaps like letters of the alphabet

to stand for any number.

We use symbols to suggest things that are so much more than the symbol itself

like the x symbol at the end of a message to a loved one

or a tearful emoji to express feelings without words.

But when symbols are used to stand for numbers,

those symbols still work within the rules of mathematics.

So plus and minus and suchlike still work in the same way,

all in that branch of maths known as algebra.

It's somehow easier to play with the numbers

when they are seen as symbols.

As you move them around and rearrange them

you can look at problems in very different ways

and find solutions in patterns

only seen from different viewpoints.

Humans learn about the world by recognising patterns in the world

from the double helix pattern of human DNA

the stuff of which they are made

to the solutions to engineering problems

in the world around them,

from the roofs of Victorian railway stations

to the structures of modern buildings,

and the various rail and road bridges,

old and new, throughout the country.

When written down as algebra,

the letter symbols used instead of numbers fit right in,

because in fact the written numbers themselves

are only symbols

for the idea of numbers that we use them for.

The whole system is made up of symbols,

like the signs for plus and minus,

and multiply and divide,

and the symbol that sits at its heart,

its point of balance, the equals sign.

And by working on each side of an equals sign,

sometimes it can be proved that two things that seem very different

are actually the same,

and one thing can be proved from another,

building up a network of mathematical truth and certainty.

And sometimes it is possible to come up with a group of symbols

that works in a very useful way

to solve common maths problems.

These are formulae that can give a true answer

simply by exchanging numbers for

the symbols in an algebra equation.

So even without using actual numbers,

the language of maths can cast a light on what is true and false,

and help us understand the creation that surrounds us.