The Trachtenberg system is a system of rapid mental calculation.
 The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly.
 It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.
In the mathematical field of algebraic number theory, the concept of principalization refers to a situation when, given an extension of algebraic number fields, some ideal (or more generally fractional ideal) of the ring of integers of the smaller field isn't principal but its extension to the ring of integers of the larger field is.
 Its study has origins in the work of Ernst Kummer on ideal numbers from the 1840s, who in particular proved that for every algebraic number field there exists an extension number field such that all ideals of the ring of integers of the base field (which can always be generated by at most two elements) become principal when extended to the larger field.
 In 1897 David Hilbert conjectured that the maximal abelian unramified extension of the base field, which was later called the Hilbert class field of the given base field, is such an extension.
 This conjecture, now known as principal ideal theorem, was proved by Philipp Furtwängler in 1930 after it had been translated from number theory to group theory by Emil Artin in 1929, who made use of his general reciprocity law to establish the reformulation.
 Since this long desired proof was achieved by means of Artin transfers of non-abelian groups with derived length two, several investigators tried to exploit the theory of such groups further to obtain additional information on the principalization in intermediate fields between the base field and its Hilbert class field.
 The first contributions in this direction are due to Arnold Scholz and Olga Taussky in 1934, who coined the synonym capitulation for principalization.
 Another independent access to the principalization problem via Galois cohomology of unit groups is also due to Hilbert and goes back to the chapter on cyclic extensions of number fields of prime degree in his number report, which culminates in the famous Theorem 94.
Genocide studies is an academic field of study that researches genocide.
 Genocide became a field of study in the mid-1940s, with the work of Raphael Lemkin, who coined the term "genocide" and is the field's founding father.
 The Holocaust was initially the primary subject matter of genocide studies, and the field received an extra impetus in the 1990s, when the Rwandan genocide took place.
Boris Grigoryevich Galerkin (Russian: Бори́с Григо́рьевич Галёркин , surname more accurately romanized as Galyorkin; 4 March [O.S. 20 February] 1871  – 12 July 1945), born in Polotsk, Vitebsk Governorate, Russian Empire, was a Jewish Soviet mathematician and an engineer.
Madonna Studies is a term which has been used to refer to a development of a field in several studios since late 1980s.
 One writer described the "institutionalization of a major subdivision of American media studies into Madonna studies".
 The field related to the study of and interpretation of the work of American pop musician Madonna using an interdisciplinary approach incorporating cultural studies and media studies.
 A notable compendium of essays titled "The Madonna Connection" was published in 1992.
 Controversy over this field of study stemmed from discussions over the intellectual worth of pursuing academic inquiry into a pop musician, with some arguing the field was nothing more than pop cultural commentary.
The Macoun Field Club is a field naturalists' club in Ottawa, Ontario, Canada for young people between the ages of 8 and 18.
 The Club is named for John Macoun, Canada's first Dominion Naturalist.
 The members get together once a week (typically Saturdays), alternating indoor meetings at which research students or scientists give presentations on their work or field of study, with outdoor field trips to either the club's study area in Stony Swamp Conservation Area or other locations.
Jakow Trachtenberg (17 June 1888 – 1953) was a Jewish mathematician who developed the mental calculation techniques called the Trachtenberg system.
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages.
 The subject looks at letters or symbols, and the sequences they form.
 Combinatorics on words affects various areas of mathematical study, including algebra and computer science.
 There have been a wide range of contributions to the field.
 Some of the first work was on square-free words by Thue in the early 1900s.
 He and colleagues observed patterns within words and tried to explain them.
 As time went on, combinatorics on words became useful in the study of algorithms and coding.
 It led to developments in abstract algebra and answering open questions.
Tom Bachtell is a self-taught artist who is an illustrator and caricaturist for The New Yorker’s Talk of the Town as well as other sections, contributing regularly for 27 years.
 He has done work for Entertainment Weekly, Newsweek, Forbes, Bon Appétit, Town & Country, Mother Jones, New York, Poetry, the New York Times, the Wall Street Journal, the New York Observer and London’s Evening Standard as well as Marshall Field, Lands' End and the chamber-music series at the University of Chicago as part of his ad-campaign clientele.
 His brush-and-ink style is considered to be reminiscent of American cartoonists from the 1920s and 1930s.
 He was a finalist for the 18th Lambda Literary Awards as illustrator along with editor Robert Trachtenberg for the book “When I Knew” under the Belles Lettres category.
The term "microbiologist" comes from the Greek "mīkros" meaning "small" βίος , and "bios", meaning "life" -λογία , combined with "-logia" meaning one who studies.
 A microbiologist (from Greek μῑκρος ) is a biological scientist who studies microscopic life forms and processes or works in the field of microbiology.
 Microbiologists investigate the growth, interactions and characteristics of microscopic organisms such as bacteria, algae, fungi, and some types of parasites and their vectors.
 They contribute much to the field by trying to understand and learn about the interaction between these microbes and the environment and also among themselves and other organisms.
 Most microbiologists are qualified to work in offices and/or research facilities, such as a laboratory as well as in the academia.
 There, they conduct experiments that help them analyze microbes and their importance.
 A microbiologist's work is often repeated or improved in order to establish accurate research.
 Most microbiologists specialize in environmental, food, agricultural, industrial or medical aspects of microbiology including: virology (the study of viruses); immunology (the study of mechanisms that fight infections); bioinformatics (the methods for storing, retrieving, organizing and analyzing biological data) and Bioremediation (using microbes as environmental mitigation strategies).
 Many microbiologists use biotechnology to advance the understanding of cell reproduction and human disease.
 Some microbiologists have contributed to knowledge of pathogens and disease-causing microbes.
 While others, study their interaction with the environment and their use as potential environmental pollution cleaners.

Question: What field of study did Boris Galerkin and Jakow Trachtenberg both work in?
Answer: mathematician