Eduard Helly was a mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and the eponym of Helly's theorem

Helly's theorem

Helly's theorem is a basic result in discrete geometry describing the ways that convex sets may intersect each other. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative proofs by and had already appeared...

, Helly families

Helly family

In combinatorics, a Helly family of order k is a family of sets such that any minimal subfamily with an empty intersection has k or fewer sets in it. In other words, any subfamily such that every k-fold intersection is non-empty has non-empty total intersection.The k-Helly property is the property...

, Helly's selection theorem

Helly's selection theorem

In mathematics, Helly's selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence. In other words, it is a compactness theorem for the space BVloc. It is named for the Austrian mathematician Eduard...

, Helly metric, and the Helly–Bray theorem

Helly–Bray theorem

In probability theory, the Helly–Bray theorem relates the weak convergence of cumulative distribution functions to the convergence of expectations of certain measurable functions. It is named after Eduard Helly and Hubert Evelyn Bray....

. In 1912, Helly published a proof of Hahn–Banach theorem

Hahn–Banach theorem

In mathematics, the Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed...

, 15 years before Hahn and Banach discovered it independently. Helly only proved the special case of the Hahn-Banach theorem for continuous functions over [a,b]. The space C[a,b] is infinite dimensional, and the general proof for the infinite dimensional case requires the Axiom of choice or something equivalent, which didn't exist in 1912, so how did Helly prove it? Was his proof even correct? The answer is that C[a,b] is a particular concrete example and he constructed a particular extension for that example. The essence of the Hahn-Banach theorem lies in its generality, which does require the axiom of choice.

As a prisoner of war in a Russian camp at Nikolsk-Ussuriysk

Ussuriysk

Ussuriysk is a city in Primorsky Krai, Russia, located in the fertile valley of the Razdolnaya River, north of Vladivostok and about from both the Chinese border and the Pacific Ocean. Population: -Medieval history:...

 in Siberia

Siberia

Siberia is an extensive region constituting almost all of Northern Asia. Comprising the central and eastern portion of the Russian Federation, it was part of the Soviet Union from its beginning, as its predecessor states, the Tsardom of Russia and the Russian Empire, conquered it during the 16th...

, Helly wrote important contributions on functional analysis.

External links