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On Certain Tendencies in the Development of Mathematics
 Lemma
 Kάποιες τάσεις στην ανάπτυξη των μαθηματικών
 Greek, Modern (1453)
 Delli, Eudoxie
 Scientific theories and disciplines > Mathematics  Complementarity  Concepts of knowledge and modes of reasoning
 2112017
 Shafarevich, Igor Rostislavovich [Author]. On Certain Tendencies in the Develepment of Mathematics
 Σύναξη [Synaxi]
 mathematical knowledge  Newton, Isaac (16431727)  Gauss, Carl Friedrich  Lobachevsky, Nikolai Ivanovich  Bolyai, Farkas  Galois, Évariste  Riemann, Bernhard  Plato  Pythagorean model  mathematical growth  mathematical beauty

 <p>Shafarevich, I. R. (1986). Kάποιες τάσεις στην ανάπτυξη των μαθηματικών. <em>Σύναξη</em>, <em>18</em>, 6572.</p>


The article is a part of Shafarevich’s talk given to the Gottingen Academy of Sciences in 1973 upon receiving the prize Hanemann. Shafarevich presented his view of the relationship between mathematics and religion.
The text of the Russian mathematician is preceded by a short introduction of the Greek editor (translator?) in which is mentioned the critics against modern scientists (their dependence on powerful economic interests, the irrational development of sciences culminating to the ecological crisis and, finally, the scientists’ isolation from real life). The consistent focus is on the oversegmentation of knowledge and the overspecialization which lead to a Babel of incomprehensibility. The modern impasses are viewed as spiritual impasses. In this perspective, scientists must wonder about the meaning of their scientific activity, searching it in the religious realm.
Shafarevich notes the multiple discoveries in mathematics, such as that of the nonEuclidean geometry, in order to suggest that pure mathematics reflects an objective reality, not a set of conventional definitions or a formalism.
He claims that mathematical growth is in itself not intentional or unified. In order to achieve directedness and unity, mathematics needs a goal, a universal meaning and point of reference above and beyond it. This goal can be set either by practical applications or by God as the significant source of inspiration in the orientation of its development.
Shafarevich opts for the latter, indicating that pure mathematics is not in itself dictated by practical applications. At this point, he concludes by going back to the Pythagorean conception of mathematical sciences (6^{th} century B.C) in its relation to religion. According to Shafarevitch, by discovering the harmony of the world, through numbers, the Pythagoreans paved the path which leads to the union with God, providing at the same time a model for the conceptual constitution of other sciences and a timeless inspiration for the possible ‘’union’’ of science and religion.
