Following Newcomb Greenleaf, 1966 the American mathematician Errett Bishop (1928-1983) proposed a small revolution in the way that mathematicians think. Bishop called his approach to mathematics ''constructive'' because of his belief that the objects of mathematics are constructed, not received from on high. Bishop supported the revolution with his great book, Foundations of Constructive Analysis (FCA), which appeared in 1967. His constructive approach was welcomed by many computer scientists. Stanford’s computer science pioneer Donald Knuth (Algorithmic Thinking and Mathematical Thinking) proposed that computer science be known as ''algorithmics''. He shows in great detail how a constructive mathematician can understand the triad
(Assumption Proof Conclusion)
in terms of
(Input data Algorithm Output data).
Knuth was suggesting constructive math could serve as a bridge between classical mathematics and computer science, an appealing intellectual unification.''

During the last 50 five years one notices the flourishing of constructive approaches to mathematics and the growth of a variety of research groups working on constructive mathematics.  During the 1920s L. E. J. Brouwer (1881-1966), the renowned Dutch mathematician and philosopher, had urged mathematicians to modify the logic used in mathematical arguments  founding an entire school of mathematical logic, known as intuitionism. It is (was) considered that Brouwer and other constructivists were more successful in their criticism of classical mathematics than in replacing it with a better alternative. In the words of Laura Crosila ''The spark that started the present abundance of constructive mathematics was the publication in 1967 of Errett Bishop's Foundations of Constructive Analysis, FCA.''  The historical and philosophical picture of constructive mathematics is complex; a number of varieties of mathematics have been developed over time including classical, Brouwerian and Russian constructive mathematics – ''each of the latter three forms of mathematics may be developed on the basis of some suitable extension of Bishop's mathematics by characteristic principles.'' Following Arend Heyting, classical mathematics can be seen as a  guide that helps the constructive mathematician develop new mathematics.

References:

Crosila, L. Bishop’s mathematics: A philosophical perspective, In Handbook of Bishop's Mathematics. Eds. D. Bridges, H. Ishihara, M. Rathjen, and H.Schwichenberg, Cambridge University Press, forthcoming.

Greenleaf, N. (2020) Agony and Failure in Bishop’s Constructive Revolution

Heyting, A. (1956). Intuitionism, an Introduction, North – Holland.

Websites

https://www.dsbridges.com/errett-bishop

https://www.britannica.com/biography/Errett-Bishop