Practice makes perfectoid: Pasts, futures, and the historiography of contemporary mathematics

Michael J. Barany

doi:10.1007/978-3-030-19071-2_83-1

Practice makes perfectoid: Pasts, futures, and the historiography of contemporary mathematics

Michael J. Barany

School of Social and Political Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

Comparing my historical account of the early years of Laurent Schwartz’s theory of distributions with number theorist Michael Harris’s narrative of the early years of Peter Scholze’s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the social and political conditions and implications of mathematical research and the communities that practice it.

Original language	English
Title of host publication	Handbook of the History and Philosophy of Mathematical Practice
Editors	Bharath Sriraman
Publisher	Springer
Pages	1-18
Number of pages	18
ISBN (Electronic)	9783030190712
ISBN (Print)	9783030190712
DOIs	https://doi.org/10.1007/978-3-030-19071-2_83-1
Publication status	E-pub ahead of print - 28 Jul 2023

Keywords / Materials (for Non-textual outputs)

expectation
horizon
temporality
confidence
contemporary mathematics
perfectoid theory
distribution theory
concepts
Fields Medal

Access to Document

10.1007/978-3-030-19071-2_83-1

Inverting hierarchies: The sociology of mathematical practice
Barany, M. J. & Kremakova, M. I., 15 Nov 2023, Handbook of the History and Philosophy of Mathematical Practice. Sriraman, B. (ed.). Springer, p. 1-22 22 p.
Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Cite this

@inbook{bdd4b1190ebf4ec39f2252b379ce5ac2,

title = "Practice makes perfectoid: Pasts, futures, and the historiography of contemporary mathematics",

abstract = "Comparing my historical account of the early years of Laurent Schwartz{\textquoteright}s theory of distributions with number theorist Michael Harris{\textquoteright}s narrative of the early years of Peter Scholze{\textquoteright}s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the social and political conditions and implications of mathematical research and the communities that practice it.",

keywords = "expectation, horizon, temporality, confidence, contemporary mathematics, perfectoid theory, distribution theory, concepts, Fields Medal",

author = "Barany, \{Michael J.\}",

year = "2023",

month = jul,

day = "28",

doi = "10.1007/978-3-030-19071-2\_83-1",

language = "English",

isbn = "9783030190712",

pages = "1--18",

editor = "Sriraman, \{Bharath \}",

booktitle = "Handbook of the History and Philosophy of Mathematical Practice",

publisher = "Springer",

address = "United Kingdom",

}

TY - CHAP

T1 - Practice makes perfectoid

T2 - Pasts, futures, and the historiography of contemporary mathematics

AU - Barany, Michael J.

PY - 2023/7/28

Y1 - 2023/7/28

N2 - Comparing my historical account of the early years of Laurent Schwartz’s theory of distributions with number theorist Michael Harris’s narrative of the early years of Peter Scholze’s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the social and political conditions and implications of mathematical research and the communities that practice it.

AB - Comparing my historical account of the early years of Laurent Schwartz’s theory of distributions with number theorist Michael Harris’s narrative of the early years of Peter Scholze’s perfectoid theory, I develop a perspective on change and temporality in mathematics that emphasizes the relationships between concepts, expectations, and communities of practice. Contemporary mathematics, understood as mathematics imbued with temporality, reflects the dynamic relationship between the people, ideas, pasts, and prospects of mathematical knowledge. Studying these historically may offer critical perspectives on the social and political conditions and implications of mathematical research and the communities that practice it.

KW - expectation

KW - horizon

KW - temporality

KW - confidence

KW - contemporary mathematics

KW - perfectoid theory

KW - distribution theory

KW - concepts

KW - Fields Medal

U2 - 10.1007/978-3-030-19071-2_83-1

DO - 10.1007/978-3-030-19071-2_83-1

M3 - Chapter (peer-reviewed)

SN - 9783030190712

SP - 1

EP - 18

BT - Handbook of the History and Philosophy of Mathematical Practice

A2 - Sriraman, Bharath

PB - Springer

ER -

Practice makes perfectoid: Pasts, futures, and the historiography of contemporary mathematics

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Research output

Inverting hierarchies: The sociology of mathematical practice

Cite this