Questions of Originality in Greek Mathematics

  Heath devotes an entire chapter to the question of the originality of Diophantus. Was algebra his sole invention? Or like Euclid was he the compiler drawing from a number of earlier sources. The method of exhaustion did not originate with Archimedes or Euclid but was developed earlier by Eudoxus who improved on an argument on the squaring of the circle by the orator Antiphon. Eudoxus was a student of Archytas, a Pythagorean, but he also traveled to Heliopolis in Egypt to study there. Archytas is believed to be the founder of mathematical mechanics and is now given credit for the Mechanical Problems in the Corpus of Aristotle rather than Aristotle himself. It is similar in nature to the mechanics of Archimedes.

So ancient learning made its way down from one generation to the next along with new discoveries as they were acquired. The scarcity of papyrus or parchment may have led to the publication of more concise summaries of what was done earlier. In Diophantus one finds there is a concerted effort to reduce formulas. Another means of transmission of ancient knowledge was from teacher to student where the chief writing instrument was the slate. The petroglyph is an even more ancient method for transmission of culture. So could the pyramids also have been a vehicle for the passage of knowledge and skills to future generations either intentionally or unintentionally?

Supplemental (Jan 18): The blocks of the Egyptian pyramids don't appear to be stacked as neatly as they were to show the sum of the power series. This can be seen by looking at the corners. The heights of a layers appear to be uniform but the blocks don't always appear to have the same lengths. This may have been standard practice of construction in ancient Egypt. Also, when Galileo cites Aristole in his dialogues he may be referring to the Mechanical Problems which are now attributed to Archytas. The author of the Mechanical Problems was once referred to as pseudo-Aristotle by the classical scholars. In the Mechanical Problems some of the arguments are found to be lacking in rigor.