"It's just too difficult," he likely told his tutor, the great Euclid of Alexandria. "Can't you show me the easy way?" Ptolemy I found Euclid's foundational work on geometry, Elements, unfathomable.

The young mathematician is believed to have retorted: "But sire, there are no royal roads to geometry."

Ever since, people have sought an easy path through mathematics and by doing so they are missing the whole point.

"It is the struggle of mathematics that is important. We keep trying to give kids devices and tricks to make it easier," said Nalini Joshi, professor of mathematics at the University of Sydney.

"Maths in schools is often presented as a rigid hierarchy," Professor Joshi said. "Teachers present as priests pointing the one, true way to a solution. This is not what maths is about."

With numbers of those taking HSC mathematics in decline, people still seem to be seeking royal roads to solving this problem.

There are none.

We must learn to celebrate the complex and creative in mathematics if it is to regain favour.

From an early age we are told that mathematics is all about right and wrong, black and white. It is the antonym of creativity and imagination. Nothing could be further from the truth.

"Mathematics is a creative enterprise just like music," Professor Joshi said. "Maths has a rhythmic framework to hold your patterns at even the most basic level. In overtures and harmonics, the complexity increases."

Young children use creativity and imagination to begin the process of separation from their parents. At high school, teenagers use creativity to fit into their peer group – and to be identified as separate.

Creativity is an essential part of this process of separation to form identity.

However, in maths our children are so often told they must go from A to B to C via a rigid pathway. This ruins their desire to create and mathematics can be lost to them.

Sitting with my sons during maths homework, they'll ask: "How do you do this sort of question?" Halfway through an explanation I'll hear: "But we aren't taught it like that at school."

But this is what's so great about mathematics. There are many pathways to an answer – and sometimes there is no solution at all.

Like a great river wandering from a mountain to the sea, there is no set path. Over time, the pathway can change. Sometimes the most direct way is not the fastest. And sometimes the fastest is not always the most satisfactory.

Each pathway will have its own little series of discoveries.

In year 3 my son's class was asked to come up with "number sentences", such as "what is nine plus three?". He suggested "What is two minus five?" and was promptly told there are no numbers below zero.

I remember a high school teacher claim there was no such thing as the square root of negative one – yet an entire branch of mathematics is based upon this concept.

Learning in all disciplines should be about encouraging and satisfying curiosity. It should be about asking impossible questions.

In few other human activities is the contemplation of philosophy, truth and logic so near to the surface: What is zero? How long is forever?

How many times have you heard a child ask another: "What is a number greater than infinity?"

The answer, of course, is simple: infinity plus one.

As children – and as adults – we should daydream and build castles in the air. Mathematics gives us the tools to ascend those heavens and scale the impossible. Maths provides ladders to our human imagination.

William Blake sums up mathematics for me in a most beautiful way. In his poem Auguries of Innocence, Blake's opening lines delve into the philosophy of mathematics: exploration of scale, nothingness and the infinite:

To see a World in a Grain of Sand And a Heaven in a Wild Flower Hold Infinity in the palm of your hand And Eternity in an hour ...

Marcus Strom is the Herald's science editor.