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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Ainan's invents mathematical notation.

Ainan has invented his own mathematical notation to express his understanding of numbers.

Now, I rather wish I could explain it, but I don't understand it. (I did sit down with him, for an explanation, but it turned out to be elusive in its complexity and I didn't have time to get to the bottom of it). It is a straightforward notation that looks simple enough when written down, but which seems to have very complex outputs. It is useful, it appears, when working with very large numbers.

The point of this observation is not about conveying a detailed understanding of his work (for that would not be of interest to most and, as I have said, I am not in a position to do so, anyway), but conveying an understanding of Ainan. He is turning his mind to other things, beyond Chemistry. His interests are spreading to Physics and Mathematics. He is beginning to do with maths, for instance, what he started to do in the early days, with Chemistry: experiment with it, to create his own projects, works, theories and practical results.

I find this heartening. You see with his wider interests in mathematical and physical areas, he looks set to become a more complete physical scientist and this will open up more options for him, in years to come.

It is sweet to note, too, his deep interest in his mathematical work. He gets a very great reward from playing with mathematical ideas in this way.

This development leaves me with less of an ability to predict his future, but more of a certainty that it will be a broad one. He is maintaining his interest in Chemistry and is continuing to develop along that line, too.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged eight years and seven months, or his gifted brothers, Fintan, five years exactly, and Tiarnan, twenty-eight months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, the Irish, the Malays, Singapore, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, wunderkind, wonderkind, genio, гений ребенок prodigy, genie, μεγαλοφυία θαύμα παιδιών, bambino, kind.

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