In genius studies, prodigies and calculus refers to the subject of noted prodigies and geniuses in respect to the age at which he or she first learned calculus (TR=104), a subject that less than 1 to 2 percent of the population, supposedly, learns.

Prodigies | Geniuses
The following is a listing of ages at which noted prodigies and or prodigies turned geniuses learned calculus, ranked via age at which calculus was learned or mastered:

# Person IQE Age
Description

1. Kim Ung-Yong
(1963-) $IQ_{E}\,$ =210 3 Began to learn differential calculus at age 3 (Ѻ); solving integral calculus problems (Ѻ) and or “intricate math equations” as he says (Ѻ) at age 4; on Nov 2, 1967, at age 4, he solved an advanced stochastic differential equation (Ѻ); at age 5, was solving complicated differential and integral calculus problems. (Ѻ)
2. Balamurali Ambati
(1977-)
4 Mastered calculus at age 4. (Ѻ)
3. Soborno Bari
(2012-)
4 Was learning trigonometry by age 3; doing calculus problems by age 4 (Ѻ). This, however, seems to be the typical over-hyped “forced prodigy” scenario, his father Rashidul Bari, mathematics and physic professor, attempting to promote some type of Bari Science Lab, is hyping his son as “4 year old Einstein” or “4 year old calculus expert”, but could only get his 13 year old son to score 610 math on the SAT. (Ѻ)
4. Michael Kearney
(1954-) $IQ_{E}\,$ =325 6 At age 6, was wrapping up homework on calculus to get his high school diploma. (Ѻ)
5. Murray Gell-Mann
(1929-)
7 Taught himself calculus at age 7. (Ѻ)
6. Terence Tao
(1975-) $IQ_{E}\,$ =230 7 Started to learn calculus when he was 7, at which age he began high school; by 9 he was already very good at university-level calculus; by 11, he was thriving in international mathematics competitions. (Ѻ)
7. Jerry Newport
(1948-)
7 At age 7, was using calculus to compute third and higher roots; self-discovered much number theory in elementary school—perfect numbers, Fibonacci, etc.—and in 2010 won title holder of ‘Most Versatile Calculator’. [2]
8. Promethea Pythaitha
(1991-) $IQ_{E}\,$ =173 7 Was taking calculus courses at Montana State University at age 7, completed her BS in mathematics at age 13, albeit officially receiving degree at 14. [2]
9. Jeremy Shuler
(2004-)
7 Studying pre-calculus by age 5 and had read William Dunham’s Journey Through Genius: the Great Theorems of Mathematics (1990), from his mother’s bookshelf; learned calculus at age 7; engineering freshman at Cornell by age 12. (Ѻ)
10. John Neumann
(1903-1957)
$IQ_{R}\,$ =190|#33
$IQ_{E}\,$ =180 8 Learned calculus at age 8 (Ѻ).
11. Adragon De Mello
(1976-) $IQ_{E}\,$ =400 9 Learned calculus at age 9 (1985) (Ѻ).
12. William Sidis
(1898-1944)
$IQ_{E}\,$ =250-300 9 Mastered differential and integral calculus at 9 or 10 years (Ѻ).
13. Henry Muhlbauer
(2003-)
9 Mastered calculus at age 9, completed BS in electrical engineering at age 15 (see: youngest college graduates) at University of Virginia.
14. Michael Grost
(1954-) $IQ_{E}\,$ =200 10 Before age 8, had worked 2 to the 80th power, on a black board, in two hours time; mother could not help much with calculus questions, so at age 10 enrolled at Michigan State University. (Ѻ)
15. Sky Choi
(1997-)
11 Taking Calculus II, Physics with Calculus I, at age 12 (2009), at Florida International University. (Ѻ)
16. John Mill
(1806-1873) $IQ_{R}\,$ =185|#85
$IQ_{E}\,$ =200 11 Learned calculus by age 11. [1]
17. Albert Einstein
(1879-1955) $IQ_{R}\,$ =220|#2
$IQ_{E}\,$ =225 12 Taught himself calculus at age 12; integral and differential calculus by 13 (Ѻ) (Ѻ); in 1935, a rabbi in Princeton showed Einstein a clipping of the Ripley’s column with the headline “Greatest living mathematician failed in mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus” (Ѻ).
18. Christopher Hirata
(1982-) $IQ_{R}\,$ =185|#75
$IQ_{E}\,$ =225 12 Was taking college-level courses in physics and multivariable calculus; at age 14, upon arriving at Caltech, he registered one of the highest scores in history on the Institute's mathematics diagnostic tests, thereby enabling him to forego freshman calculus and sophomore differential equations for a more difficult upper-division class (Ѻ).
19. Richard Feynman
(1918-1988) $IQ_{R}\,$ =190|#35 13 Was reading Calculus for the Practical Man at age 13 (Ѻ), and had learned differential and integral calculus by age 13 (Ѻ) or age 15. (Ѻ)

