Rózsa Péter

Happy Ada Lovelace Day!

Rózsa Péter (1905-1977) was a Hungarian mathematician and early contributor to the theory of (primitive) recursive functions. She received her PhD in 1935 from (what is now) Eötvös Loránd University in Budapest. Her fellow student Laszlo Kálmár had introduced her a few years earlier to the then brand-new work of Gödel, and she proceeded to study the class of (primitive) recursive functions first clearly defined by Gödel in his 1931 incompleteness paper. In a number of articles in the 1930s, she laid the groundwork for the study of hierarchies of sub-recursive functions and clarified the notion of primitive recursive function. I’ll just mention four of her contributions on the subject: In her paper, “Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion” (Math. Ann., 1935) she showed that course-of-values recursion and nested recursion can be reduced to ordinary primitive recursion. In “Konstruktion nichtrekursiver Funktionen” (Math. Ann., 1935), Pétér simplified and expanded on Ackermann’s work, and proved that there are multiply recursive but not-primitive recursive functions. In “Über die mehrfache Rekursion” (Math. Ann., 1937), she studied multiple recursion in more detail and showed that the hierarchy of k-recursive functions is proper. In “Zusammenhang der mehrfachen und transfiniten Rekursionen” (JSL, 1950), she proved the equivalence of k-fold recursion and transfinite recursion along ωk. Her early work on primitive recursive function theory is set out in her monograph, Rekursive Funktionen (1951), translated into English as Recursive Functions (1967). She also wrote a popular book on mathematics, Playing with Infinity, which was translated into 14 languages.

Pétér was barred from teaching in 1939 due to her Jewish heritage, but obtained positions at the Budapest Teacher’s College in 1945 and at her alma mater in 1955. She was the first female mathematician to be elected to the Hungarian Academy of Sciences. She retired in 1976.

Women in Science (San Diego Supercomputer Center)
Biographies of Women Mathematicians (Agnes Scott College)
MacTutor History of Mathematics Archive

Philosophy of Mathematical Practice Online

If you have access to Oxford Scholarship Online, you can now read Mancosu’s excellent collection The Philosophy of Mathematical Practice via the internets.

Contemporary philosophy of mathematics offers us an embarrassment of riches. But anyone familiar with this area will be aware of the need for new approaches that will pay closer attention to mathematical practice. This book provides a unified presentation of this new wave of work in philosophy of mathematics. This new approach is innovative in at least two ways. First, it holds that there are important novel characteristics of contemporary mathematics that are just as worthy of philosophical attention as the distinction between constructive and non constructive mathematics at the time of the foundational debates. Secondly, it holds that many topics that escape purely formal logical treatment — such as visualization, explanation, and understanding — can be nonetheless be subjected to philosophical analysis. The book comprises an introduction and eight sections. Each section consists of a short introduction outlining the general topic followed by a related research article. The eight topics selected represent a broad spectrum of contemporary philosophical reflection on different aspects of mathematical practice: visualization, diagrammatic reasoning and representational systems, mathematical explanation, purity of methods, mathematical concepts, philosophical relevance of category theory, philosophical aspects of computer science in mathematics, philosophical impact of recent developments in mathematical physics.

Robin Milner, 1934-2010

Robin Milner died on March 20. He was a leading theoretical computer scientist who developed the LCF theorem prover, the ML programming language, and introduced the π-calculus. He was founding director of the Laboratory for Foundations of Computer Science at the University of Edinburgh and then Professor of Computer Science at Cambridge. Milner was a Fellow of the Royal Society, a Fellow of the ACM, and winner of the Turing Award.

People Who Oscillate

From today’s mini-AIR:

The Oscillating Humans Project, announced here, is searching for a living specimen – an exemplar – of an oscillating human.

DEFINITION: For purposes of the project, an Oscillating Human is someone who consistently, repeatedly, over many years, expresses opinions directly opposite to opinions he or she expressed earlier, always ignoring and/or denying the existence of copious, easily found clear documentation of the earlier opinions.

PURPOSE: The exemplary person, once identified, will serve as an example for teachers to use in logic classes. To minimize the chance of lawsuits, the exemplar must be a “public person”, with (as stated above) for whom there is copious, easily found, clear documentation of years and years of oscillation.

If you know of an outstanding specimen, please send:

1. The name and a 20-word biographical sketch of the person.
2. Several URLs pointing to clear, unarguable documentation.

Send to: OSCILLATING HUMANS PROJECT: marca AT improbable.com

NOTE: This is an education project. It is NOT an exercise in naming people you don’t like. No screeds, please.

Oscillating Humans Literature Review

Published research about this form of human oscillation may be scarce. One of the few apparently relevant items — judging it by its title, if not by its contents, is this British study:

“Oscillation of Human Performance as a Personality Measure,” Michael A. Tainsh, Perceptual and Motor Skills, vol. 35, no. 2, October 1972, pp. 677-8.

Truly pertinent citations will be welcomed.