Blanuša was born in Osijek, Austria-Hungary (today Croatia), into an ethnic Serb family. He attended elementary school in Vienna and Steyr in Austria and gymnasium in Osijek and Zagreb. He studied engineering in both Zagreb and Vienna and also mathematics and physics. His career started in Zagreb, where he started to work and lecture. His student Mileva Prvanović completed her doctorate in 1955, the first in geometry in Serbia. Blanuša was the dean of the Faculty of Electrical Engineering, Zagreb in the 1957-58 school year. He received the Ruđer Bošković prize in 1960. He died in Zagreb.
In mathematics, Blanuša became known for discovering the second and third known snarks in 1946 (the Petersen graph was the first), triggering a new area of graph theory. The study of snarks had its origin in the 1880 work of P. G. Tait, who at that time had proved that the four color theorem is equivalent to the statement that no snark is planar. Snarks were so named later by the American mathematician Martin Gardner in 1976, after the mysterious and elusive object of Lewis Carroll's poem The Hunting of the Snark.
Blanuša's most important works were related to isometric immersions of two-dimensional Lobachevsky plane into six-dimensional Euclidean space and generalizations, in the theory of the special functions (Bessel functions), in differential geometry, and in graph theory. His results are included in the Japanese mathematical encyclopedia Sugaku jiten in Tokyo, published by Iwanami Shoten in 1962.
His works were mostly related to the theory of relativity. He discovered a mistake in relations for absolute heat Q and temperature T in relativistic phenomenological thermodynamics, published by Max Planck in Annalen der Physik in 1908.
- Q0 and T0 are the corresponding classical values, and a=(1-v2/c2)1/2
in the relation → Q=Q0a, T=T0a really should be → Q=Q0/a, T=T0/a
This correction was published in Glasnik, the journal relating to mathematics, physics and astronomy in 1947 in the article "Sur les paradoxes de la notion d'énergie". It was rediscovered in 1960, and the correction is still wrongly attributed to H. Ott in the mainstream scientific literature.