# Ernst Paul Specker

### Quick Info

Zürich, Switzerland

Zürich, Switzerland

**Ernst Specker**was a Swiss mathematician who made decisive contributions towards shaping directions in topology, algebra, mathematical logic, combinatorics and algorithms.

### Biography

**Ernst Specker**'s parents were Margreth Branger and Karl Specker. Ernst was the middle child of his parents' three sons. The family background is described in [2]:-

His great-grandfathers were citizens of four different Swiss cantons. The ancestor from Thurgovia was a carpenter, the ancestor from Zürich a schoolteacher, the ancestor from the canton of Grisons was a farmer and the ancestor from the canton of Appenzell drove pack-horses over mountain passes, importing wine from Italy. his grandfathers followed their fathers in becoming a carpenter and a farmer. Ernst's father studied law and worked in the civil service.Ernst attended kindergarten in Zürich. He then studied at an elementary school for four years before falling out with one of his teachers. He persuaded his parents that he had been badly treated and they arranged for him to be sent to a different elementary school, still in Zürich, this one attached to the Zürich Teacher College for Women. Ernst was happy at this school but his health broke down when he contracted tuberculosis after beginning secondary school. In 1934 he was sent to a sanatorium in Davos, then after he was released from the sanatorium he lived with his maternal grandmother who lived in Davos. By 1935 he was back at his secondary school but had been left rather crippled by the illness. He did begin to develop an interest in mathematics at this time but later said that [2]:-

... getting into mathematics is much more difficult than getting into poetry. For instance, when I first learned about the formula for the number of diagonals in a polygon, I was quie excited about it and wanted to find a formula of my own. But as you can guess, nothing came out of it.Indeed he did love literature, poetry in particular. It is easy to see how he could read poems and then write his own poetry, but trying to produce his own mathematics was of a different order of difficulty.

After the summer of 1936 his illness returned with increased vigour and he had to return to Davos where he lived with his grandmother again this time spending over three years confined to bed. He was given lessons by teachers from a local private school, studying mathematics, physics, chemistry, and foreign languages. He seems to have seen little of his parents (or any other family members except his grandmother) during these years. In the spring of 1940 he returned to Zürich although he was now badly crippled and needed crutches to get about. He studied at Professor Tschulok's private school so that he would be prepared to take the university entrance examinations. Of course in 1940 most of Europe was at war, but Switzerland remained neutral and there were many outstanding teachers at the school who were in Switzerland for political reasons. Specker passed his university entrance examinations in the autumn of 1940. His father pressed him to study law at university but Specker wanted to study mathematics at the Eidgenössische Technische Hochschule (ETH) in Zürich. Specker's parents were rather unhappy about this but in the end they consented.

In his first term at ETH he attended linear algebra lectures by Michel Plancherel and calculus lectures by W Saxer. He also attended a colloquium given by Beno Eckmann. During the Easter vacation Specker returned to his grandmother at Davos and read the

*Grundzüge der Theoretischen Logik*Ⓣ by Hilbert and Ackermann. Back at ETH after the vacation ended, he attended a projective geometry course given by Kollros and also attended lectures by Paul Finsler at the University of Zürich. His main teachers for the rest of his undergraduate studies were Gonseth, Hopf and Bernays. It was Hopf who supervised the dissertation for his diploma on

*Fundamental groups and second homotopy groups of closed three-dimensional manifolds*.

From 1945 to 1948 Specker was employed as an assistant at ETH, working first for Saxer, then for Hopf and Plancherel. He attended Bernays' seminar on

*Axiomatics and Logistics*and one of the topics studied led to Specker's paper

*Nicht konstruktiv beweisbare Sätze der Analysis*Ⓣ (1949). Roman Sikorski also attended the seminar and interaction with him led to Specker's paper

*Sur un problème de Sikorski*Ⓣ (1949). He submitted his doctoral thesis

*Die erste Cohomologiegruppe von überlagerungen und Homotopieeigenschaften dreidimensionaler Mannigfaltigkeiten*Ⓣ in 1948 and was awarded a two year postdoctoral fellowship. We noted above that Specker was crippled by the illness he had suffered. However in 1948-49 he underwent surgery and his health improved dramatically. He was then able to travel to the United States to spend the academic year 1949-50 at the Institute for Advanced Study at Princeton. There he attended lectures by Church, Siegel and Steenrod. He also attended Deane Montgomery's seminar and discussed problems on recursive analysis with Gödel.

Specker returned to ETH for session 1950-51 when he substituted for Hopf in teaching a course on linear algebra. In 1951 he submitted his habilitation thesis to ETH and became a privatdozent. As well as teaching at ETH he also lectures at Geneva and at Neuchätel over the following years. In 1953 he published

*The axiom of choice in Quine's New Foundations for Mathematical Logic*. I Novak Gál writes in a review:-

Specker here proves the following important results which were long a subject for conjecture:Specker was promoted to professor at ETH in 1955 and the following year he married Suzanne; they had three children, Dorothea born in 1957, Adrian born in 1959 and Margaret born in 1962.

- the axiom of infinity is provable in Quine's "New Foundations";
- the axiom of choice is disprovable in "New Foundations";
- the generalized continuum hypothesis is also disprovable in "New Foundations".

Specker's contributions to mathematics are reviwed in [5] where his 32 publications up to 1979 are divided into 10 categories: topology, recursive analysis, combinatorial set theory, type theory, axiomatic set theory, Ramsey's theorem, arithmetic, logic of quantum mechanics, algorithms, and miscellaneous. Examples of his later papers are

*The fundamental theorem of algebra in recursive analysis*(1969),

*Die Entwicklung der axiomatischen Mengenlehre*Ⓣ (1978), (with H Kull)

*Direct construction of mutually orthogonal Latin squares*(1987),

*Application of logic and combinatorics to enumeration problems*(1988).

In 1987 Specker gave his farewell lecture at the ETH Zürich

*Postmoderne Mathematik: Abschied vom Paradies?*. This is published as [3] and presents problems of infinity in the form of a fairy tale. The volume [1] list 42 publications by Specker. We end this biography by quoting from the Preface:-

Ernst Specker has made decisive contributions towards shaping directions in topology, algebra, mathematical logic, combinatorics and algorithms over the last 40 years. We have derived great pleasure from marking his seventieth birthday by editing the majority of his scientific publications, and thus making his work available in a unified form to the mathematical community. In order to convey an idea of the richness of his personality, we have also included one of his sermons.

### References (show)

- G Jäger, H Läuchli, B Scarpellini and V Strassen (eds.),
*Ernst Specker Selecta*(Birkhäuser Verlag, Basel, 1990). - J Meon, The story of a friend, in
*G Jäger, H Läuchli, B Scarpellini and V Strassen (eds.), Ernst Specker Selecta*(Birkhäuser Verlag, Basel, 1990), xi-xxiii. - E Specker, Postmoderne Mathematik: Abschied vom Paradies?,
*Dialectica***42**(3) (1988), 163-169. - H Wang, Specker's mathematical work from 1949 to 1979,
*Enseign. Math. (2)***27**(1-2) (1981), 85-98. - H Wang, Specker's mathematical work from 1949 to 1979, in
*Logic and algorithmic, Zurich, 1980*(Univ. Genève, Geneva, 1982), 11-24.

### Additional Resources (show)

Other websites about Ernst Specker:

### Honours (show)

Honours awarded to Ernst Specker

Written by J J O'Connor and E F Robertson

Last Update November 2006

Last Update November 2006