His father, Atmaram Bapu Dalvi, was a social reformer and was Vice President of the Bombay Arya Samaj in 1880.
He systematically examined Newton's rule for finding the number of imaginary roots and in 1869 he wrote and published a book entitled "An Examination of Sir Isaac Newton's Rule for finding the Number of Imaginary Square Roots in an Equation",[3] in which he provides mechanical and geometric theorems and gives a direct and complete proof and disproof of the equation.
One of his critics while writing to the Editor pointed out that in 1669, when Sir Isaac Newton was Lucasian Professor of Mathematics, he used to jot down portions of his lectures, definitions, propositions, examples partially wrought out as were necessary.
His successor Professor Whiston found this manuscript and published it in 1707 long after Sir Issac Newton had first written it down so these omissions persisted.
Helena Blavatsky in her book - "From the Caves and Jungles of Hindustan" referred to him as possibly the greatest mathematical genius in the world.
[citation needed] She wrote that according to Sir James Braithwaite Peile, Director of National Education in India, Dalvi proved that the great Newton was mistaken from the beginning to the end in his "Rule for Imaginary Square roots" and the application of this Newtonian rule does not bring about the intended result.
1881, v2, April, p151, Memorandum [to Geometry on the Principles of the Ancient Hindu Philosophy].DA Dalvi gives a geometric explanation for the three famous problems of antiquity.