[1] Balanos was born in Ioannina, a major center of the Greek Enlightenment movement during that time.

[2] He was a student of Methodios Anthrakites director of the local Gouma (later Balaneios) school.

On the other hand, he expanded and reprinted the work of his teacher Methodios Anthrakites The Way of Mathematics (Greek: Οδός Μαθηματική, 1749).

He published this in Venice in 1756, and attempted to gain international recognition for his solution from the community of mathematicians, and in particular Leonhard Euler and the members of the Saint Petersburg Academy of Sciences.

His son Kosmas Balanos rejected the solution in a work published in 1816 after his own death, Αντιπελάργησις (Antipelargisis, Against the Stork).