Mathematicians writing for mathematicians

We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised...

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Published in:	Synthese (Dordrecht) Vol. 198; no. Suppl 26; pp. S6233 - S6250
Main Authors:	Andersen, Line Edslev, Johansen, Mikkel Willum, Sørensen, Henrik Kragh
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Science + Business Media 01.11.2021 Springer Netherlands Springer Nature B.V
Subjects:	Audiences Case studies Cognition & reasoning Collaboration Contextualism Education Epistemology Logic Mathematicians Metaphysics Philosophy Philosophy of Language Philosophy of Science Proof theory S.I.: ENABLING MATHEMATICAL CULTURES Scholarly publishing Writing Contextualization The nature of proof Mathematical audience Mathematical argument Mathematical publication
ISSN:	0039-7857, 1573-0964
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Abstract	We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.
AbstractList	We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between. We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did not yet have experience writing research papers for mathematicians. Thus, one main purpose of revising the paper was to make it take into account the intended audience. For this reason, the changes made to the initial draft and the authors’ purpose in making them provide a window for viewing how mathematicians write for mathematicians. We examined how their paper attracts the interest of the reader and prepares their proofs for validation by the reader. Among other findings, we found that their paper prepares the proofs for two types of validation that the reader can easily switch between.
Author	Sørensen, Henrik Kragh Andersen, Line Edslev Johansen, Mikkel Willum
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Cites_doi	10.7208/chicago/9780226270982.001.0001 10.1007/978-94-007-6534-4_11 10.5951/jresematheduc.43.4.0358 10.1016/0001-8708(79)90018-5 10.1093/philmat/nkm023 10.1007/s10649-015-9605-3 10.1093/acprof:oso/9780199296453.003.0005 10.1007/s11229-018-1778-8 10.1090/S0273-0979-1994-00502-6 10.1093/mind/fzv140 10.1006/jabr.1998.7467 10.1007/978-94-007-6534-4_3 10.1093/philmat/7.1.5 10.1007/978-3-319-28582-5_15 10.1007/978-94-007-6534-4_5 10.1023/A:1022131513275 10.1017/CBO9781139171472
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References_xml	– reference: RavYWhy do we prove theorems?Philosophia Mathematica1999754110.1093/philmat/7.1.5 – reference: ThurstonWPOn proof and progress in mathematicsBulletin of the American Mathematical Society19943016117710.1090/S0273-0979-1994-00502-6 – reference: JohnsonRHManifest rationality: A pragmatic theory of argument2000Mahwah, NJLawrence Erlbaum Associates – reference: DahnBIRobbins algebras are Boolean: A revision of McCune’s computer-generated solution of Robbins problemJournal of Algebra1998208252653210.1006/jabr.1998.7467 – reference: PaseauACWhat’s the point of complete rigour?Mind201612517720710.1093/mind/fzv140 – reference: HershRSome proposals for reviving the philosophy of mathematicsAdvances in Mathematics197931315010.1016/0001-8708(79)90018-5 – reference: MandersKMancosuPThe Euclidean diagramThe philosophy of mathematical practice2008OxfordOxford University Press8013310.1093/acprof:oso/9780199296453.003.0005 – reference: JohansenMWMisfeldtMLarvorBAn empirical approach to the mathematical values of problem choice and argumentationMathematical cultures: The London meetings 2012–20142016ChamSpringer25926910.1007/978-3-319-28582-5_15 – reference: Krabbe, E. C. W. (2013 [1997]). Arguments, proofs, and dialogues. In A. Aberdein & I. J. Dove (Eds.), The argument of mathematics (pp. 31–45). Dordrecht: Springer. – reference: InglisMAlcockLExpert and novice approaches to reading mathematical proofsJournal for Research in Mathematics Education20124335839010.5951/jresematheduc.43.4.0358 – reference: OlsonRHouston, we have a narrative: Why science needs story2015ChicagoUniversity of Chicago