Tudor Ganea was a Romania

Romania

Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...

n mathematician, known for his work in algebraic topology

Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...

, especially homotopy

Homotopy

In topology, two continuous functions from one topological space to another are called homotopic if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions...

 theory. Ganea left Communist Romania

Communist Romania

Communist Romania was the period in Romanian history when that country was a Soviet-aligned communist state in the Eastern Bloc, with the dominant role of Romanian Communist Party enshrined in its successive constitutions...

 to settle in the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 in the early 1960s. He taught at the University of Washington

University of Washington

University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...

.

Work

In 1957, Ganea published in the Annals of Mathematics

Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.-History:The journal began as The Analyst in 1874 and was...

a short, yet influential paper with Samuel Eilenberg

Samuel Eilenberg

Samuel Eilenberg was a Polish and American mathematician of Jewish descent. He was born in Warsaw, Russian Empire and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor...

, in which the celebrated Eilenberg−Ganea conjecture was formulated. The conjecture is still open.

Just before he died, Ganea attended the Symposium on Algebraic Topology, held February 22-26, 1971 at the Battelle Seattle Research Center, in Seattle. At the symposium, he was not able to give a talk, but he did distribute a preprint containing a list of unsolved problems. One of these problems, regarding the Lusternik–Schnirelmann category, came to be known as Ganea's conjecture

Ganea conjecture

Ganea's conjecture is a claim in algebraic topology, now disproved. It states thatwhere cat is the Lusternik–Schnirelmann category of a topological space X, and Sn is the n dimensional sphere....

. Many particular cases of this conjecture were proved, until Norio Iwase provided a counterexample in 1998.

Quote

My algebraic topology professor, Tudor Ganea, used to say that "mathematics progresses by faith and hard work, the former augmented and the latter diminished by what others have done".

From: "Eightfold Way: The Sculpture", by Helaman Ferguson

Helaman Ferguson

Helaman Rolfe Pratt Ferguson is an American sculptor and a digital artist, specifically an algorist.Ferguson's mother died when he was about three and his father went off to serve in the Second World War. He was adopted and raised in New York. He was a graduate of Hamilton College and received a...

 with Claire Ferguson, in The Eightfold Way: The Beauty of Klein's Quartic Curve, edited by Silvio Levy, MSRI Publications, vol. 35, 1998

External links