He started studying medicine in 1852, but spent his last two years at the University of Leiden in mathematics and physics studying under Frederik Kaiser. In 1857 he graduated with the Ph.D. dissertation work The comet of the years 1556, 1264 and 975, and its alleged identity.
Donati's comet (now officially designated C/1858 L1 and 1858 VI), the second most brilliant comet of the 19th century, had been considered to be a return of the comets of 1556, 1264, and 975. Earlier, in 1856, Karl Ludwig von Littrow had discovered at the Vienna State Archives a pamphlet by Joachim Heller containing observations of the Great Comet of 1556 as well as a broadsheet by Paul Fabricius with a map of the comet's course. Using Littrow's discovered materials, Hoek proved conclusively that the comets of 1264 and 1556 were not identical, and that Donati's comet did not therefore represent their reappearance.
In 1859 he was associate professor of astronomy at the University of Utrecht and Director of the Royal Observatory Sonnenborgh. In collaboration with Anthonid Cornelis Oudemans, he wrote Recherches de la d'quantite ether contenue dans les Liquids (Research of the amount of aether contained in liquids) (1864) and Sur les contractions dans les Melanges de Liquids (On contractions in mixtures of liquids).
- Welsink, Dick (2001). "Who's who in ‘Jan van Zutphen's afscheidsmaal’ van Piet Paaltjens". Nieuw Letterkundig Magazijn 19: 34–38. Retrieved 4 July 2012.
- Martin Hoek at the Mathematics Genealogy Project
- Véron, P. and Tammann, G.A. "Astronomical Broadsheets, Forerunners of the lAU Circulars". ESO. Retrieved 4 July 2012.
- Herschel, A. S. (translator) (1917). "Observations by Fabricius and Heller of the Comet of 1556; being the substance of a paper by Karl von Littrow in "Sitzungberichte der Wiener Akademie"". Monthly Notices of the Royal Astronomical Society 77: 633–643 and 643A. Bibcode:1917MNRAS..77..633H. Retrieved 4 July 2012.
- Rafael Ferraro (2007). "Hoek's experiment". Einstein's Space-Time: An Introduction to Special and General Relativity. Springer. pp. 33–35. ISBN 0387699465.
- Hoek, M. (1868). "Determination de la vitesse avec laquelle est entrainée une onde lumineuse traversant un milieu en mouvement". Verslagen en mededeelingen 2: 189–194.