Press10.7208/chicago/9780226270982.001.0001 – reference: Dexter, L. A. (1970/2006). Elite and specialized interviewing. Colchester: ECPR Press. – reference: MisfeldtMJohansenMWResearch mathematicians’ practices in selecting mathematical problemsEducational Studies in Mathematics20158935737310.1007/s10649-015-9605-3 – reference: RavYA critique of a formalist-mechanist version of the justification of arguments in mathematicians’ proof practicesPhilosophia Mathematica20071529132010.1093/philmat/nkm023 – reference: AberdeinADoveIJThe argument of mathematics2013DordrechtSpringer – reference: LakatosIProofs and refutations: The logic of mathematical discovery1976New YorkCambridge University Press10.1017/CBO9781139171472 – reference: AndersenLEAcceptable gaps in mathematical proofsSynthese201810.1007/s11229-018-1778-8 – reference: Hilbert, D. (1925/1967). On the infinite. In J. Heijenoort (Ed.), From Frege to Gödel: A source book in mathematical logic, 1879–1931 (pp. 369-392). Cambridge, MA: Harvard University Press. – reference: Krabbe, E. C. W. (2013 [2008]). Strategic maneuvering in mathematical proofs. In A. Aberdein & I. J. Dove (Eds.), The argument of mathematics (pp. 181–193). Dordrecht: Springer. – reference: FallisDIntentional gaps in mathematical proofsSynthese2003134456910.1023/A:1022131513275 – reference: DufourMAberdeinADoveIJArguing around mathematical proofsThe argument of mathematics2013DordrechtSpringer617610.1007/978-94-007-6534-4_5 – reference: PerelmanCOlbrechts-TytecaLThe new rhetoric: A treatise on argumentation1969Notre DameThe University of Notre Dame Press – volume-title: Houston, we have a narrative: Why science needs story year: 2015 ident: 2145_CR18 doi: 10.7208/chicago/9780226270982.001.0001 – ident: 2145_CR14 doi: 10.1007/978-94-007-6534-4_11 – ident: 2145_CR9 – volume: 43 start-page: 358 year: 2012 ident: 2145_CR10 publication-title: Journal for Research in Mathematics Education doi: 10.5951/jresematheduc.43.4.0358 – volume-title: Manifest rationality: A pragmatic theory of argument year: 2000 ident: 2145_CR12 – volume: 31 start-page: 31 year: 1979 ident: 2145_CR8 publication-title: Advances in Mathematics doi: 10.1016/0001-8708(79)90018-5 – ident: 2145_CR4 – volume: 15 start-page: 291 year: 2007 ident: 2145_CR22 publication-title: Philosophia Mathematica doi: 10.1093/philmat/nkm023 – volume: 89 start-page: 357 year: 2015 ident: 2145_CR17 publication-title: Educational Studies in Mathematics doi: 10.1007/s10649-015-9605-3 – start-page: 80 volume-title: The philosophy of mathematical practice year: 2008 ident: 2145_CR16 doi: 10.1093/acprof:oso/9780199296453.003.0005 – volume-title: The argument of mathematics year: 2013 ident: 2145_CR1 – year: 2018 ident: 2145_CR2 publication-title: Synthese doi: 10.1007/s11229-018-1778-8 – volume: 30 start-page: 161 year: 1994 ident: 2145_CR23 publication-title: Bulletin of the American Mathematical Society doi: 10.1090/S0273-0979-1994-00502-6 – volume: 125 start-page: 177 year: 2016 ident: 2145_CR19 publication-title: Mind doi: 10.1093/mind/fzv140 – volume-title: The new rhetoric: A treatise on argumentation year: 1969 ident: 2145_CR20 – volume: 208 start-page: 526 issue: 2 year: 1998 ident: 2145_CR3 publication-title: Journal of Algebra doi: 10.1006/jabr.1998.7467 – ident: 2145_CR13 doi: 10.1007/978-94-007-6534-4_3 – volume: 7 start-page: 5 year: 1999 ident: 2145_CR21 publication-title: Philosophia Mathematica doi: 10.1093/philmat/7.1.5 – start-page: 259 volume-title: Mathematical cultures: The London meetings 2012–2014 year: 2016 ident: 2145_CR11 doi: 10.1007/978-3-319-28582-5_15 – start-page: 61 volume-title: The argument of mathematics year: 2013 ident: 2145_CR5 doi: 10.1007/978-94-007-6534-4_5 – volume: 134 start-page: 45 year: 2003 ident: 2145_CR6 publication-title: Synthese doi: 10.1023/A:1022131513275 – volume-title: Proofs and refutations: The logic of mathematical discovery year: 1976 ident: 2145_CR15 doi: 10.1017/CBO9781139171472
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