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Building a Library of Mechanized Mathematical Proofs: Why Do It? and What Is It Like to Do? [chapter]

R. D. Arthan
2010 Lecture Notes in Computer Science  
. . . or even serious, but misguided "provers" of P = NP Specification: take β (x,y) chosen in the appropriate quadrant where: - Give a flavour of what it is like to develop a theory like the calculus  ...  Proposal We should use computers to support mathematical endeavours. • I will describe one approach that offers: high assurance (1 = 2) extensiblity and programmability access to a large library of existing  ... 
doi:10.1007/978-3-642-15582-6_27 fatcat:ujjfgqjrcjeszcuqvjhbvsd66m

Why Markets Crash and What Law Can Do about It

Frank Partnoy
1999 Social Science Research Network  
WHAT LAW CAN Do ABOUT IT Given the above theories of why markets crash, what can law do about crashes?  ...  Second, what can law do about it?  ... 
doi:10.2139/ssrn.183473 fatcat:sye3xy3n2fecrmaltoguvcfiky

The Significance of Meaning: Why Do Over 90% of Behavioral Neuroscience Results Fail to Translate to Humans, and What Can We Do to Fix It?

J. P. Garner
2014 ILAR journal  
The vast majority of drugs entering human trials fail. This problem (called "attrition") is widely recognized as a public health crisis, and has been discussed openly for the last two decades.  ...  The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.  ...  out the connection to Fisher's original writings), Karen Parker, Amy Lossie, and Edmond Pajor.  ... 
doi:10.1093/ilar/ilu047 pmid:25541546 pmcid:PMC4342719 fatcat:oqyjenn2yjdndnx3htv2oayqge

Educación financiera: ¿por qué la necesitamos? [chapter]
Financial education: why do we need it?

Adriana Toledo
2021 ESTRATEGIA NACIONAL DE EDUCACIÓN FINANCIERA (ENEF) En búsqueda de un Brasil mejor  
Financial citizenship entails an individual's ability to make the right choices, exercising their rights and fulfilling the associated duties. It is a concept taken from the term citizenship.  ...  Capitalism is a system predominated by private ownership and the constant quest for profit and the accumulation of wealth.  ...  Benjamin Franklin Ten years of the National Strategy for Financial Education (ENEF) Have you heard about financial education? Do you know what it means? Why do we need it?  ... 
doi:10.52343/riemmaeditora.978-65-00-16994-2.1 fatcat:dwfyhhsglnbx7fx7ol3unqywa4

Why do we Still Believe in Newton's Law ? Facts, Myths and Methods in Gravitational Physics [article]

Alexander Unzicker
2008 arXiv   pre-print
a common origin (4) it is useful to consider the present situation under a historical perspective and (5) it could well be that we still do not understand gravity.  ...  Not to claim that we do know when we do not - this is the third. That's the kind of attitude I'd like to popularize. There is little hope for success.' (Karl Popper)  ...  The author thanks for discussions with Karl Fabian, Hannes Hoff and Jan Bernkopf, and for the encouraging comments by gr-qc readers.  ... 
arXiv:gr-qc/0702009v8 fatcat:r2d7zo7lyjb43orym7xc4sk5vu

Mathematical Proof Between Generations [article]

Jonas Bayer, Christoph Benzmüller, Kevin Buzzard, Marco David, Leslie Lamport, Yuri Matiyasevich, Lawrence Paulson, Dierk Schleicher, Benedikt Stock, Efim Zelmanov
2022 arXiv   pre-print
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice.  ...  This article investigates the gap between the different definitions of a proof and possibilities to build bridges.  ...  In set theory, λ < ℵ 1 has a different meaning from λ < ω 1 even though ℵ 1 = ω 1 . • The libraries of formalized mathematics still have many gaps, and what they do have is difficult to find.  ... 
arXiv:2207.04779v1 fatcat:3lmx76l72vfx5hs3a6tqpdwhh4

Proof assistants: History, ideas and future

H. Geuvers
2009 Sadhana (Bangalore)  
In this paper I will discuss the fundamental ideas behind proof assis tants: What are they and what is a proof anyway?  ...  But there is still a long road ahead and I will indicate what we believe is needed for the further proliferation of proof assistants.  ...  You want to find out what the facts are, and what you do is in that respect sim ilar to what a laboratory technician does, but it is different in its degree of precision and information.'  ... 
doi:10.1007/s12046-009-0001-5 fatcat:nnrgwwfdxjhqnfdoye7s4665su

Proof script pragmatics in IMPS [chapter]

