In intellectual rankings, greatest mathematician ever is an epitaph given to a person, depending on ranking methodology, some rankings of which are listed below, that classify, list, or describe someone as being the greatest thinker in the field of mathematics of all time; the work-in-progress ranking of which is shown below; the IQ column shows the mathematician's real IQ and ranking position amid the top 1000 geniuses of all time:

#

Person
Other RankingsMeta-analysis Ranking
Publication


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1195
—
16		Euler 75Leonhard Euler
(1707-1783) 		(Cattell 1000:512)
[RGM:101|1,500+]
(Murray 4000:14|CS / 1|M)
(CR:103)		 (4,4,4,4,1) (12%) (64283)
2.190
—
23		Gauss 75Carl Gauss
(1777-1855)		(Cattell 1000:848)
[RGM:39|1,500+]
(Murray 4000:4|M)
(CR:73) 		(7,3,2,5,2) (10%) (50699)
3.220
—
2		 Newton 75Isaac Newton
(1643-1727) 		(Cattell 1000:14)
[RGM:3|1,500+]
(Murray 4000:2|CS / 1|P / 2|M)
(CR:595) 		(1,1,1,0,10) (1%) (9199)"On the Quadrature of Curves" (1706)
4.185
—
55		Euclid 75Euclid
(c.340-280BC)		(Cattell 1000:501)
[RGM:50|1,500+]
(Murray 4000:19|CS / 3|M)
(CR:65)		(6,6,3,0,5) (8%) Elements (c.300BC)
5.190
—
39		Archimedes 75Archimedes
(287-212BC)		(Cattell 1000:414)
[RGM:9|1,330+]
(Murray 4000:20|M / 5|T)
(CR:28)		(8,2,0,0,3) (10%)The Method of Mechanical Theorems (c.250BC)
6.195
—
13		Descartes 75Rene Descartes
(1596-1650) 		(Cattell 1000:23)
[RGM:33|1,500+]
(Murray 4000:6|CS / 7|M / 4|WP)
(CR:290) 		(9,17,9,0,9) (2%) "The Geometry" (1637)
7.190
—
24		Lagrange 75Joseph Lagrange
(1736-1813)		(Cattell 1000:512) [RGM:558|1,500+]
(CR:114) 		(3,8,0,0,6) (61065) (6%)
8.195
—
21		Gottfried Leibniz 75 newGottfried Leibniz
(1646-1716)
(Cattell 1000:34)
[RGM:32|1,500+]
(Murray 4000:14|CS / 6|M / 11|WP)
(CR:252) 		(2,10,0,0,7) (66592) (6%)"A New Method for Maxima and Minima, and Also for Tangents, Which Stops at Neither Fractions nor Irrational Quantities, and a Singular Type of Calculus for These" (1686)
9.190
—
44		 Henri Poincare 75Henri Poincare
(1854-1912)		[RGM:471|1,500+]
(CR:64) 		(90,7,6,0,20)
10.180
—
86		Pythagoras 75Pythagoras
(c.570-490BC) 		(Cattell 1000:89)
[RGM:15|1,500+]
(CR:86)		(0,29,0,1,8) (3%)
11.180
—
115		Bernhard Riemann 75Bernhard Riemann
(1826-1866) 		[RGM:280|1,500+]
(Murray 4000:10|M)
(CR:14) 		(38,5,7,0,21)
12.175
—
215		David Hilbert 75David Hilbert
(1862-1943) 		[RGM:421|1,500+]
(Murray 4000:11|M) 		(0,9,5,0,24) (20414)
13.175
—
292		Girolamo Cardano 75Gerolamo Cardano
(1501-1576) 		(Murray 4000:14|M)
(CR:8)		(10,91,11,3,0)
14.175
—
224		Pierre Fermat 75Pierre Fermat
(1601-1665)		(Cattell 1000:893)
[RGM:628|1,500+]
(Murray 4000:5|M)
(CR:8) 		(17,12,0,0,13)
15.170
—
394		Felix Klein 75Felix Klein
(1849-1925)
(9,45,0,0,11)
16.
Georg Cantor 75Georg Cantor
(1845-1918)		[RGM:478|1,500+]
(Murray 4000:8|M)		(0,25,13,6,30) (1)
17.165
—
455		Évariste Galois 75Evariste Galois
(1811-1832)		[RGM:517|1,500+] (84,14,8,0,23)
18.185
—
47		Pascal 75Blaise Pascal
(1623-1662) 		[RGM:42|1,500+]
(Murray 4000:9|M)		(19,35,10,0,41)
19.160
—
528		Augustin Cauchy 75Augustin Cauchy
(1789-1857)		 [RGM:315|1,500+]
(Murray 4000:18|M)
(CR:10)		(15,21,0,0,15)
20.175
—
307		Jacob Bernoulli 75Jacob Bernoulli
(1654-1705)		(Murray 4000:12|M)
(CR:12) 		(28,53,0,0,56)
21.175
—
276		Adrien Legendre 75Adrien Legendre
(1752-1833)		(Murray 4000:16|M) (11,0,0,0,0)
22.
Diophantus 75Diophantus
(c.207-293) 		(Murray 4000:13|M) (26,38,0,0,0)
23.
 Francois Viete 75Francois Viete
(1540-1603)		(Murray 4000:15|M) (22,48,0,0,0)
24.
 Leonardo Fibonacci 75Leonardo Fibonacci
(1170-1250) 		(Murray 4000:19|M) (21,30,0,0,0)
25.
John Wallis 75John Wallis
(1616-1703)		(Murray 4000:17|M) (34,0,0,0,0)
26.185
—
84		Jean d'Alembert 75 Jean d'Alembert
(1717-1783)		(Cattell 1000:124)
(CR:28) 		(14,44,0,0,0)
27.
William Hamilton 75William Hamilton
(1805-1865)
(34,39,0,0,0)
28.190
—
33		Christiaan Huygens 75Christiaan Huygens
(1629-1695)
(Eells 100:24)
39.
Srinivasa Ramanujan 75Srinivasa Ramanujan
(1887-1920)
(25,0,19,0,0)
30.190
—
30		Pierre Gassendi 75Pierre Gassendi
(1592-1655)

