PYTHAGORAS

Historia Mathematica, 1989

In this article, two questions are posed: Just how reliable is the evidence concerning Pythagoras's mathematical studies, and can we reconstruct his contribution to mathematics? All known fragments of evidence by fourth-century B.C. authors on Pythagoras's mathematical investigations are examined, and it is shown that all the discoveries they mentioned belong to the sixth century B.C. The opinion that the Pythagoreans ascribed their own discoveries to Pythagoras is refuted, and it is shown that we are able to establish logically his contribution to mathematics.Der Aufsatz behandelt die Frage, ob es sichere Zeugnisse über Pythagoras' mathematische Beschäftigungen gibt und ob wir auf dieser Grundlage seinen Beitrag zur Mathematik rekonstruieren können. Im Aufsatz werden Zeugnisse der Autoren aus dem 4 Jh. v.u.Z. über Pythagoras' mathematische Forschungen gesammelt, und es wird gezeigt, daß alle seine Entdeckungen wirklich dem Ende des 6 Jh. v.u.Z. angehören. Im Aufsatz wird die ältere Meinung abgelehnt, daß die Pythagoreer ihre Entdeckungen dem Pythagoras zugeschrieben haben, und es wird gezeigt, daß wir in der Lage sind, seinen Beitrag zur Mathematik abzugrenzen.

The College Mathematics Journal, 2009

Pythagoras can be seen as a mathematician and a mystical philosopher. His theory of numbers and his mystical philosophy of the transmigration of the soul are outstanding. There are various postulations as to the originality of Pythagoras in his philosophy. The question is how can we justify him as either a mathematician or mystic? Which of these thought mostly affect or has influence on mankind? The essence of this paper is to make clarifications on this issue.

Frequently considered, in earlier periods of Western culture, as a symbol or, at the very least, as an almost legendary individual,1 Pythagoras is nevertheless perceived during the Renaissance as retaining more of an historical consistency, and the reality of his existence remains generally unquestioned, if somewhat imprecise. Among other exponents of the supposed prisca theologia,2 he stands as a typical example of a single individual retaining the characteristics of a prophet, holy man, seeker of wisdom, political adviser, scientist, musician and philosopher alike, all qualities which play a central role in the culturally widened humanistic de��nitions of a "Pythagorean" philosophy. One must of course keep in mind that philosophy is here considered as being essentially of a revelatory nature, and much akin to a divine illumination, an empowerment which some of the Early Modern Humanists frequently bestowed on antique thinkers and religious ��gures,3 endowing them with a prophetic status almost equal to that hitherto reserved by Christianity for the Jewish Scriptures. As recently outlined by Christiane L. Joost-Gaugier, the in��uence of (neo) Pythagoreanism in the Renaissance is both manifold and widespread.4 It covers most areas in the realms of science and the arts,5 but is nevertheless 1 Something he already was, for the most part, in Plato's or Aristotle's time; Riedweg 2008, 42�f.; Macris 2018, 810-818 (with bibliography). 2 Gentile 2012. 3 They were probably also in��uenced by the "divine" character commonly attributed to Pythagoras by his Hellenistic bio/hagiographers. Macris 2003 and 2006. 4 Allen 2014; Joost-Gaugier 2009 (this study is, however, to be consulted with extreme caution). 5 Perillié 2005. In this respect one must also recall the important role played by mathematics (in general) in the encyclopedic reorganization of knowledge launched by some of the ��rst Humanists, as exempli��ed-among others-by G. Valla's (1447-1500) De expetendis et fugiendis rebus (Venice 1501), which includes a section on arithmology: see Tucci 2008 (I am indebted to M. Ghione for this reference).

Science & Education, 2013

In this book Martinez considers a number of 'myths' (or 'apparent myths') that are found in the history of mathematics, and asks the question: ''[H]ow does history change when we subtract the many small exaggerations and interpolations that writers have added for over 2000 years?'' (p. xvi) He criticizes many writers who, as he argues, have invented history, while he distinguishes invention of historical stories from invention in the growth of mathematics itself, which he commends. Martinez uses the case of Pythagoras, and the findings of his analysis of different historical texts referring to Pythagoras, as a recurring theme in the book to exemplify his thesis that there is ''common mismatch between speculations and evidence in history'' (p. xvii) and that, ''by being careful with sources, we can replace historical myths with accounts that are better and true'' (p. 204). He notes that ''Pythagoras was a religious leader who eventually became misinterpreted as a great mathematician and astronomer'' (p. 211), and he explains that most mathematical achievements commonly attributed to Pythagoras ''are symptoms of our unwillingness to confront uncertainty, to plainly admit: I don't know what happened'' (p. 214). Furthermore he claims that, even if Pythagoras were no longer regarded as a notable mathematical figure of the past, ''we should all still study Pythagoras, not to memorize [sic] his alleged achievements but to sharpen our skepticism'' so that ''[t]he aim would not be to distrust everything Pythagorean but to analyze historical claims against evidence'' (p. 204). 1

A History of Pythagoreanism. Ed. by Carl Huffman. Cambridge, 2014. P. 88-111

In this paper, an approach to Pythagoras’ Theorem is presented within the historical context in which it was developed and from the underlying intellectual outline of the Pythagorean School. This was analyzed from a rationalism standpoint. An experiment is presented to the reader so that they, through direct observation, can analyze Pythagoras’ Theorem and its relation to the creation of knowledge. The theory of knowledge conceptualization is used.