On November 2, 2021, I published a post titled, Are IQ and Intelligence Illusory Concepts? It was a post that generated a considerable response. (accessible at: https://www.intelligence-and-iq.com/are-iq-and-intelligence-illusory-concepts/) In that post, it was argued that the existence of child prodigies establishes the fact that not all members of our species are identical in cognitive ability. Some children show precocious abilities long before thousands of hours of effort were available to them. Today, I provide a brief description of two such prodigies, mathematician John von Neumann, who displayed genius from early in life, and the modern-day prodigy, Terrence Tao.
Johnny von Neumann was a wunderkind, manifesting signs of genius in early childhood. He could recite, in ancient Greek, long sections from Homer’s Odyssey and often showcased his photographic memory by repeating verbatim pages of text and numbers immediately after reading them. He could divide two eight-digit numbers in his head at age 6 and was proficient in calculus at age 8. He had a voracious appetite for learning and was schooled in his early years by tutors. He acquired his high school education at the prestigious Lutheran Gymnasium. At the age of 21 he earned a degree in chemical engineering from the Swiss Federal Institute in Zürich and the next year, completed a doctorate in mathematics from the University of Budapest. In the years that followed, he made significant contributions to almost every branch of mathematics, in addition to inventing game theory and laying the foundations of computer science. He was also one of the first people to understand the significance of Gödel’s Theorem.
As one might expect, there were eccentricities that accompanied this brilliance, not unusual in those with extreme gifts. Near the end of World War II, while working on the Manhattan Project, von Neumann modified the ENIAC (computer) to make it programmable. Robert Oppenheimer had engaged him to calculate the height at which the atomic bomb should be detonated to exact maximum damage. Time was tight and the race to develop the bomb was heating up. “Johnny,” as he was addressed by his friends and colleagues, was revered for his brilliant computing power, and had done the calculations by hand, arguing that the Project could not afford to wait a week or two for the computer to verify his calculations. However, Oppenheimer overruled him, and everyone waited impatiently as the computer chugged through the extensive calculations. It was the middle of the night when the giant machine, composed of 18,000 vacuum tubes, spewed its final output. The excited scientists waited to telephone von Neumann, to share the good news, until after 10:00 a.m. because everyone knew that von Neumann was a late sleeper. The conversation is reported to have unfolded something like this:
Von Neumann (sleepily answering the telephone): Johnny here.
Scientist: Dr. von Neumann, the computer has finished its calculations and they verify that your computations are correct!
Von Neumann: You wake me up early in the morning to tell me that I’m right? Please don’t call me when I’m right; call me when I’m wrong! (and hangs up!)
Terrence Tao
Terrence Tao, the son of two highly educated immigrants from Hong Kong, was born in Australia on July 17, 1975. Within two years after his birth, his parents recognized that he was percocious when they saw him teaching older children arithmetic he had learned by watching Sesame Street. By age seven, he was teaching himself calculus from a textbook, and when just 8 years old, he became one of only two children in the history of the Johns Hopkins’ Study of Exceptional Talent program to have achieved a score of 700 or greater on the math section of the SAT. By 9 years of age he was attending university level mathematics courses, and at age ten, he was participating in the International Mathematics Olympiads, winning a bronze medal in 1986, a silver medal in 1987 and a gold medal in 1988–the youngest ever to win each. Mainly self-taught, he earned a B.Sc. degree from Flinders University in Australia at age 16 and a Masters Degree the next year. By 1996, at age 21, he graduated from Princeton University with a Ph.D. in mathematics, and by age 24 had attained the rank of full professor at the University of California at Los Angeles. Following a prodigious period of research publications, he was awarded in 2006 at the age of 31, a Fields medal (called the Nobel Prize of mathematics) for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.
John von Neumann and Terrence Tao are examples of prodigies who were fortunate enough to be immersed in environments that enabled them to learn at their own pace, unencumbered by the constraints of classrooms designed for a median demographic. We are all beneficiaries of their talent and commitment, enhanced by those who nurtured their gifts.