“If we take the mathematics, and those mixed sciences to which they are applicable, it will be universally admitted that their most successful cultivators in France during the seventeenth century were Descartes, Pascal, Fermat, Gassendi, and Mersenne.”
— Henry Buckle (1856), History of Civilization, Volume One (pg. 499-50)

(add)

Meta-analysis ranking
The adjacent box shows a combined meta-analysis summary ranking (combination of 5 different rankings below) of the greatest mathematicians ever (known descendants listed as well), the numbers in brackets being the rank of each mathematician of each ranking study (below), in chronological order. Meta-analysis ranking positions (a,b,c,d,e) come from the following sources:

a. W.C. Eells (1962) | mathematics professor
(100 greatest list)
b. James Allen (1998) | mathematics historian
(180 greatest list)
c. Clifford Pickover (2001) | science historian
(10 greatest list)
d. Alex Bellos (2010) | mathematician
(10 greatest list)
e. Top 10 Lists (2012) | public vote
(64 choices)

The "percentage" is the percentage of votes from the 2012 The-Top-Tens.com’s listing of the “Greatest Mathematician of All Time”, the ranking of this list shown by position five or "e" in the bracketed listing. The hyperlinked number, shown next to some mathematicians, e.g. Hilbert (20,414), shows the number of descendents, according to the data base at the mathematics genealogy project, a sixth factor taken into account in the meta analysis ranking.

Eells’ 1962 rankings
See main: Eells 100 mathematicians
In the 1962 issue of Mathematics Teacher, American mathematician W.C. Eells’ published a listing of who he considered to be 100 greatest mathematicians of all time: [1]

