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 +

Monday, June 11, 2007

Johann Carl Friedrich Gauss

Some of history's greatest thinkers began life as child prodigies. What is interesting, to me, is that not everyone seems to know this.

Johann Carl Friedrich Gauss was a classic and remarkable case of child prodigy, emerging from an unpromising background. He was born on the 30th April 1777 in Brunswick, Germany. Neither of his parents were educated - indeed, his father was a stone mason. So, the young Gauss was very much on his own, in his early education. Yet, he was not without success. By the age of three he had somehow taught himself reading and arithmetic to a proficient degree.

One day, his father was adding up some figures, on paper, concerning the family finances. The young Gauss, three, peered over at his father's work and pointed out an arithmetical error - which Gauss had checked in his head.

In time, Gauss came to the attention of the Duke of Brunswick and, as was the custom of the day - and a good custom it was too - Gauss was to receive the patronage and support of the Duke of Brunswick, throughout much of his career. The Duke awarded Gauss a fellowship to the Collegium Carolinum, which he attended from 1792 to 1795 and thence he went to the University of Gottingen, which he attended from 1795 to 1798.

It was while at the University that Gauss began the train of mathematical breakthroughs that were to characterize his work and life. In 1796, he proved that any polygon with a number of sides equal to a Fermat prime may be constructed with a compass and straightedge. This was a major mathematical discovery since the problem of construction of such shapes had bedevilled mathematicians since the Ancient Greeks. It took the young Gauss to finally solve it.

Admission to University seems to have electrified Gauss into creative action. The construction problem was solved on March 30, 1796. A few days later, on April 8th, he proved the Quadratic Reciprocity law, which allowed one to determine the solvability of any quadratic function in modular arithmetic.

Modular arithmetic? Oh, he invented that, too. Then he came up with the Prime Number Theorem about the distribution of primes amongst all integers, on May 31st. On July 1oth he discovered that any positive integer is the sum of, at most, three triangular numbers. On October 1st, he published some work on the number of solutions of polynomials with coefficients in finite fields.

This outburst of creativity was not a solitary occurrence in Gauss' life. He went on to make lifelong contributions in many fields. I wrote in detail of that one year to give you some idea of what he was capable of. In 1799, he proved the fundamental theorem of algebra. In 1801, he published his book on number theory, Disquisitiones Arithmeticae, a magnum opus which he had actually completed at the age of 21, though he delayed publishing (this was a chronic tendency of his, failing to publish until, in his perfectionism, he was satisfied with his work. Had he published all that was later to be found in his notebooks, it is estimated that he would have advanced mathematics fifty years, single-handedly. However, in delaying publication, other mathematicians often got to publish Gaussian results before he did, though he had reached the same conclusions decades ahead of them).

In that same year, 1801, Giuseppe Piazzi discovered the planetoid Ceres. He tracked it for a few months, across three degrees of sky, but was unable to locate it again. (It had been lost behind the glare of the sun.) The astronomers of the time were unable to calculate an orbit sufficiently well on so little information to be able to predict the path of an object. Gauss, however, just 23 at the time, took on the project. In three months of work, he revolutionized how orbital calculations were performed, devising an approach which still stands as the foundation of such calculations today. He accurately stated where the object could be expected to be seen in the night sky - and Ceres was duly found again. This single piece of work catapulted Gauss to fame - and was later key in securing him the lifelong position of astronomer at Gottingen.

Gauss' achievement with Ceres puzzled many, for it seemed a feat beyond possibility. He was asked how he had done such an intricate calculation. He replied: "I used logarithms." When asked how he had looked up so many logarithms in so short a time, he dumbfounded them, by saying: "Who needs to look them up? I calculated them in my head."

Thus Gauss carried into his adult life the childhood ability as a mental calculator that he had shown at the age of three.

Gauss put his mental calculation to another practical use through performing a geodesic survey of the state of Hanover. In so doing, he developed what we know today as the Normal Distribution - or more properly, Gaussian distribution.

In the 1820s he collaborated with the physicist Wilhelm Weber and contributed much to the areas of optics, acoustics, mechanics and magnetism. Indeed, in 1833 he invented the telegraph, which was to later revolutionize communications that century.

