Kuchnia i dacza: produktywne przestrzenie radzieckiej matematyki

In the late 1960s and 70s, due to the Soviet regime’s crackdown on dissident activities and rising anti-Semitic policies, many mathematicians from “undesirable” groups faced discrimination and serious administrative restrictions on work and study at top-ranking official institutions. To overcome such barriers, the mathematical community built extensive social networks around informal or semi-formal study groups and seminars, which formed a parallel social infrastructure for learning and research. As   result, mathematical activity began shifting from public educational and research institutions into private or semi-private settings — family apartments, summer dachas, and countryside walks. For many Soviet mathematicians, instead of being a refuge from work, their home apartments and dachas became their primary working spaces — places where they did their research, met with students, and exchanged ideas with colleagues. At the intersection of work and private life, a tightly knit mathematical community emerged, whose commitment to scholarship went beyond formal duty or required curriculum, a community practicing mathematics as a “way of life.” The parallel social infrastructure functioned in tense interdependency with official institutions and borrowed some characteristics of the official system it opposed.Pod koniec lat sześćdziesiątych i siedemdziesiątych, w wyniku tłumienia przez reżim sowiecki działalności dysydenckiej i nasilającej się polityki antysemickiej wielu matematyków z „niepożądanych” grup spotkało się z dyskryminacją i poważnymi ograniczeniami administracyjnymi w pracy i badaniach w najważniejszych oficjalnych instytucjach. Aby pokonać te bariery, społeczność matematyczna zbudowała rozległe sieci społecznościowe wokół nieformalnych lub półformalnych grup badawczych i seminariów, które utworzyły równoległą infrastrukturę społeczną do nauki i badań. W rezultacie działalność matematyczna zaczęła przenosić się z publicznych instytucji edukacyjnych i badawczych do środowisk prywatnych lub półprywatnych — mieszkań rodzinnych, letnich daczy i spacerów na wsi. Dla wielu radzieckich matematyków ich mieszkania i dacze, zamiast być schronieniem przed pracą, stały się główną przestrzenią pracy — miejscami, w których prowadzili badania, spotykali się ze studentami i wymieniali się pomysłami z kolegami. Na skrzyżowaniu pracy i życia prywatnego wyłoniła się zwarta społeczność naukowa, której oddanie matematyce wykraczało daleko poza jakiekolwiek formalne obowiązki zawodowe lub wymogi związane z nauką, społeczność praktykująca matematykę jako „sposób na życie”. Równoległa infrastruktura społeczna funkcjonowała w napiętej współzależności z oficjalnymi instytucjami i częściowo odzwierciedlała niektóre cechy systemu, któremu miała się przeciwstawić

Mathematical Research in High School: The PRIMES Experience

Consider a finite set of lines in 3-space. A joint is a point where three of these lines (not lying in the same plane) intersect. If there are L lines, what is the largest possible number of joints? Well, let’s try our luck and randomly choose k planes. Any pair of planes produces a line, and any triple of planes, a joint. Thus, they produce L := k(k − 1)/2 lines and and J := k(k − 1)(k − 2)/6 joints. If k is large, J is about [[√2]/3]L[superscript 3/2]. For many years it was conjectured that one cannot do much better than that, in the sense that if L is large, then J ≤ CL[superscript 3/2], where C is a constant (clearly, C ≥ [√2]/3]). This was proved by Larry Guth and Nets Katz in 2007 and was a breakthrough in incidence geometry. Guth also showed that one can take C = 10. Can you do better? Yes! The best known result is that any number C > 4/3 will do. This was proved in 2014 by Joseph Zurer, an eleventh-grader from Rhode Island [Z]

The Road to Servomechanisms: The Influence of Cybernetics on Hayek from the Sensory Order to the Social Order

This paper explores the ways in which c ybernetics influenced the works of F. A. Hayek from the late 1940s onwar d. It shows that the concept of negative feedback, borrowed from cybernetics, was central to Hayek's attempt of giving an explanation of the principle to the emergence of human purposive behavior. Next, the paper discusses Ha yek's later uses of cybernetic ideas in his works on the spontaneous formation of social orders. Finally, Hayek's view on the appropriate scope of the use of cybernetics is considered

Vygotsky in English: What Still Needs to Be Done

At present readers of English have still limited access to Vygotsky’s writings. Existing translations are marred by mistakes and outright falsifications. Analyses of Vygotsky’s work tend to downplay the collaborative and experimental nature of his research. Several suggestions are made to improve this situation. New translations are certainly needed and new analyses should pay attention to the contextual nature of Vygotsky’s thinking and research practice

The Rise of Modern Science

This course studies the development of modern science from the seventeenth century to the present, focusing on Europe and the United States. Key questions include: What is science, and how is it done? How are discoveries made and accepted? What is the nature of scientific progress? What is the impact of science on society? What is the impact of society on science? Topics will be drawn from the histories of physics, chemistry, biology, psychology, and medicine.AcknowledgementThis class is based on the one originally designed and taught by Prof. David Jones. His Spring 2005 version can be viewed by following the link under Archived Courses on the right side of this page

The Univariate Flagging Algorithm (UFA): An interpretable approach for predictive modeling

In many data classification problems, a number of methods will give similar accuracy. However, when working with people who are not experts in data science such as doctors, lawyers, and judges among others, finding interpretable algorithms can be a critical success factor. Practitioners have a deep understanding of the individual input variables but far less insight into how they interact with each other. For example, there may be ranges of an input variable for which the observed outcome is significantly more or less likely. This paper describes an algorithm for automatic detection of such thresholds, called the Univariate Flagging Algorithm (UFA). The algorithm searches for a separation that optimizes the difference between separated areas while obtaining a high level of support. We evaluate its performance using six sample datasets and demonstrate that thresholds identified by the algorithm align well with published results and known physiological boundaries. We also introduce two classification approaches that use UFA and show that the performance attained on unseen test data is comparable to or better than traditional classifiers when confidence intervals are considered. We identify conditions under which UFA performs well, including applications with large amounts of missing or noisy data, applications with a large number of inputs relative to observations, and applications where incidence of the target is low. We argue that ease of explanation of the results, robustness to missing data and noise, and detection of low incidence adverse outcomes are desirable features for clinical applications that can be achieved with relatively simple classifier, like UFA