Eric Schechter

Last updated
Eric Schechter
Born (1950-08-01) August 1, 1950 (age 71)
Nationality American
Alma mater University of Chicago
Scientific career
Fields Mathematics
Institutions Vanderbilt University
Doctoral advisor Jerry L. Bona

Eric Schechter (born August 1, 1950) is an American mathematician, retired from Vanderbilt University with the title of professor emeritus. His interests started primarily in analysis but moved into mathematical logic. Schechter is best known for his 1996 book Handbook of Analysis and its Foundations, which provides a novel approach to mathematical analysis and related topics at the graduate level.

Contents

Important works

Schechter has authored a number of articles in analysis, differential equations, mathematical logic, and set theory. He is best known for writing two textbooks covering advanced material but written at an introductory level:

Handbook of Analysis and its Foundations was reviewed at length by the Society for Industrial and Applied Mathematics review, which wrote:

Every once in a while a book comes along that so effectively redefines an educational enterprise -- in this case, graduate mathematical training -- and so effectively reexamines the hegemony of ideas prevailing in a discipline -- in this case, mathematical analysis -- that it deserves our careful attention. This is such a book. [1]

Schechter also maintains two webpages that are frequently cited:

Politics

Schechter is involved in political activism of the democratic socialist variety. His mathematical homepage includes a few anti-war statements, [2] and his political home page includes a long essay about progressive ideology. [3] He has worked as an organizer for the Nashville Peace Coalition, protesting the wars in Iraq and Afghanistan. [4] At a meeting for the living wage movement on Vanderbilt's campus, he remarked that it is hard to bring up politics in a non-political environment, and expressed that people did not talk much about politics in the mathematics department at Vanderbilt. [5] His father, Henry Schechter, was a deputy of the AFL-CIO. [6]

In 2010, Schechter ran for Tennessee's 5th Congressional District seat against incumbent congressman Jim Cooper, [7] but was defeated in the Democratic primary. Schechter describes himself as "a different kind of Democrat." [8]

Related Research Articles

In the philosophy of mathematics, constructivism asserts that it is necessary to find a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves a verificational interpretation of the existential quantifier, which is at odds with its classical interpretation.

Stephen Cole Kleene American mathematician

Stephen Cole Kleene was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star, Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism.

Willard Van Orman Quine American philosopher and logician

Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978.

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

Gottlob Frege German philosopher, logician, and mathematician (1848–1925)

Friedrich Ludwig Gottlob Frege was a German philosopher, logician, and mathematician. He worked as a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. In the early 21st century, Frege was widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever.

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.

Frank Ramsey (mathematician) British mathematician, philosopher, and economist

Frank Plumpton Ramsey was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of Ludwig Wittgenstein and, as an undergraduate, translated Wittgenstein's Tractatus Logico-Philosophicus into English. He was also influential in persuading Wittgenstein to return to philosophy and Cambridge. Like Wittgenstein, he was a member of the Cambridge Apostles, the secret intellectual society, from 1921.

Errett Albert Bishop was an American mathematician known for his work on analysis. He expanded constructive analysis in his 1967 Foundations of Constructive Analysis, where he proved most of the important theorems in real analysis by constructive methods.

Solomon Feferman American philosopher and mathematician

Solomon Feferman was an American philosopher and mathematician who worked in mathematical logic.

In mathematics, an element of a set is any one of the distinct objects that belong to that set.

Samson Abramsky

Samson Abramsky is a computer scientist who holds the Christopher Strachey Professorship at the Department of Computer Science, University of Oxford. He has made contributions to the areas of domain theory, the lazy lambda calculus, strictness analysis, concurrency theory, interaction categories, geometry of interaction, game semantics and quantum computing.

Carl Gustav Hempel German writer and philosopher

Carl Gustav "Peter" Hempel was a German writer and philosopher. He was a major figure in logical empiricism, a 20th-century movement in the philosophy of science. He is especially well known for his articulation of the deductive-nomological model of scientific explanation, which was considered the "standard model" of scientific explanation during the 1950s and 1960s. He is also known for the raven paradox.

Ivor Grattan-Guinness

Ivor Owen Grattan-Guinness was a historian of mathematics and logic.

Kenneth Binmore English mathematician and game theorist born 1940

Kenneth George "Ken" Binmore, is an English mathematician, economist, and game theorist, a Professor Emeritus of Economics at University College London (UCL) and a Visiting Emeritus Professor of Economics at the University of Bristol. As a founder of modern economic theory of bargaining, he made important contributions to the foundations of game theory, experimental economics, evolutionary game theory and analytical philosophy. He took up economics after holding the Chair of Mathematics at the London School of Economics. The switch has put him at the forefront of developments in game theory. His other interests include political and moral philosophy, decision theory, and statistics. He has written over 100 scholarly papers and 14 books.

Dov M. Gabbay is an Israeli logician. He is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London.

William S. Hatcher (1935–2005) was a mathematician, philosopher, educator and a member of the Baháʼí Faith. He held a doctorate in mathematics from the University of Neuchatel, Switzerland, and bachelor's and master's degrees from Vanderbilt University in Nashville, Tennessee. A specialist in the philosophical alloying of science and religion, for over thirty years he held university positions in North America, Europe, and Russia.

<i>The Principles of Mathematics</i> Book by Bertrand Russell

The Principles of Mathematics (PoM) is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.

Elliott Mendelson was an American logician. He was a professor of mathematics at Queens College of the City University of New York, and the Graduate Center, CUNY. He was Jr. Fellow, Society of Fellows, Harvard University, 1956–58.

Robert B. Talisse

Robert B. Talisse is an American philosopher and political theorist. He is currently Professor of Philosophy and Chair of the Philosophy Department at Vanderbilt University in Nashville, Tennessee, where he is also a Professor of Political Science. Talisse is a former editor of the academic journal Public Affairs Quarterly, and a regular contributor to the blog 3 Quarks Daily, where he posts a monthly column with his frequent co-author and fellow Vanderbilt philosopher Scott Aikin. He earned his PhD in Philosophy from the City University of New York in 2001. His principal area of research is political philosophy, with an emphasis on democratic theory and liberalism.

Tom Kahn U.S. social democrat

Tom David Kahn was an American social democrat known for his leadership in several organizations. He was an activist and influential strategist in the Civil Rights Movement. He was a senior adviser and leader in the U.S. labor movement.

References