#	Person	IQE	Age	Description

1.	Kim Ung-Yong (1963-)	$IQ_{E}\,$ =210	3	Began to learn differential calculus at age 3 (Ѻ); solving integral calculus problems (Ѻ) and or “intricate math equations” as he says (Ѻ) at age 4; on Nov 2, 1967, at age 4, he solved an advanced stochastic differential equation (Ѻ); at age 5, was solving complicated differential and integral calculus problems. (Ѻ)
2.	Balamurali Ambati (1977-)		4	Mastered calculus at age 4. (Ѻ)
3.	Soborno Bari (2012-)		4	Was learning trigonometry by age 3; doing calculus problems by age 4 (Ѻ). This, however, seems to be the typical over-hyped “forced prodigy” scenario, his father Rashidul Bari, mathematics and physic professor, attempting to promote some type of Bari Science Lab, is hyping his son as “4 year old Einstein” or “4 year old calculus expert”, but could only get his 13 year old son to score 610 math on the SAT. (Ѻ)
4.	Michael Kearney (1954-)	$IQ_{E}\,$ =325	6	At age 6, was wrapping up homework on calculus to get his high school diploma. (Ѻ)
5.	Murray Gell-Mann (1929-)		7	Taught himself calculus at age 7. (Ѻ)
6.	Terence Tao (1975-)	$IQ_{E}\,$ =230	7	Started to learn calculus when he was 7, at which age he began high school; by 9 he was already very good at university-level calculus; by 11, he was thriving in international mathematics competitions. (Ѻ)
7.	Jerry Newport (1948-)		7	At age 7, was using calculus to compute third and higher roots; self-discovered much number theory in elementary school—perfect numbers, Fibonacci, etc.—and in 2010 won title holder of ‘Most Versatile Calculator’. [2]
8.	Promethea Pythaitha (1991-)	$IQ_{E}\,$ =173	7	Was taking calculus courses at Montana State University at age 7, completed her BS in mathematics at age 13, albeit officially receiving degree at 14. [2]
9.	Jeremy Shuler (2004-)		7	Studying pre-calculus by age 5 and had read William Dunham’s Journey Through Genius: the Great Theorems of Mathematics (1990), from his mother’s bookshelf; learned calculus at age 7; engineering freshman at Cornell by age 12. (Ѻ)
10.	John Neumann (1903-1957)	$IQ_{R}\,$ =190\|#33 $IQ_{E}\,$ =180	8	Learned calculus at age 8 (Ѻ).
11.	Adragon De Mello (1976-)	$IQ_{E}\,$ =400	9	Learned calculus at age 9 (1985) (Ѻ).
12.	William Sidis (1898-1944)	$IQ_{E}\,$ =250-300	9	Mastered differential and integral calculus at 9 or 10 years (Ѻ).
13.	Henry Muhlbauer (2003-)		9	Mastered calculus at age 9, completed BS in electrical engineering at age 15 (see: youngest college graduates) at University of Virginia.
14.	Michael Grost (1954-)	$IQ_{E}\,$ =200	10	Before age 8, had worked 2 to the 80th power, on a black board, in two hours time; mother could not help much with calculus questions, so at age 10 enrolled at Michigan State University. (Ѻ)
15.	Sky Choi (1997-)		11	Taking Calculus II, Physics with Calculus I, at age 12 (2009), at Florida International University. (Ѻ)
16.	John Mill (1806-1873)	$IQ_{R}\,$ =185\|#85 $IQ_{E}\,$ =200	11	Learned calculus by age 11. [1]
17.	Albert Einstein (1879-1955)	$IQ_{R}\,$ =220\|#2 $IQ_{E}\,$ =225	12	Taught himself calculus at age 12; integral and differential calculus by 13 (Ѻ) (Ѻ); in 1935, a rabbi in Princeton showed Einstein a clipping of the Ripley’s column with the headline “Greatest living mathematician failed in mathematics.” Einstein laughed. “I never failed in mathematics,” he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus” (Ѻ).
18.	Christopher Hirata (1982-)	$IQ_{R}\,$ =185\|#75 $IQ_{E}\,$ =225	12	Was taking college-level courses in physics and multivariable calculus; at age 14, upon arriving at Caltech, he registered one of the highest scores in history on the Institute's mathematics diagnostic tests, thereby enabling him to forego freshman calculus and sophomore differential equations for a more difficult upper-division class (Ѻ).
19.	Richard Feynman (1918-1988)	$IQ_{R}\,$ =190\|#35	13	Was reading Calculus for the Practical Man at age 13 (Ѻ), and had learned differential and integral calculus by age 13 (Ѻ) or age 15. (Ѻ)

