The boy who knew too much: a child prodigy

This is the true story of scientific child prodigy, and former baby genius, Ainan Celeste Cawley, written by his father. It is the true story, too, of his gifted brothers and of all the Cawley family. I write also of child prodigy and genius in general: what it is, and how it is so often neglected in the modern world. As a society, we so often fail those we should most hope to see succeed: our gifted children and the gifted adults they become. Site Copyright: Valentine Cawley, 2006 +

Saturday, April 07, 2007

Ainan explores mathematics

Mathematics, at school, for a Primary 2 student is not a very exciting affair. Indeed, in Ainan's school they have got as far as addition and subtraction - and no further. Needless to say, Ainan had long begun to fret at the pace of things and had all but adjudged maths to be boring. Then something wonderful happened: he began to discover it for himself.

A couple of weeks ago, Ainan picked up a maths book and began to read. He soon found it more interesting than he had thought. Within days, he was beginning to enthuse about maths - and the range of mathematical ideas that he has absorbed in that short time is quite remarkable.

His conversation now concerns transcendental numbers, irrational numbers, perfect numbers, primes, semiperfect numbers, weird numbers, powerful numbers, mathematical constants, folke's constant, skewe's number (any spelling mistakes are my own since I am rendering what I here him speak of), factorials, roots, squares, cubes, powers, indices, sublime numbers, amicable numbers (he was particularly taken by these), imaginary numbers, (and many others) he has taken to inventing his own constants, writing equations, playing with functions, designing mathematical just goes on. He has even written a maths book to encapsulate his new experience in words and pictures.

I also note something interesting. He has begun to absorb mathematical facts in great detail - much as he did with chemistry. His speech is peppered with numbers to the seventeenth decimal - which he has learnt as easily as you or I might remember our own names. He knows pi to seventeen decimal places. He knows e to a similar precision. He knows many, many different numbers, each of which are examples of the classes of numbers that he has come to know. He remembers the products of all the calculations of mathematical functions that he has been playing with. (For instance, he learnt many "conjective numbers"). He is beginning to draw relationships and associations between numbers and divine his own patterns within them. He is making number references in his speech - defining the numbers he sees in the everyday world in terms of other numbers about which he knows something interesting.

What is amazing about all of this is that mere days ago none of it existed. He had not developed any spontaneous interest in maths at all - apart from an interest in hyperdimensional four, five and higher dimensional shapes which he had nursed for over four years.

Ainan has just decided, one day, to look at maths. This is the same thing that happened one day, with chemistry - and look how far he has come with that, in a short time.

Even now, Ainan retains an ability to surprise me.

Now that his interest in maths has awakened, he is asking that I buy maths texts for him - so I shall make a trip tomorrow to do just that. I think Ainan's best teacher is himself. So, I will let him do just that - pick up a book and teach himself maths.

It is a happy moment for me, as a father, to see him develop this interest in mathematics - because I know how important it is to support his primary interest in the physical sciences. Without good maths behind him, some branches of the physical sciences would have been forever closed to him. Looking at how he has begun to enthuse about maths, I don't think that will be a problem for him. If he tackles maths as he has chemistry, there is no telling just how "numerate" he will be in a few months time.

(If you would like to read more of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and four months, or his gifted brothers, Fintan, three and Tiarnan, fourteen months, please go to: I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

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posted by Valentine Cawley @ 9:56 PM 


Blogger Howard said...

I must say that I am very glad Ainan has found mathematics so able a friend .

What book is he requesting to buy from you ? What level of mathematics is he learning now ?

Indeed , I would just have to say that Primary 1 to 6 is a painful process as they make mathematics fun- not interesting . They spark up the pages with cartoonic characters , the mathematical depth is very little . The ratio of the mathematuical depth to the cartoon would be 1:2^10 .

I myself , could be called a young amateur mathematician . YAM Howard .
My current interests in mathemmatics is namely number theory and calculus and trigonometry .I think number theory could be called my favourite subject though .

11:44 PM  
Anonymous Anonymous said...

Bravo, Ainan! It's wonderful to watch a child discover a love for mathematics.

Does he like fractals? Check out the Mandelbrot set!

Another interesting constant is the Golden Ratio.

Have fun :)

12:41 AM  
Blogger Valentine Cawley said...

We don't know what books are available...he just wants books on maths that can expand his understanding. So, we are just going to look and see what is out there and pick one or two up to get him going.

Good luck with your own mathematical interests.

Best wishes

9:00 AM  
Blogger Valentine Cawley said...

Thanks for the suggestions. Ainan is familiar with the golden ratio (knows to many decimal places too) but has not yet met any fractals. I will have to seek out the Mandelbrot set for him.

Thanks for your wishes to you.

9:05 AM  
Blogger EbTech said...

Oh wow, the Mandelbrot Set! I was first introduced to it many, many years ago, and to date it remains one of the most amazing things I have ever seen!

Especially for those who have yet to appreciate the beauty in mathematics, it is truly a sight to behold. Here is one of my favourite zoom-in videos:

The Mandelbrot Set can be generated by iterations of a complex number formula:
z = z^2 + c

Thus, it is not fair to say that the Mandelbrot Set was designed by a computer, nor by its programmer. It is an intrinsic property of the formula. Therefore, I view the Mandelbrot Set as one of nature's hidden masterpieces. And how wonderful at that!

I recommend downloading a free fractal generator so that you and Ainan can explore its infinite intricacies for yourselves. It's really worth it!

Fractal geometry is one of the newest branches of mathematics. Its founding father, BenoƮt Mandelbrot, is still alive today.

1:42 PM  
Blogger Valentine Cawley said...

Thanks for the link. I will make sure Ainan gets to see it.

Kind regards

2:27 PM  

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