János Lajos Neumann is born in Budapest, Austria-Hungary (present-day Hungary), to Max Neumann, a wealthy banker, and Margit Kann. The family was Jewish but not religiously observant.

Demonstrates exceptional mathematical abilities from a very young age. He could reportedly perform complex calculations in his head by age six and was familiar with calculus by age eight. He also possessed a remarkable memory.

Attends the prestigious Fasori Evangélikus Gimnázium, where he receives exceptional instruction in mathematics from Miklós Schweitzer, a promising young mathematician. Neumann and Schweitzer form a close bond. His father insisted he pursue chemistry as a more secure career path.

Enrolls at the University of Berlin to study chemistry, following his father's wishes. He simultaneously studies mathematics privately with mathematicians such as Erhard Schmidt.

Transfers to ETH Zurich (Swiss Federal Institute of Technology) to continue his studies in chemical engineering, receiving a diploma in chemical engineering in 1925. He attends lectures in mathematics as well.

Simultaneously with his studies in Zurich, submits his doctoral thesis on set theory to the University of Budapest and is awarded a PhD in Mathematics. His advisor was Leopold Fejér.