 We may have a fair amount of information about what Speusippus thought about numbers, preserved in pseudo-Iamblichus’ Theologumena arithmeticae (already mentioned). This book is a compilation from various authors: Anatolius, Nicomachus of Gerasa, possibly Iamblichus himself, possibly authors unknown. It discusses various properties of each of the first ten numbers. When it gets to the number 10, the ‘decad’, after a section that looks as if it descends from Nicomachus, it begins to speak of Speusippus and a book of his which it says was entitled ‘On Pythagorean Numbers’ and was compiled from various Pythagorean writings, especially those of Philolaus (82.10–15: that the book had that title and that Philolaus or any other Pythagorean was a source for Speusippus are both problematic claims). After what purports to be a description of the book (82.15–83.5), it introduces a long quotation from Speusippus himself concerning the number 10.