Subsequent to his death on February 23rd, 1855, his brain was taken from his skull and weighed. It was, perhaps not surprisingly, significantly heavier than usual, at 1,492 grams and, the examiner stated that it was "highly and deeply convoluted". It was theorized that this unusual manifestation of the brain accounted for his genius.

Johann Carl Friedrich Gauss, began life as a self-educated child prodigy, born of uneducated parents, who could not, therefore, assist him but, by the end of his days, he was accounted, by many, as "the greatest mathematician since antiquity".

(If you would like to read about Ainan Celeste Cawley, seven years and six months, a scientific child prodigy, or his gifted brothers, Fintan, three, or Tiarnan, sixteen 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 children and gifted adults in general. Thanks.)

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posted by Valentine Cawley @ 3:26 PM 


Blogger Fábio F said...

Great summary on Gauss' life and achievements. In my opinion, he was the greatest mathematician ever and the archetype of a child prodigy.

1:05 AM  
Blogger Valentine Cawley said...

Thanks Fabio. Yes, Gauss shows that prodigies can lead to great lives and creative outcomes...if they have the proper opportunities.

1:34 AM  
Blogger Libb Thims said...

I've added a bio of your son to the IQ: 200 (±) candidates page at the eoht wiki. Be sure to point your son towards the elective affinities problem (especially being that he likes chemistry), it will be sure to keep his mind busy for many years, as this problem was worked on by many of the accelerated minds: Johann Goethe (IQ=225), William Sidis (IQ=250-300), and Christopher Hirata (IQ=225). If he wants to publish on this, down the road, send me an article of his for publication in the Journal of Human Thermodynamics.
Good luck, Libb Thims

3:21 AM  
Blogger Valentine Cawley said...

Dear Libb,

Thanks for your interest in Ainan. However, I tried to find the bio you mention and I couldn't find it on the eoht website. Could you provide a link to it? Thanks very much.

Re. elective affinities. I will let Ainan know about the problem and allow him to decide whether to consider it. Thanks.

1:35 PM  
Blogger Libb Thims said...


I just watched your TV interview a few minutes ago. Interesting stuff. I’ve been a collector of 200+ biography IQs for some years now. So far I have Ainan listed here:

and here:

I’m making my second annual YouTube “IQ: Smartest person ever” video this week, and will include Ainan in the listing (about thirty people for this year). Send me an email ( and I will let you know when the video is posted, etc., and also for further correspondence.

Regarding elective affinities, the biggest problem Ainan is most-likely to run into, down the road (as those such as William Sidis (IQ=300) and Michael Kearney (IQ=325) did), is the understanding of why he’s learning. Take, for example, Adragon De Mello (IQ=400), who in 1987 set the record for becoming the youngest college graduate (computational mathematics, at age 11), but thereafter withdrew from accelerated learning and now works at a hardware store.

Chapter four of Goethe’s 1809 novella Elective Affinities will give Ainan a starting point on this question; for it took Goethe, the highest ranked genius, by IQ, of all-time, to study chemistry and human existence for over forty years to be able to write this chapter. Hirata (IQ=225), likewise, the youngest-ever winner of the International Physics Olympiad (1996, age 13), attempted solution on this problem in 2000.

The key linkage between Hirata’s solution and Goethe’s solution (as well as Sidis’ 1920 solution, involving entropy S) is "chemical affinity" A, the biggest chemistry concept in Goethe’s day, otherwise known as "Gibbs free energy" (G=H-TS), in modern times, such that affinity equates to the negative of the change in free energy, a relation proved in 1882 by German physician-physicist Herman Helmholtz:

A = – ΔG

All other problems in chemistry pale in comparison to this one, which may explain why accelerated minds are often drawn to it, independently. My interest in bring this up to you is to save Ainan some time in searching (if in fact he does become drawn in this direction). It took me, for instance, twelve years and a thousand plus books to even become aware of Goethe’s chapter four:

Let me try to sum up the difficulty of the problem. The most intellectually-difficult subject that one can take in college is chemical engineering. The most intellectually-difficult subject in chemical engineering is chemical thermodynamics. The most intellectually difficult subject in chemical thermodynamics is human chemical thermodynamics. The first to attempt solution in human chemical thermodynamics was Goethe, the said to be smartest person of all time:


10:31 PM  
Blogger Libb Thims said...