1. Isaac Newton
2. Gottfried Leibniz
3. Joseph Lagrange (Euler genealogy)
4. Leonhard Euler (Euler genealogy)
5. Pierre Laplace
6. Euclid
7. Carl Gauss
8. Archimedes
9. Rene Descartes
10. Gerolamo Cardano
11. Adrien-Marie Legendre
12. Pitagora
13. Gaspard Monge
14. Jean d'Alembert
15. Augustin Cauchy
16. Joseph Fourier
17. Pierre Fermat
18. John Napier
19. Blaise Pascal
20. Apollonius
21. Leonardo Fibonacci
22. François Viete
23. Ptolemy
24. Christiaan Huygens (Euler genealogy)
25. Regiomontanus		26. Diophantus
27. Colin Maclaurin
28. Jacob Bernoulli (Bernoulli family)
29. Pappus
30. Bonaventura Cavalieri
31. Carl Jacobi
32. Johann Bernoulli (Bernoulli family)
33. John Wallis
34. William Hamilton
35. Niccolò Tartaglia
36. Heron
37. Jean-Victor Poncelet
38. Bernhard Riemann
39. Siméon Poisson
40. Niels Abel
41. Michel Chasles
42. Luigi Cremona
43. Gilles Roberval
44. Roger Boscovich
45. Galileo Galilei
46. Alexis Clairaut
47. Johann Lambert
48. Isaac Barrow
49. Jacques Strum
50. Simon Stevin		51. Augustus de Morgan
52. Brook Taylor
53. Johannes Kepler
54. Daniel Bernoulli (Bernoulli family)
55. Girard Desargues
56. Henri Briggs
57. James Sylvester
58. Lazare Carnot
59. Pierre Maupertuis
60. Charles Babbage
61. Charles Hermite
62. Thales
63. Henry Smith
64. Sofia Kovalevskay
65. Luca Pacioli
66. Hippocrates (of Chois)
67. Gerbert
68. Alfred Clebsch
69. Julius Plucker
70. Hermann Grassmann
71. Peter Dirichlet
72. Arthur Cayley
73. Muhammed al-Khwārizmi
74. Roger Cotes
75. Abraham De Moivre		76. George Boole
77. Karl Weierstrass
78. Sophus Lie
79. Nikolai Lobachevsky
80. Ahmes (the scribe)
81. Jean-Charles Borda
82. Eugenio Beltrami
83. Paolo Frisi
84. Evariste Galois
85. Evangelista Torricelli
86. Jean-Étienne Montucla
87. Otto Hesse
88. Jordanus de Nemore
89. Plato
90. Henri Poincare
91. Jakob Steiner
92. Edmond Halley
93. Andre Ampere
94. Guillaume L'Hospital
95. William Thomson
96. Boethius
97. Ehrenfried Tschirnhausen
98. Bhaskara II
99. Eratosthenes
100. Zeno of Elea

The key (Eells 100:#) is shorthand for each persons W.C. Eells ranking.

Allen's 1998 ranking
In 1998, American computer programmer (turned mathematics history hobbyist) James Allen decided to practice his HTML skills by making a listing of the top thirty greatest mathematicians listing. In his own words: [2]

“When I was first learning to create html pages, for some reason I chose to build a list of great mathematicians as a practice page, even though I wasn't qualified to make such a list without a lot of advice. Since then I've invested a lot of time reading mathematical histories and biographies and revising the page. I'm proud of it now: please read it! (With 60 mini-biographies, the single page has now grown to over 100 kilobites).”

Allen's ranking, as of 2012, has become Google search top result for "greatest mathematicians" and currently lists the 100 “Greatest Mathematicians of All Time”, ranked in approximate order of greatness, born before 1930, whose work has breadth, depth, and historical importance (the numbers in brackets being the position in Eells' 1962 ranking): [3]

1. Isaac Newton (1)
2. Archimedes (8)
3. Carl Gauss (7)
4. Leonhard Euler (4) (Euler genealogy)
5. Bernhard Riemann (38)
6. Euclid (6)
7. Henri Poincare (90)
8. Joseph Lagrange (3)
9. David Hilbert (0)
10. Gottfried Leibniz (2)
11. Alexandre Grothendieck (0)
12. Pierre Fermat (17)
13. Niels Abel (40)
14. Évariste Galois (84)
15. John Neumann (0)
16. Karl Weierstrass (77)
17. Rene Descartes (9)
18. Carl Jacobi (31)
19. Srinivasa Ramanujan (0)
20. Brahmagupta (0)
21. Augustin Cauchy (15)
22. Peter Dirichlet (71)
23. Hermann Weyl (0)
24. Eudoxus of Cnidus (0)
25. Georg Cantor (0)		26. Muhammed al-Khwārizmi (73)
27. Arthur Cayley (72)
28. Emma Noether (0)
29. Pythagoras (0)
30. Leonardo Fibonacci (21)
31. Kurt Godel (0)
32. Aryabhata (0)
33. Charles Hermite (0)
34. Apollonius of Perga (0)
35. Blaise Pascal (19)
36. Pierre Laplace (5)
37. Richard Dedekind (0)
38. Diophantus (26)
39. William Hamilton (34)
40. Bháscara Áchárya (0)
41. Gaspard Monge (13)
42. George Boole (76)
43. Stefan Banach (0)
44. Jean d'Alembert (14)
45. Felix Klein (0)
46. Ferdinand Eisenstein (0)
47. Jacques Hadamard (0)
48. Francois Viete (22)
49. Johannes Kepler (53)
50. Elie Cartan (0)		51. Jean-Victor Poncelet (37)
52. Archytas of Tarentum (0)
53. Jacob Bernoulli (28) (Bernoulli family)
54.

