### A perspective on mathematics

On the 5th February 2013, Ainan confided: "The reason I like the Ackermann function is because it is so simple."

Some might not agree. The Wikipedia article on the Ackermann function states: "In computability theory the

**Ackermann function**, named after Wilhelm Ackermann is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive."

As maths goes, the Ackermann function is simple enough - but the point is that this is the view of a boy who has just turned 13. I suspect this is not a common view therefore.

Ainan is growing into a young mathematician, along with his other attributes. He studies maths every semester at Taylor's University and is steadily growing in knowledge, skill, competence and confidence. He even makes up his own maths.

The other day, he was trying to explain to me a mathematical system he had designed. He was very enthusiastic about it. What struck me more than his enthusiasm was his repetition of: "It is so simple Daddy."

I looked at the page he was writing on, densely scrawled with mathematical notation and thought that most people would disagree.

Ainan is still growing intellectually. Each year sees him becoming more complex, more adept and that bit more beyond the expected. He is only 13, now...near the beginning of that year of his life. Thus, he still has quite a few years of intellectual growth left to him. It is becoming clear that he has already journeyed further, intellectually, than most ever do - yet he is still quite early on in his journey. I am left to wonder: how far will he go?

I look forward to being witness to his growth - and an assistant to it, when I can be.

*Posted by Valentine Cawley*

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Labels: Ackermann Function, Ainan Celeste Cawley, Ainan's education, becoming, computability theory, intellectual growth, mathematical notation, on learning, primitive recursive, young mathematician

*posted by Valentine Cawley @ 11:48 AM*4 comments