“Terence Tao”, M. A. Clements1984-08 (, )⁠:

This article is a biographical account of Terence Tao’s mathematical development.

Born in 1975 he has exhibited a formidable mathematical precociousness which the author describes in some detail.

The paper also presents the social and family context surrounding this precociousness and discusses the educational implications of this data.

…Mrs Tao’s role, then, is more one of guiding and stimulating Terence’s development than one of teaching him. She said that Terence likes to read mathematics by himself, and he often spent 3 or 4 hours after school reading mathematics textbooks…Terence tends to read whole books rather than parts of books. He is keen to receive advice on which books he should read next. His father told me that he has a remarkable memory for virtually everything he reads. On several occasions when I spoke with Terence about mathematics he punctuated the conversation by saying ‘Oh yes, I’ve read about that’. He then went and got a book, quickly found the relevant section, and showed it to me.

…I made arrangements to come back in order to continue my assessment of Terence. As I was leaving Billy showed me some of Terence’s efforts, over the last 2 years, on the family’s Commodore computer. Terence had taught himself BASIC language (by reading a book) and had written many programs on mathematics problems. Some of the names of his programs were ‘Euclid’s algorithm’, ‘Fibonacci’ and ‘Prime Numbers’. His ‘Fibonacci’ program, shown in Figure 5, is interesting in that a careful reading of it will reveal something of Terence’s creative, lively personality. Also, it is fascinating to observe that Terence wrote many of his programs early in 1982, when he was 6 years old.

…In the first report the clinical psychologist stated that although Terence was only 44 years old he was functioning intellectually more like an 8 to 10 year-old. He added that Terence would require careful supervision during his schooling to see that his intellectual, social and emotional needs were met adequately. In the second report the psychologist stated that Terence was in the 95th percentile range for 11 year olds on the Raven’s Controlled Projection Matrices test (a primarily non-verbal test of reasoning). In the third report Terence, at age 6 years 4 months, is said to have gained maximum or near maximum scores on the Wechsler Intelligence Scale for children, with there being no difference between his verbal and performance (practical, non-verbal) intelligence. His overall Mental Age was 14 years (very superior range of intellect for a 6 year-old). The psychologist indicated that while the situation seemed quite favourable at that time, with Terence accepting normal progression through the school grades, special arrangements might have to be made for his transition to secondary and tertiary education.

…the first published statement about Terence appeared several years ago. Newsletter 13 of the South Australian Association for Gifted and Talented Children, August 1980, contained the following excerpt (Leon = Terence Tao):

Leon (not his real name), one of our Saturday Club children, enjoyed Mae Cuthbert’s Calculator Games afternoon at Putteney. At one point the calculator threw up the number sequence 9,182,736. Mae challenged the children to find the next 4 numbers in the series, Leon thought for a moment and then replied ‘4554’, He was right. (Had you worked out that the number series consisted of the answers to the 9× table? [ie. 9, 18, 27, 36, 45, 54…])

Leon has just turned 5. He starts school in a month’s time.

…From my assessment of Terence’s mathematical abilities and interests the following characteristics stand out:

  1. He has a prodigious long-term memory for mathematical definitions, proofs and ideas with which he has become acquainted;

  2. While he has well developed spatial ability, when attempting to solve mathematical problems he has a distinct, though not conscious, preference for using verbal-logical, as opposed to visual, thinking (see Lean & Clements1981, pp. 267–299; Sheckels & Eliot1983, pp. 811–816);

  3. He is capable of understanding mathematical writing even when such writing makes considerable use of sophisticated mathematical terminology and symbolism;

  4. He especially likes analysis (differential and integral calculus), algebraic structures, number theory, and computing;

  5. He tends to grasp abstract concepts quickly, and does not need to have these concepts presented to him by means of concrete embodiments;

  6. While he is capable of formulating appropriate solution strategies for unseen, challenging problems, at present he is usually happy to immerse himself further into the world of mathematics. He especially enjoys reading about the history of mathematics, and learning how to apply those algorithms which are needed in his special fields of interest (eg. algorithms for solving second-order differential equations);

  7. He learns mathematics at an amazing rate. In 1983, for example, he seems to have learnt most of the mathematics normally covered in syllabuses for Years 11 and 12 and, in addition, has mastered much of the mathematics typically found in first-year university programs (speed in learning is a characteristic of most exceptionally gifted children in mathematics—see House 1983, p. 231; Vance 1983, p. 22);

  8. If he finds he does not know some area of mathematics which interests him (or he needs) he consults books to find out the information he needs. He learns well, from books, without the aid of a tutor;

  9. Once having obtained a ‘solution’ to a problem he does not like to check his work and, if asked to do so, sometimes gives an impression that he would rather proceed with new work;

  10. He does not take pride in setting out his work in a way that will communicate easily with others. In presenting written solutions he is usually content to write just enough to convince the reader he can do the problem.

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Terence Tao