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Greatest mathematician ever
#  Person  Metaanalysis Ranking  Publication 
1  Leonhard Euler (17071783)  (4,4,4,4,1) (12%) (64283)  
2.  Carl Gauss (17771855)  (7,3,2,5,2) (10%) (50699)  
3.  Isaac Newton (16431727)  (1,1,1,0,10) (1%) (9199)  "On the Quadrature of Curves" (1706) 
4.  Euclid (c.340280BC)  (6,6,3,0,5) (8%)  Elements (c.300BC) 
5.  Archimedes (287212BC)  (8,2,0,0,3) (10%)  The Method of Mechanical Theorems (c.250BC) 
6.  Rene Descartes (15961650)  (9,17,9,0,9) (2%)  "The Geometry" (1637) 
7.  Joseph Lagrange (17361813)  (3,8,0,0,6) (61065) (6%)  
8.  Gottfried Leibniz (16461716)  (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.  Henri Poincare (18541912)  (90,7,6,0,20)  
10.  Pythagoras (c.570490BC)  (0,29,0,1,8) (3%)  
11.  Bernhard Riemann (18261866)  (38,5,7,0,21)  
12.  David Hilbert (18621943)  (0,9,5,0,24) (20414)  
13.  Girolamo Cardano (15011576)  (10,91,11,3,0)  
14.  Pierre Fermat (16011665)  (17,12,0,0,13)  
15.  Felix Klein (18491925  (9,45,0,0,11)  
16.  Georg Cantor (18451918)  (0,25,13,6,30) (1)  
17.  Évariste Galois (18111832)  (84,14,8,0,23)  
18.  Blaise Pascal (16231662)  (19,35,10,0,41) 
Metaanalysis ranking
The adjacent box shows a combined metaanalysis 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.
Metaanalysis 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 TheTopTens.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.
More ranking lists will be added as time allows.
Eells’ 1962 rankings
See main: Eells 100 mathematiciansIn 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. AdrienMarie Legendre
12. Pitagora
13. Gaspard Monge
14. Jean D'Alembert
15. Agustin 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. Regiomontanus26. 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. JeanVictor 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 Stevin51. 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 alKhwārizmi
74. Roger Cotes
75. Abraham De Moivre76. George Boole
77. Karl Weierstrass
78. Sophus Lie
79. Nikolai Lobachevsky
80. Ahmes (the scribe)
81. JeanCharles Borda
82. Eugenio Beltrami
83. Paolo Frisi
84. Évariste Galois
85. Evangelista Torricelli
86. JeanÉtienne Montucla
87. Otto Hesse
88. Jordanus de Nemore
89. Plato
90. Henri Poincare
91. Jakob Steiner
92. Edmond Halley
93. AndréMarie Ampere
94. Guillaume L'Hospital
95. William Thomson
96. Boethius
97. Ehrenfried Tschirnhausen
98. Bhaskara II
99. Eratosthenes
100. Zeno of Elea
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 minibiographies, the single page has now grown to over 100 kilobites).”
The page, 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 alKhwārizmi (73)
27. Arthur Cayley (72)
28. Emma Noether (0)
29. Pythagoras (0)
30. Leonardo Fibonacci (21)
31. Kurt Gödel (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. JeanVictor Poncelet (37)
52. Archytas of Tarentum (0)
53. Jacob Bernoulli (28) (Bernoulli family)
54.
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) Runnersup 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), whose revolutionary discoveries are 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) 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. 
TheTopTens.com’s 2012 listing
The following is the 2012 current ranking (by percentage vote) of TheTopTens.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. Aryabhatta (9%) (0,32,0,0)
5. Euclid (8%) (6,6,3,0)
6. Joseph Lagrange (6%) (3,8,0,0)
7. Gottfried Leibnitz (6%) (2,10,0,0)
8. Pythagoras (3%) (0,29,0,1)
9. Rene Decartes (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 AlKhowarizmi
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 Minkowski51. 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. JeanVictor 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.
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, told to the Queen of Prussia
“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 (date), Publication [8]
Images
The following is a related 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 overstressing").
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. 7882). Oxford University Press.
5. Bellos, Alex. (2010). “The 10 Best Mathematicians”, The Guardian, Apr 10.
6. Greatest Mathematician of All Time (2012) – TheTopTens.com.
7. Leonard Euler (banner) – StandardTutorials.com.\
8. MyintU, TYn, and Debnath, Lokkenath. (2007). Linear Partial Differential Equations for Scientists and Engineers (pdf) (pg. vii). Springer, 2011.
External links
● Greatest mathematician of All Time (2009) – TheScienceForum.com.
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