Is God a Mathematician_ - Mario Livio [121]
the philosopher Iamblichus reports: Iamblichus ca. 300 ADa, b.
to the Pythagoreans, God was not: See discussion in Netz 2005.
“the safest generalization that can be made”: Whitehead 1929.
Who was this relentless seeker: The titles of texts about Plato and his ideas can, of course, by themselves fill an entire volume. Here are just a few texts that I found to be very helpful. On Plato in general: Hamilton and Cairns 1961, Havelock 1963, Gosling 1973, Ross 1951, Kraut 1992. On mathematics: Heath 1921, Cherniss 1951, Mueller 1991, Fowler 1999, Herz-Fischler 1998.
According to an oration by the fourth century: The oration was written in 362 AD, but it did not give any details on the contents of the inscription. The words of the inscription come from a marginal note in a manuscript of Aelius Aristides. The note may have been written by the fourth century orator Sopatros, and it reads (in a translation by Andrew Barker): “There had been inscribed at the front of the School of Plato, ‘Let no one who is not a geometer enter.’ [That is] in place of ‘unfair’ or ‘unjust’: for geometry pursues fairness and justice.” The note seems to imply that Plato’s inscription replaced “unfair or unjust person” in a sign that was common in sacred places (“Let no unfair or unjust person enter”) with the phrase “one who is not a geometer.” This story was later repeated by no fewer than five sixth century Alexandrian philosophers, and it eventually made its way into the book Chiliades, by the twelfth century polymath Johannes Tzetzes (ca. 1110–80). For a detailed discussion see Fowler 1999.
I was disappointed to discover: A summary of many unsuccessful archaeological attempts can be found in Glucker 1978.
The first century philosopher and historian: Discussed in Cherniss 1945, Mekler 1902.
To which the Neoplatonic philosopher: Cherniss 1945, Proclus ca. 450.
“What we require is that those who take”: Plato ca. 360 BC.
“The science of figures, to a certain degree”: Washington 1788.
is no more real than shadows projected: An interesting discussion of the allegory can be found in Stewart 1905.
Plato’s views formed the basis: For interesting discussions of Platonism and its place in the philosophy of mathematics, see Tiles 1996, Mueller 1992, White 1992, Russell 1945, Tait 1996. For excellent presentations in popular texts, see Davis and Hersh 1981, Barrow 1992.
mathematics becomes closely associated with the divine: For a discussion of this topic see Mueller 2005.
He argued that in true astronomy: Plato’s comments on astronomy and planetary motion appear in the Republic (Plato ca. 360 BC), in Timaeus, and in Laws. G. Vlostos and I. Mueller discuss the implications of Plato’s position (Vlostos 1975, Mueller 1992).
to help publicize a novel entitled: The novel is Uncle Petros and Goldbach’s Conjecture, by A. K. Doxiadis (Doxiadis 2000).
innocent-looking example known as Catalan’s conjecture: For a detailed description see Ribenboim 1994.
Some mathematicians, philosophers, cognitive scientists: I shall discuss these opinions extensively in chapter 9.
“According to the prophets, the last”: Bell 1940.
Chapter 3. Magicians: The Master and the Heretic
“Some existing things are natural”: Aristotle ca. 330 BCa, b; see also Koyré 1978.
Using a clever thought experiment: Galileo 1589–92.
virtually complete system of logical inference: This and other logical constructs will be discussed extensively in chapter 7.
When the historian of mathematics: Bell 1937.
written by one Heracleides: This is mentioned in commentaries on the Measurement of a Circle by the mathematician Eutocius (ca. 480–540 AD); see Heiberg 1910–15.
more interested in the military accomplishments: Plutarch ca. 75 AD.
Archimedes was born in Syracuse: His year of birth has been determined based on the Chiliades, by the twelfth century Byzantine writer Johannes Tzetzes.
Archimedes spent some time in Alexandria: Evidence discussed in Dijksterhuis 1957.
This immediately triggered a solution: The Roman architect Marcus Vitruvius Pollio (first