Michael Fekete was born in Zenta, Austria-Hungary (today Senta, Serbia). He received his PhD in 1909 from the University of Budapest (later renamed Eötvös Loránd University). He studied under Lipót Fejér. After completing his PhD he switched to University of Göttingen, which was considered a mathematics hub. In 1914, he returned to the University of Budapest, where he attained the title of Privatdozent.[2]
Fekete also worked as a private math tutor. Among his students was János Neumann. In 1922, Fekete published a paper together with Neumann on extremal polynomials, which was Neumann's first scientific paper.[3] Fekete dedicated the majority of his scientific work to the transfinite diameter.