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Invention | Calculus

See main: Prodigies and calculus; See also: Greatest mathematician ever; History of differential equations

An interesting benchmark, among individuals claiming or being cited with a 200+ IQ, as well as other unknown IQs listed on this page, is the age at which calculus was learned. Firstly, of course, Newton (1665) and Leibniz (1674), independently invented calculus and later differential equations:

Isaac Newton
(1643-1727) at age 22 (1665) invented the first form of the calculus, which he called "the method of fluxions and fluents" (Ѻ) (Ѻ).
Gottfried Leibniz
(1646-1716) at age 28 (1674) independently invented his own variant of the calculus (Ѻ).

	Isaac Newton (1643-1727)	at age 22 (1665) invented the first form of the calculus, which he called "the method of fluxions and fluents" (Ѻ) (Ѻ).
	Gottfried Leibniz (1646-1716)	at age 28 (1674) independently invented his own variant of the calculus (Ѻ).


Korean child prodigy Kim Ung-Yong (1963-) solving a differential equation at age 7 on the Japanese Fuji TV show in 1969. (Ѻ)

Korean child prodigy Kim Ung-Yong (1963-) solving a differential equation at age 7 on the Japanese Fuji TV show in 1969. (Ѻ)

After the publication of Leibniz’s calculus publications, in 1684-1686, James Bernoulli and John Bernoulli began to work with him in the initial development of Leibnizian calculus—during which time James Bernoulli introduced the term “integral”, in suggesting the name “calculus integralis”, in place of Leibnitz’s original term “calculus summatorius”, for the inverse of “calculus differentialis”. [3]

Swiss mathematician Leonhard Euler (1707-1783), sometime in or around his age 15 completion of university studies, learned mathematics from John Bernoulli, and thereafter would pen some 75-volumes, becoming the most prolific mathematician of all time, ranking him, according to C.H. Edwards, along with Archimedes, Newton, and Gauss, as the one of the big four “incomparable giants of mathematics.” [3]

At age 22, Marquis de Condorcet (1743-1794) published his An Essay on the Integral Calculus, which Jean d’Alembert praised as “work indicating great talent”, and about which Joseph Lagrange said “it opens up for us a new field for the perfection of integral calculus.” [1]

Keys
The following are IQ keys:

IQ_{R}\,

is The currently-estimated via meta-analysis genius ranking studies reality or real IQ as shown with top 500 geniuses ranking #.

IQ_{E}\,

is the highest-known IQ estimate, per sources, test calculations, ratio IQs, etc.

References
1. Cox, Catharine, M. (1926). Early Mental Traits of Three Hundred Geniuses (Genetic Studies of Genius Series) (calculus, 3+ pgs.). Stanford University Press.
2. List of child prodigies – Wikipedia.
3. Edwards, C.H. (1994). The Historical Development of the Calculus (pg. 268). Springer.

Videos
● Mueller, Scott. (2012). “6 Year Old Prodigy Solving a Problem Using Some Calculus” (Ѻ), YouTube, Oct 24.
● Anon. (2012). “African Child Math Genius” (Ѻ), two 8-year olds who passed the Cambridge A-level maths (supposedly a world record), Jan 1.