third century wisdom of Diophantus gives us the essential truth about teaching and learning mathematics

The Google facsimile of the 1621 edition of Diophantus’s Arithmetica lays out, in original Greek and Latin translation, the essentials for success in teaching and learning mathematics.  Also included is the translation of the second half by Heath.

When I first studied and learned to love mathematics I was beset by friends and family who stridently claimed that this field of study was closed to them because of some biological, or other, reason.  This always seemed to undervalue my own effort in getting off the first page.

Teachers of mathematics cannot be permitted to admit that nature is able to restrict the ability to learn the subject but the oriental wisdom of the student making their way to the master is a precondition for success when things seem difficult; in tales of martial arts the student must somehow prepare themselves to learn.


  1.  Mathematics appears rather difficult if one is not familiar with it.
  2. Students need energy, eagerness and enthusiasm.
  3. When such motivation is backed up by good teaching rapid learning results.

In school we struggle because of item 1 and bear our hearts to gain item 2, being so often rebuffed.  I suppose that we get paid for 1 and 2 because, when item 3 is achieved the job is it’s own reward.