After completing the Hogere Burgerschool in Alkmaar,[1] Hamburger studied chemistry at Utrecht University, where he received his doctorate in 1883,[1][2] on the determination of urea in urine.

[1] He subsequently worked with Utrecht ophthalmologist and physiologist Franciscus Cornelis Donders for seven years, and completed a medical degree.

[1] Throughout his academic career he emphasised the importance of physical chemistry in health science, and he actively opposed vitalism (i.e. the view that living organisms are somehow governed by different principles from inanimate substances).

[7][8] This was initially thought to be a passive phenomenon, but was later linked to active transport by the band 3 exchanger (SLC4A1).

[9] He was a member of the Royal Netherlands Academy of Arts and Sciences (Koninklijke Nederlandse Akademie van Wetenschappen) and received a number of honorary degrees,[2] including from the University of Aberdeen, the Veterinary College at Utrecht and the University of Padua.