The author describes how the historiography of ancient Greek mathematics, around 1970 seemingly a topic on which everything that could be known (given the source situation) was already known, has returned to new but different life in recent decades. ``With some oversimplification'', the conclusion (p. 139) sums up the changes that characterize this new life: (1) ``Pythagoras [the mathematician] out, Pythagoreans in (but without attributing to them a monopoly over the mathematical sciences'' -- and indeed with global doubts as to whether it is warranted to speak at all of ``Pythagorean mathematics'' (p. 138). (2) ``Fifth century out, fourth and third centuries in'', as a consequence of the detailed study of sources, of which the fifth century has left us none. (3) ``Mathematical reconstructions out, textual studies in'', perhaps in consequence of declining confidence that our mathematical understanding is a ``universal reason'' (p. 134) that allows us to reconstruct how early Greek mathematicians must have thought. ``Textual studies'' as intended by the author includes attention to the role of diagrams, to the detailed logical build-up of works, and to the Greek mathematicians' use of the theoretical tools at their disposal (the author's own work, which he is to modest to advertise). (4) ``What the Greeks could and should have done out, but what they actually did in'' (reviewer's observation: thus a return to the sound interpretation of Ranke's Wie es eigentlich gewesen). Thus, ``the history of Greek mathematics (and probably the history of mathematics in general) has become a branch of the history of ideas more than a branch of mathematics, as it used to be''. The epitaph (p. 136) of the much regretted Wilbur Knorr (1945-1997) should be quoted: ``the greatest historian of Greek mathematics in the second half of the twentieth century (and the restriction `second half' may be unnecessary)''.