From Selected Topics in the History of Mathematics by Aaron Strauss (1973):
Today Pythagoras is known predominantly as a mathematician. However, in his own day and age (which was also the day and age of Buddha, Lao-Tsa, and Confucious), he was looked upon as the personification of the highest divine wisdom by his followers to whom he preached the immortality of the soul. The whole lot of them were often ridiculed by ancient Greek society as being superstitious, filthy vegetarians. . . .
Pythagorean number theory was closely related to number mysticism. Odd numbers were male while even numbers were female. (Shakespeare: “there is divinity in odd numbers”). Individual integers had their own unique properties:
1 generator and number of reason
2 1st female number – number of opinion
3 1st male number – number of harmony, being composed of unity and diversity
4 number of justice or retribution (square of accounts)
5 number of marriage, being composed of the first male and female numbers
6 number of creation
7 signified the 7 planets and 7 days in a week
10 holiest number of all composed of 1+2+3+4 which determine a point, a line, and space respectively (later it was discovered that 10 is the smallest integer n for which there exist as many primes and nonprimes between 1 and n)
17 the most despised and horrible of all numbers
The rectangles with dimensions 4 x 4 and 3 x 6 are interesting in that the former has area and perimeter equal to 16 and the latter has area and perimeter equal to 18. Possibly 17’s horror was kept under control by being surrounded by 16 and 18.
The whole book (actually comb-bound lecture notes) is great. It’s too bad Strauss died so young. I pulled it off the shelf to check my memory following this blog discussion. Indeed I’d been confused. I’d remembered 4 being the number of justice and 17 being the evil number, so I just assumed that the Pythagoreans viewed even numbers as male and odd numbers as female.
Just imagine what these ancient Greeks would’ve been able to do, had they been given the modern tools of statistical significance. I can see it now:
Pythagoras et al. (-520). Are numbers gendered? Journal of Experimental Psychology: General, Vol. -2390, pp. 31-36.