We have all heard that mathematics uses a universal language, that it underpins the construction of our world, that every individual is born with the ability to operate with the concepts of mathematics to find answers to fundamental questions about ourselves and our relationship to the physical universe.

Yet there are voices that doubt its universality because, being a language, it is an abstract invention of our species, with which we work in infinite situations.

What happens if someone tells you that they disagree with the axioms, those statements that are considered true, which serve as starting points for all subsequent arguments and reasoning?

You think that mathematics, which proves the various variants of reality, rests unconditionally on precisely these statements, which cannot be proved. And axioms are many!

There are two ways of understanding:

one in which mathematics is an object of study in itself, as the architecture of a platonic world, an intellectual construct, an extremely stable projection of the human mind

and the second, as a model of the relationship between the objects of the physical universe

In our attempts to intersect mathematical structures with those of the surrounding reality, we have encountered countless paradoxes. In physics we must explain them, using the whole language of mathematics. Mathematicians, however, remove paradox from the discussion by creating additional axioms. We enter a territory of interference with philosophy.

I think we should not confuse mathematical language (which is, of course, invented) with the structure of mathematics, which we are constantly discovering. We advance in knowledge and other segments reveal themselves to us. The horizon becomes more transparent.

Intervals of an Infinite Line speaks about my fascination on set theory, an area of mathematics systematically explored relatively recently (late 19th century) by Georg Cantor and Richard Dedekind. The constituent elements of a set become special entities, we use them in relation to neighborhoods, they place themselves in countless contradictory situations because they are of any nature and can define arbitrary realities. By analogy with the physical universe the theory does not overlap perfectly with ordinary perception. The segments analyzed are as large as the whole. The consistency of the mathematical universe is hidden in every fraction of infinity, in multitudes, abstractions, logical repetitive structures. In the poetry of existence.

The project was presented at Aparte Gallery, Iasi (March 2023), powered by The Centre for Contemporary Photography Iasi, The Multidisciplinary Research Institute in Art of "George Enescu" National University of Arts from Iasi.