Cardano 12

From Hmolpedia
Jump to navigation Jump to search
The 1560 ranking of the top 12 "outstanding men in serious studies", by Gerolamo Cardano, from Archimedes (1st) to Vitruvius (12th).[1]

In genius studies, Cardano 12 (LH:12) refers to a list of twelve outstanding men, in the serious studies among the sciences, complied and ranked by Gerolamo Cardano, in 1550 to 1560, in his encyclopedic two-volume On the Subtle of Things.[1] It is one of the first attempts at genius ranking in history.


In 1550, Gerolamo Cardano, in his two-volume encyclopedia On the Subtlety of Things, in his chapter "On the Sciences", a chapter mostly on the geometrical of Euclid, some digression on optics, meteorology, music, and some astronomical notes, ends the chapter with a discussion on the ability to "know the future", citing historical examples such as the various prophets and seers of antiquity, e.g. Epimenides, the Sibyls, the oracles, etc., or to "natural arts", e.g. astrology, physiognomy, metoposcopy (forehead line reading), chiromancy (palm reading), navigation, agriculture, medicine, dream interpretation; or to prodigies, omens, and auguries, and other "discredited skills". Cardano says that because some of these are reliable and others unreliable, it would not be reputable to attend to them, nor safe to ignore them altogether. Then then says: "all truth is divine, and proceeds from the best".


On this so-called "ability to predict" is the hardest of all abilities platform, Cardano jumps to the following:

“In serious studies, outstanding men are found in more abundance, and I have chosen twelve of them, leaving to each his own judgement.”
— Gerolamo Cardano (1560), On the Subtlety of Things, Volume Two (pg. 816) [1]

Cardano, following this statement, then gives his "top 12" ranking, as tabulated below, changing per edition; those three names shown above his finalized "top 12" ranking (1560), he defines as "those who surpassed human powers and are regarded as closer to some divinity (symbolized: ↑D)"; those shown below, are runners up he discusses in passing, at the end of this top twelve ranking; the HR column shows each person current Hmolpedia top 2000 minds rankings (HR), if ranked:

