Foreword by Professor Emeritus of the University of Athens Maro K. Papathanasiou .

It is an eternal axiom of comparison the saying "The subject is to the superior" . From this principle it was not possible to exclude the present work of Diophantus "On Polygonal Numbers". The fact that a minimal part of it survived (only 4 propositions and a problem with an incomplete proof survived), was enough to establish it as the "poor relative" of the "Arithmetic" of the same author.

Another reason that contributed to the marginalization of this work is the recognition of "Arithmetic" as the first form of Algebra in the World.

But an in-depth study overturns the "minor project" view. "On Polygonal Numbers" has great evidential force. The geometric proofs of the four surviving propositions show great imagination and keen mathematical intuition. The highlight of the work, however, is the problem that follows the 4 propositions and of which only a part of the proof survives. This section led notable later mathematicians to interesting completions of the solution.