|Left: a photo and caption of German thinker Johann Goethe (age 15), from the 1927 Journal of Heredity article “The Child Hood of Genius”, by scientist Paul Papenoe.  Right: a 1987 article, by Cathie Spense, on American reserve energy theory forced-genius prodigy William Sidis, America's so-called "greatest" child prodigy.|
“For every child prodigy that you know about, at least 50 potential ones have burned out before you even heard about them.”— Itzhak Perlman (c.1990), Israeli-American violinist
The discussion here of "burning out" here needs further discussion, as this is a thermal word, in need of dissection.
The following, among the 1,000+ Hmolpedia biographies, are noted child prodigies, listed chronologically by date of reaction start (inception):
IQ=225+ cited (retrospect)
|At 6½ was arranging and conducting plays on the miniature puppet theater stage, and had learned of Faust; at age 7, to sugar the pill of grammar, he invented a novel in which the members of a family in various parts of the world wrote letters to each other in six different languages and styles; at age 9, built his own alter to nature out of his father’s natural history collection, surmounting it with a candle, which he lit when making his devotions; at age 15, completes his first landscape drawings of the Frankfurt area; studies the works of Plato, Aristotle, Plotin, and the Stoics; age 16, enters the University of Leipzig: starts to read law; further lessons on drawing with Adam Oeser; age 17 first reading of Shakespeare; age 18, began his studies in chemistry, particularly the work of Paracelsus and Susanne Klettenberg; and was conducting chemical experiments in his attic using a draught furnace (heat), so to reveal the "principle [secret principle] that permeates the whole universe."|
|IQ=195||At age 3, corrected an error in his father's calculations of wages to be paid to his fellow workers; claimed to have learned to calculate before he could talk.|
|IQ=185||Entered Glasgow University at age 10.|
|Known as "America's greatest child prodigy"; BS mathematics at Harvard at age 16; thermodynamic theory of everything at age 18.|
|IQ:200 cited (retrospect)||Able to divide eight digit numbers in his head, exchange jokes in classical Greek, and to memorize the names, numbers, and addresses in phone books (displayed as a game to guests), all by the age of six; his early mathematical ability is said to have been a product of his intrigue of his grandfather’s ability to rapidly perform complex mathematical calculations.|
|IQ=160||A precocious child, cited with an IQ of 170 at age 9; at age 15, after finishing high school, he entered the University of Minnesota at age to study biochemistry, interested in science as a goal in itself, rather than a way to establish a career.|
|IQ=140-185?±||Performing with the New York City Opera Children’s Chorus at age 11; winning a number of state and national awards in mathematics, language, and computer science, and gifted talent searches by age 15; graduated first out of 225 students in high school, and at age 22 graduated first out of about 550 students of the MIT school of engineering, simultaneously completing three undergraduate degrees: SB in physics, SB in electrical science and engineering, and SB in mathematics.|
IQ:225 cited (age 16)
|was noticed to have an accelerated mind at an early age. At age 3, he entertained himself, at the grocery story, by calculating the total bill of items in his parent's shopping cart, item-by-item, by weight, quantity, discounts, and sales tax. He was also reading the Dr. Seuss series to himself, able to recite the alphabet backwards, and had coded the alphabet sequence numerically, e.g. that the letter ‘O’ was 15th in the sequence. In 1st grade, he was doing algebra. By age 12, he was talking college-level courses in physics and multivariable calculus. At age 13, gained fame by winning gold medal at the 1996 International Physics Olympiad (IPhO), an international competition among the world’s smartest math and science students (up to age 19), becoming the youngest medalist ever. At age 14, Hirata entered the California Institute of Technology (Caltech) and two years later began working with NASA on a project exploring the possibility of colonizing Mars. At age 18, completed his BS in mathematics at the Caltech, with a 4.2 GPA, and PhD in astrophysics in 2005 at Princeton,|
|IQ:200 cited (age 15)|
Encyclopedia | Read
It is semi-frequently reported that so-and-so prodigy read so-and-so encyclopedia before age so-and-so; tidbits of which gets passed around and elaborated on to an exaggerated extent as prodigy fodder folklore.
In 1866, Friedrich Nietzsche (age 22) read through Friedrich Lange’s A History of Materialism, the seeming first proto encyclopedia of materialism, after which he wrote: 
“Kant, Schopenhauer, and this book by Lange – I don’t need anything else.”
American forced prodigy Edith Stern is reported to have read read an entire encyclopedia, of some sort, before age 4. By age 4.5 four, she read straight through volume one of the Encyclopedia Britannica (Ѻ), and by age 5 had read through the entire set. 
It is widely reported, e.g. by Clifford Pickover (1998), among others (Ѻ)(Ѻ), that Bill Gates, by age 8 or 9, had read the entire 1960 edition of The World Book Encyclopedia.
This, however, does not seem to be the case, but rather an elaboration of the fact that he attempted to read the entire set. He later recalled: “I was determined to read straight through every volume.” By the time he reached the letter P, however, he had discovered a more detailed encyclopedia, and decided he would never have enough time or patience to read the entire new set. (Ѻ)
Some prodigies not only burn out, as Itzhak Perlman (c.1990) points out, but crack under pressure and commit suicide.
A noted example, is American prodigy Brandenn Bremmer (1991-2005), shown below left, in 2001, at age 10, next to the stack of books he had absorbed to finish high school prior to entering college that year, who shot himself in the head four years later (Ѻ)(Ѻ)(Ѻ):
Another example is Chris (or Justin) Chapman (1996-) who in 2002, at age 6, was purported, by his mother Elizabeth Chapman, via underlying motive fabrication, to have an IQ of 298, and was removed by child services after he attempted suicide a year latter.
1. Popenoe, Paul. (1927). “The Childhood of a Genius: A Review” (extract), Journal of Heredity. 18(4): 145-51.
2. Leiter, Brian. (2007). Nietzsche on Morality (pg. #). Routledge. 2014.
3. Cohen, Richard. (1977). “Edith Project Produced Genius, Not Perfection” (Ѻ), Washington Post Special, in: The Milwaukee Sentinel, Apr 9.
● List of child prodigies – Wikipedia.