# 1550/1554 1560 Hmolpedia Cardano commentary
↑D Ptolemy (IQ:175|#241) A person above outstanding talent, who surpassed human powers, and is regarded as closer to some divinity.
↑D Hippocrates (IQ:175|#235) A person above outstanding talent, who surpassed human powers, and is regarded as closer to some divinity.
↑D Plotinus (IQ:170|#421) A person above outstanding talent, who surpassed human powers, and is regarded as closer to some divinity.
1. Archimedes (IQ:190|#39) Archimedes is the first , not just an account over the works of his now published, but on account of the pieces of engineering used repeatedly to destroy the Roman forces, as Plutarch testifies. And his life of Marcus Marcellus, Plutarch describes a marvelous inventions of Archimedes, and we mentioned others just as remarkable, and the evidence of Galen, not so much on the first author untold subjects there's one beyond imitation. Nor the man who disdained ‘Greeklings’, a named used by Cicero for this sort of person, praising his talent, and searching for his tomb amid the ruins and brambles of the town of Syracuse.
2. Ptolemy Aristotle (IQ:195|#9) Second comes to Aristotle, the Stagirite, tutor of Alexander the Great of Macedonia, who did marvelous work on natural and divine things and on dialectic; it investigated life, habits, and anatomy of animals with wonderful flair on individual fields of study he wrote what met with approval, yet over the course of so many centuries no notable mistake could be found in his writings. Theophrastus and Duns Scotus envied his talent.
3. Aristotle Euclid (IQ:185|#54) On a similar criteria, the third place goes to Euclid, to Scotus [Duns Scotus], and to Ioannes Suisset [Swineshead] (whom ordinary people call the ‘calculator’), and with equal expectation; but you could should get preference through seniority and usefulness. He has two outstanding strengths: the unshakeable stability of the doctrines of the book of the Elements, and a perfection so complete that you could not rightly compare any other work to that one. It follows, that the only people who can distinguish truth from falsehood in difficult problems are those who have Euclid for a friend. He was descended from Megara, and he wrote much else that still survives, of equal subtlety, but much less useful.
4. Euclid Duns Scotus (IQ:150|#893) Next comes Ioannes Scotus [Duns Scotus], Scotland was his homeland, and his doctrine earned him an equal distinction everywhere as he settled teacher.
5. Duns Scotus John Suisset Ioannes Suisset [Richard Swineshead] was an inhabitant of the same island, with the sobriquet ‘calculator’; all posterity has striven to solve one single problem [argumentum] of his, which is contrary to experience about mutual action. People say that when he was old, we wept at not understanding his discoveries when reading about them. I think this makes it certain that, as I wrote in the book De Animi Immortalitate, the Barbarians are not our inferiors in talent, since under a foggy Sky and divided by a whole spear, Britain has sent forth two men of such distinguished talent.
6. John Suisset Apollonius (IQ:170|#385) The sixth place, goes to Apollonius of Perge, who was almost of an age with Archimedes. He wrote a notable books on the elements of conics, but of these up till now only the first four have been published, so foully defiled by the translator that you could not fairly even call them published.
7. Apollonius Archytas Next to him, but much senior, should be placed Archytas of Tarentum, so that an Italian too can take his seat among such distinguished men. Beside the flying pigeon of wood that he is said to have constructed, he found a genuine proof of how to place 2 lines in continued proportion between two other proposed lines, a proof that among ten other false ones Eutocius handed down.
8. Archytas Khwarizmi (IQ:170|#526) After him comes Mahomet son of Moses [Al Khwarizmi], the Arab, inventor, so to speak, of the art of algebra; through this invention, he got a name from the name of the art.
9. Khwarizmi Kindi (IQ:160|#763) Ninth, is Alchindus [Al Kindi], an Arab himself, an example of his publications, which Averroes remembered, is the surviving book on the basis of the six quantities, which we will hand on for printing, since there is nothing more gifted.
10. Kindi Jabir Aflah After him comes Heber the Spaniard [Jabir Aflah], for a very famous discovery: since Ptolemy searches with huge labor for a sixth out of the five quantities, this man with three in the same category looks for a fourth period and he altered much of the state of heaven for the better, so that you can readily grasp all the highest tides in cold weather are much less of a trouble to chilly natures.
11. Jabir Aflah Galen (IQ:170|#474) Eleventh, in subtlety, but most famous in the art is Galen, with his Methods, Pulses, and dissections. But it's so verbose, and so tedious in a zeal to contradict, that you could hardly stand anyone else; thereafter great deterioration of the arts took place, which the men of our own time have tried to make good. Those who regard Galen as equal to Hippocrates admit by that statement that they understand neither of them; Hippocrates is far more different from Galen than Galen is from any child.
12. Galen Vitruvius (IQ:165|#557) Last of all comes Vitruvius, and if he had written of his own discoveries, not those of others, he could have been classified with the first. Most distinguished in Vitruvius is the way his clocks worked, either though floats and water, or in adjustment to the rising of the stars from the zodiac, or by means of an analemma which is common to plane and spherical apertures. Hero vied with him.
Homer (IQ:175|#311) Who would not admire his passions.
Virgil (IQ:170|#393) Who would not admire his solemnity.
Cicero (IQ:180|#103) Who would not admire his ability to rouse pity and copiousness.
Quintilian Who would not admire the oratory and the effects linked to the meaning of worlds.

On the three in the "higher category" (Forrester, 2013), Cardano comments:

“To Galen, I owe my belief that I can understand many things; to Hippocrates, my knowledge of the arts; I admire Ptolemy because I can barely understand him. I link the fame of these men, because if the legacies of the rest had perished, with the treatises I have in mind and the assistance of which these men rely, I do not see why I could not restore the details, even if I could not. But I understand well enough that in my whole lifetime I could not create seven lines of the work of one of them.”
— Gerolamo Cardano (1560), On the Subtle of Things, Volume Two (pg. 820)

Cardano's list of 12 thinkers, in last two centuries or so, has become an underground classic of sorts, being referred to as Cardano's list of: "men excelled in the force of genius and invention" (Hutton, 1795), "twelve greatest minds" (Sarton, 1927), "greatest thinkers of all time" (Sarton, c.1930)[2], or "ten greatest intellects in history" (Durant, 1953), among other variants. Generally, it seems to be one of the first attempts at ranking geniuses, methodologically.


