When advice, is not advice.

Long ago, my brother Josh was starting out on his career in the financial world.

(I have referred to him elsewhere in one story that told of his savant-like gift for mental calculation. As I noted then, he has the gift, but he does not have a savant's impairment - but is, in fact, profoundly gifted.)

It was at this time that he was given what I have recently come to regard as a mischievous piece of advice. This supposedly helpful adviser was aware of Josh's ability to do complex calculations instantly and instinctively, in his mind, without reference to a calculator or computer. In the financial world, at that time, there were many roles which involved the manipulation of numbers, the analysis of numerical data and the ability to understand all things mathematical. There would seem, therefore, to be one obvious piece of advice that Josh could have been given...but what he was actually advised to do was something altogether different.

This adviser told Josh, as I heard the story, many years ago, to steer clear of any role that involved direct interaction with numbers. He argued that it would become unbearable, for one such as Josh, with his innate understanding of number, to be surrounded by numbers, all day. Josh, as a young man, just out of University, took this advice at face value - and duly steered clear of any role having such direct and considerable daily involvement with numbers.

Think about that for a moment. Josh had a unique gift for instant calculation and interpretation of numbers. He could do what no other could, numerically. The possible implications for effective outcomes for one such as that, placed in a situation which allowed the interpretation of numbers to have a real world effect, are boundless. Truly, he could have done something very interesting indeed. Yet, he was advised not to become involved with numbers. I wonder at the mischief behind such advice. Josh was being advised to avoid playing to his greatest strength, being advised to hide his talents, to operate in an area in which they would have no direct use. Such advice could only have been meant unkindly, I think - unless the adviser truly misunderstood the situation - but I think that unlikely.

Josh never did apply his numerical gift, professionally, as far as I am aware. He took the advice and let his calculatory gift lie dormant and rarely called upon. That is, I feel, a pity.

I tell this tale for an obvious reason. You or your children may have unusual gifts. At various times others, in a position of authority, may advise you or your children as to careers and courses. I would evaluate their advice with the story above in mind - and ask these questions:

Does the advice take note of the innate strengths of the child? Does the advice play to the strengths of the child - or does it ignore them? Is the adviser someone likely to be in competition at the organization with your child? If so, then look more closely still at the advice that is being given.

The gifted are not welcomed everywhere. Sometimes people feel threatened by their gifts - and do what they can to hide them, obstruct them or otherwise interfere with their expression.

Had Josh become directly involved with numbers, in an area in which the rapid understanding of their meaning and possibilities had real world implications, he would have become, in all probability, the best in his field, in the world - for no other could compete with him, in the matter of mental calculation.

In taking the advice he was given, he turned away from his most unusual strength, and played to others, instead - but I can't help but wonder what would have happened had he exercised a gift that no-one else could challenge him in.

Ensure that your child is never left to wonder such a thing, too: play to their strengths, whatever they may be.

(I should point out that Josh has led a fulfilling and interesting career, since. Yet, the point remains that there are applications for his unused gift that would have been truly remarkable.)

(If you would like to read about Ainan Celeste Cawley, Josh's nephew, a scientific child prodigy, aged seven years and six months, or his gifted brothers, Fintan, three, and Tiarnan, sixteen 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, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children, and gifted adults. Thanks.)

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: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html 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.)