I just watched your TV interview a few minutes ago. Interesting stuff. I’ve been a collector of 200+ biography IQs for some years now. So far I have Ainan listed here:

and here:

and here:

I’m making my second annual YouTube “IQ: Smartest person ever” video this week, and will include Ainan in the listing (about thirty people for this year). Send me an email ( and I will let you know when the video is posted, etc., and also for further correspondence.


10:33 PM  
Blogger Valentine Cawley said...

Hi Libb,

Thanks for your further postings.

By the way, which TV interview is this? (I have done several over the past few years). What were your thoughts on it?

I will be in further touch via email.

Thanks for the links to the listings. I will take a look.

Kind regards


5:24 PM  
Blogger Libb Thims said...

The interview I watched is this one:

Sorry for harping on so much about affinities and free energy, above, but being that Ainan seems accelerated in learning ability (particularly in chemistry), it might be a topic he will enjoy. If I could have gone back to age 15 and had someone explained the basic outline of this view to me I would have been very happy.

Here’s the basic homework problem I would suggest to Ainan.

(1) Go down to the local library, and calculate the molecular formula for a human being.
(2) Explain, in terms of chemistry and physics, why this particular molecule moves about on a surface and reacts with other like molecules over many decades?

The answer sheet for what has been done so far, historically, for question one is listed here:

The answer sheets for what has been done so far, historically, for question two are listed here: (67+ theories) (16+ theories)|+categorical (363+ theories)

I’m guessing that, in a way, you are looking for intellectual glory for Ainan. Then only thing I can tell you about this subject is that although it will attract much criticism and attack from minds not able to grasp the big picture, the future will be ripe with Nobel Prizes on the repercussions of this topic. Belgian chemist Ilya Prigogine was the first to win a Nobel Prize on this topic, with his 1970s theory humans are “dissipative structures”.

My work on this topic, likewise, has already been submitted to the Nobel Prize committee, particularly by Russian physical chemist Georgi Gladyshev, in 2007, someone who has been working on this problem science 1978. Suggest to Ainan, to note, that these types of intellectual endeavors should be thought of more as a hobby, rather than a career.


1:53 AM  
Blogger Libb Thims said...

Here’s another example perspective to show you that it is not a simple problem, in the 1920s, Albert Einstein (IQ=160-225), who owned a 52-volume set of Goethe’s collected works, and thus would have likely known about Goethe’s chapter four, was queried about something similar to above (involving genetics), to which he responded "How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?" This is only one aspect of the problem. By solving questions (1) and (2) above, one can bring solution to bear on all questions of human phenomena.

2:13 AM  
Blogger Valentine Cawley said...

Ah yes. That interview. He was quite a combative interviewer in some ways, so I had to pay close attention to what he was trying to say. His purpose may not have been positive. Off camera, he was very nice...on camera he TURNED. It was an educational experience. I think I handled him OK though, given that I hadn't a clue what he would ask.

Thanks for the tips and links re. affinities. I will see what Ainan thinks of them. He tends to set his own problems and interests though, so there is no telling whether it would take his interest.

Let me know how your site/videos develop.

Kind regards

3:30 PM  
Blogger Libb Thims said...

Here’s the newly-finished four-part video on the grouped meta-analysis ranking of individuals said to have a 200+ range IQ:

Part one:

Part two:

Part three:

Part four:

Ainan is mentioned in parts 1 and 2. Let me know that he thinks?
Let me know

2:51 PM  
Blogger Valentine Cawley said...

Thanks Libb, we will take a look. I predict though that his reaction, will be quite reserved, since he is not generally effusive. We will see.

Thanks for taking an interest in him.

I will post further on the videos here, once we have both viewed them.

Thank you.

1:05 AM  

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