Of note, knowing that Cardano was the inheritor of the collected works of Leonardo Vinci (1452-1519 ACM), it is curious not to see Vinci in the above list, considering that we tend to rank Vinci so high presently? In fact, throughout Cardano's On the Subtle of Things, Vinci is only mentioned twice times, twice for his art works on anatomy, with a passing remark about a Last Supper (Vinci or not is uncertain), and for how Vinci, along with two other men, had attempted the art of flying, the two other men ending very badly. Either this has to do with the proximal genius effect, or Vinci has just become oversold, in modern times?


The following are related quotes:

Cardan, in his 16th book De Subtilitate, ranks Vitruvius as one of the 12 persons, whom he supposes to have excelled all men in the force of genius and invention; and would not have scrupled to have given him the first place, if it could be imagined that he had delivered nothing but his own discoveries. Those 12 persons were, Euclid, Archimedes, Apollonius Pergæus, Aristotle, Archytas of Tarentum, Vitruvius, Achindus, Mahomet Ibn Moses the inventor or improver of Algebra, Duns Scotus, John Suisset surnamed the Calculator, Galen, and Heber of Spain.”
— Charles Hutton (1795), Mathematical and Philosophical Dictionary (§: Vitruvius) [3]
Cardan named, as the ten greatest intellects in history, men not overwhelmingly Christian: Archimedes, Aristotle, Euclid, Apollonius of Perga, Archytas of Tarentum, al Khwarizmi, al-Kindi, Geber, Duns Scotus, and Richard Swineshead, all scientists except Duns.”
Will Durant (1953), The Story of Our Civilization, Volume Five: the Renaissance (pg. 692)[4]
Cardano prepared a list of the 12 men who "excelled all others in the force of genius and invention." This list includes eight from my List of 200: Archimedes, Euclid, Apollonius, al-Khowârizmi, Archytas, Aristotle, Ptolemy, al-Kindi, and four other names: John Duns Scotus, Richard Swineshead (aka John Suisset) the Calculator, Galen of Pergamum (physician), and Jabir ibn Aflah (astronomer and mathematician whose works were translated into Latin). (Sources show "Heber of Spain" as the 12th name; it is my assumption that this refers to Geber of Spain, an alternate name for Jabir ibn Aflah. There was another Geber, the very famous 8th-century scientist and chemist Jabir ibn Hayyan, and a "pseudo-Geber" named after Jabir ibn Hayyan; perhaps Cardano conflated these figures. However in another work, Cardano calls specific attention to Jabir ibn Aflah and writes that Regiomontanus borrowed his ideas from that Jabir.) When Copernicus obsoleted Ptolemy's cosmology during Cardano's lifetime, Cardano removed Ptolemy and added Marcus Vitruvius Pollio (engineer) to keep the list at twelve names.”
— James Allen (2013), “Discussion”, [5]

End matter


  1. 1.0 1.1 1.2 (a) Cardano, Gerolamo. (1550). On the Subtlety of Things (De Subtilitate rerum). Publisher, 1560.
    (b) Cardano, Gerolamo. (1560). The De Subtilitate of Girolamo Cardano, Volume One (translator: John Forrester). ACMRS, 2013.
    (c) Cardano, Gerolamo. (1560). The De Subtilitate of Girolamo Cardano, Volume Two (translator: John Forrester) (§16: On the Sciences, pgs. 773-822; top 12, pgs. 812-822. ACMRS, 2013.
  2. Sarton, George. (1967). Introduction to the History of Science (pg. 738). Williams.
  3. Hutton, Charles. (1795). Mathematical and Philosophical Dictionary (txt). Publisher.
  4. Durant, Will; Durant, Ariel. (1953). The Story of Our Civilization, Volume Five: the Renaissance, a History of Civilization in Italy from 1304 to 1576 (pg. 692). Publisher.
  5. Discussion (Greatest Mathematicians) –

Further reading

  • Sarton, George. (1927). Introduction to the History of Science, Volume One, from Homer to Omar Khayyam (Kindi, pg. 575). Carnegie.

External links