Kuiper studied at University of Leiden in 1937-41, and worked as a secondary school teacher of mathematics in Dordrecht in 1942-47.

He completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.

In February to June 1954, he went for a second time to Ann Arbor where he met Raoul Bott and his student Stephen Smale.

In 1957, he was notably one of the six participants to the first Arbeitstagung, an informal seminar animated by Friedrich Hirzebruch, which later became very popular among mathematicians; he saw at this occasion Alexander Grothendieck presenting his first revolutionary works in algebraic geometry.

[4] He finally served as director of the Institut des Hautes Études Scientifiques from 1971 until his retirement in 1985, then stayed there as a long-term visitor for six years.