The shorthand (Allen 100:#) is key for each person's Allen top 100 mathematicians ranking.

Pickover's 2001 ranking
In American science biographer Clifford Pickover's listing in his 2001 Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, in which he devotes a chapter to "A Ranking of the 10 Most Influential Mathematicians", based on, supposedly, surveys and interviews with mathematicians (the numbers in the brackets being the position in Eells' 1962 ranking and Allen's 1998 ranking, respectively): [4]

1. Isaac Newton (1,1)
2. Carl Gauss (3,7)
3. Euclid (6,6)
4. Leonhard Euler (4,4)
5. David Hilbert (0,9)
6. Henri Poincare (90,7)
7. Bernhard Riemann (38,5)
8. Evariste Galois (84,14)
9. Rene Descartes (9,17)
10. Blaise Pascal (19,35)

Runners-up Girolamo Cardano, Kurt Godel, Georg Cantor, and John Napier. 		Bellos 2010 top 10
The following is the 2010 listing of the “10 Best Mathematicians” by Brazilian mathematician Alex Bellos (author of the recent book Alex's Adventures in Numberland), ordered via ranking of "revolutionary discoveries said to have changed the world" (the numbers in the brackets being the position in Eells' 1962 ranking, Allen's 1998 ranking, and Pickover's 2001 ranking, respectively): [5]

1. Pythagoras (0,29,0)
2. Hypatia (0,~140,0)
3. Girolamo Cardano (10,91,11)
4. Leonhard Euler (4,4,4)
5. Carl Gauss (7,3,2)
6. Georg Cantor (0,25,13)
7. Paul Erdos (0,95,0)
8. John Conway (0,~140,0)
9. Grigori Perelman (0,~140,0)
10. Terrance Tao (0,0,0)

The last three of which, to note, are still reactive (living) and seem to be more of celebrity mathematicians, rather than the "greatest" as history may show.

The-Top-Tens.com’s 2012 listing
The following is the 2012 current ranking (by percentage vote) of The-Top-Tens.com’s listing of the “Greatest Mathematician of All Time”: [6]

1. Leonhard Euler (12%) (4,4,4,4)
2. Carl Gauss (10%) (7,3,2,5)
3. Archimedes (10%) (8,2,0,0)
4. Aryabhata (9%) (0,32,0,0)
5. Euclid (8%) (6,6,3,0)
6. Joseph Lagrange (6%) (3,8,0,0)
7. Gottfried Leibniz (6%) (2,10,0,0)
8. Pythagoras (3%) (0,29,0,1)
9. Rene Descartes (2%) (9,17,9,0)
10. Isaac Newton (1%) (1,1,1,0)
11. Felix Klein (9,45,0,0)
12. Brahmagupta (0,20,0,0)
13. Pierre Fermat (17,12,0,0)
14. Alexandre Grothendieck (0,11,0,0)
15. Augustin Cauchy (15,21,0,0)
16. Apollonius
17. Pierre Laplace (5,36,0,0)
18. Niles Abel (40,13,0,0)
19. John Neumann (0,15,0,0)
20. Henri Poincare (90,7,6,0)
21. Bernhard Riemann (38,5,7,0)
22. Bhascar Acharya
23. Évariste Galois (84,14,8,0)
24. David Hilbert (0,9,5,0)
25. Srinivasa Ramanujan (0,19,0,0)		26. Karl Weierstrass
27. Peter Dirichlet
28. Omar Al Khayyam
29. Jean Serre
30. Georg Cantor (0,25,13,6)
31. Muhammad Al-Khowarizmi
32. Sridhar Acharya
33. Johannes Kepler (53,49,0,0)
34. Albert Einstein
35. Hippocrates
36. James Maxwell
37. Galileo Galilei
38. Jacob Steiner
39. Aristotle
40. Kurt Godel
41. Blaise Pascal (19,35,10,0)
42. Abu Biruni
43. Christiaan Huygens
44. Liu Hui
45. Nicolai Lobachevsky
46. Alex Clairaut
47. Jean Darboux
48. Panini
49. Johann Lambert
50. Hermann Minkowski		51. Pafnuti Chebyshev
52. Charles Hermite
53. Richard Dedekind
54. George Boole
55. Andrey Kolmogorov
56. Jacob Bernoulli
57. Hipparchus
58. Alhazen
59. Godfey Hardy
60. Andrew Weil
61. Jean-Victor Poncelet
62. Jacques Hadamard
63. Francois Viate
64. Elie Cartan

The numbers in the brackets being the position in Eells' 1962 ranking, Allen's 1998 ranking, Pickover's 2001 ranking, Bellos's 2010 ranking, respectively.

Leonard Euler
A related greatest mathematician image made by Indian mathematician Vinod Sir. [7] Euler also gets extra ranking points for blowing out both his eyes in the name of the proof; see: genius page (section: "physical and mental over-stressing").
Quotes
The following are notable and or relevant quotes:

“Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half.”
— Gottfried Leibniz (1700), told to the Queen of Prussia

“If we take the mathematics, and those mixed sciences to which they are applicable, it will be universally admitted that their most successful cultivators in France during the seventeenth century were Descartes, Pascal, Fermat, Gassendi, and Mersenne. Fermat, among these, was one of the most profound thinkers of the seventeenth century, particularly as a geometrician, in which respect he was second only to Descartes. The most important steps are those concerning the geometry of infinites, applied to the ordinates and tangents of curves; which he completed in or before 1636.”
— Henry Buckle (1856), History of Civilization, Volume One (pg. 499-50)

“The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.”
— Felix Klein (c.1900) (Ѻ)

“One of the properties inherent in mathematics is that any real progress is accompanied by the discovery and development of new methods and simplifications of previous procedures … The unified character of mathematics lies in its very nature; indeed, mathematics is the foundation of all exact natural sciences.”
— David Hilbert (c.1910), Publication [8]

“You will see it written that Hadamard was the last of the universal mathematicians (see: last person to know everything) —the last, that is, to encompass the whole of the subject, before it became so large that this was impossible. However, you will also see this said of Hilbert, Poincare, Klein, and perhaps of one or two other mathematicians of the period. I don't know to whom the title most properly belongs, though I suspect the answer is actually Gauss.”
— John Derbyshire (2003), Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics [9]

See also
● Greatest chemist ever
● Greatest physicist ever
● Greatest thermodynamicist ever
● Greatest philosopher ever
● Greatest engineer ever		● Polymath
● Last person to know everything
● Universal genius
● Last universal genius 		● Genius IQs (top 1000 geniuses)
● IQ: 200+ | Smartest person ever
● IQ: 150+ | Smartest woman ever

References
1. Eells, W.C. (1962). “100 Greatest Mathematicians of All Time” (link), Mathematics Teacher, 7(55).
2. James Dow Allen (about) – FabPedigree.com.
3. Allen, James Dow. (1998). “The Greatest Mathematicians of All Time”, FabPedigree.com.
4. Pickover, Clifford. (2001). Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning (ch. 36: A Ranking of the 10 Most Influential Mathematicians Who Ever Lived, pg. 78-82). Oxford University Press.
5. Bellos, Alex. (2010). “The 10 Best Mathematicians”, The Guardian, Apr 10.
6. Greatest Mathematician of All Time (2012) – The-Top-Tens.com.
7. Leonard Euler (banner) – StandardTutorials.com.
8. Myint-U, TYn, and Debnath, Lokkenath. (2007). Linear Partial Differential Equations for Scientists and Engineers (pdf) (pg. vii). Springer, 2011.
9. Derbyshire, John. (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (pg. 159) (Ѻ). Joseph Henry Press.

External links
● Greatest mathematician of All Time (2009) – TheScienceForum.com.

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