William M. Farmer, Joshua D. Guttman, Mark E. Nadel, F. Javier Thayer
1994 Lecture Notes in Computer Science  
This paper introduces the imps proof script mechanism and some practical methods for exploiting it.  ...  "Proof by Emacs" is one among a range of techniques that imps supports to allow the mathematician to do what he would like to do anyway, but in a more convenient and reliable way.  ...  -To provide mathematical research with mechanized support covering a range of concrete and abstract mathematics, eventually with the help of a large theory library of formal mathematics.  ... 
doi:10.1007/3-540-58156-1_25 fatcat:hu3gcvyfwzadxor364di5fm3ny

Prove-It: A Proof Assistant for Organizing and Verifying General Mathematical Knowledge [article]

Wayne M. Witzel, Warren D. Craft, Robert D. Carr, Joaquín E. Madrid Larrañaga
2020 arXiv   pre-print
Prove-It uses a highly-flexible Jupyter notebook-based user interface that documents interactions and proof steps using LaTeX.  ...  We review Prove-It's highly expressive representation of expressions, judgments, theorems, and proofs; demonstrate the system by constructing a traditional proof-by-contradiction that √(2)∉ℚ; and discuss  ...  INTRODUCTION & MOTIVATION Prove-It is an open-source Python library that has been designed as a general-purpose theorem prover to support structured proof [1] development to build formal proofs in a manner  ... 
arXiv:2012.10987v2 fatcat:7qcog2ba7fez5hnszkvq5itady

MACHINE-ASSISTED PROOFS

JAMES DAVENPORT, BJORN POONEN, JAMES MAYNARD, HARALD HELFGOTT, PHAM HUU TIEP, LUÍS CRUZ-FILIPE
2019 Proceedings of the International Congress of Mathematicians (ICM 2018)  
proof of Kepler Conjecture.  ...  Also , the algorithms underpinning their conjectures. 1976 "Every Planar Map is Four-Colorable": 256 pages + computation [2] . 1989 Revised Four-Color Theorem proof published [3] . 1998 Hales announced  ...  Many thanks are due to my colleague Andrew V. Sutherland.  ... 
doi:10.1142/9789813272880_0038 fatcat:wlts6ghnvjgbpbigwbzzoqpuae

Towards the animation of proofs – testing proofs by examples

Susumu Hayashi, Ryosuke Sumitomo, Ken-ichiro Shii
2002 Theoretical Computer Science  
Logically, proof animation is merely a contrapositive of "proofs as programs", which is an application of Curry-Howard isomorphism to formal program development.  ...  In this paper, we introduce the notion of proof animation, which is a new application of the principle of "Curry-Howard isomorphism" to formal proof development.  ...  It is also a response to discussions with his friends in the Coq team on the paper [11] . The ÿrst author would like to thank them.  ... 
doi:10.1016/s0304-3975(00)00350-9 fatcat:lhtwroijgza4xmjfsh5lyox7qi

Proof, Message and Certificate [chapter]

Andrea Asperti
2012 Lecture Notes in Computer Science  
We claim that it is important to prevent the divorce between these two epistemological functions, discussing the implications for the field of mathematical knowledge management.  ...  purpose of proofs, emphasizing the dichotomy between message and certificate.  ...  I would also like to thank the anonymous reviewers for their detailed and stimulating comments.  ... 
doi:10.1007/978-3-642-31374-5_2 fatcat:momn5n67sfem3bt2styrau2cbe

Mathematical Method and Proof

Jeremy Avigad
2006 Synthese  
This view fails to explain why it is very often the case that a new proof of a theorem is deemed important.  ...  On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem.  ...  The challenge now is to clarify what it is that we think proofs are doing, and understand the mechanisms by which they do it.  ... 
doi:10.1007/s11229-005-4064-5 fatcat:4ienrswtvzbetaw74oxyu7omzi

Universality of Proofs (Dagstuhl Seminar 16421)

Gilles Dowek, Catherine Dubois, Brigitte Pientka, Florian Rabe, Marc Herbstritt
2017 Dagstuhl Reports  
The seminar was motivated by the fact that it is nowadays difficult to exchange proofs from one proof assistant to another one.  ...  The seminar aims at providing a comprehensive overview of the existing techniques for interoperability and going further into the development of a common objective and framework for proof developments  ...  We identify the notion of an MCSat-friendly inference system, and define a generic MCSat calculus that is sound and complete for satisfiability in the union of n arbitrary theories (including for instance  ... 
doi:10.4230/dagrep.6.10.75 dblp:journals/dagstuhl-reports/DowekDPR16 fatcat:5isaoju43faxfdxb3tx7xoi7py

Towards a Comprehensive Conception of Mathematical Proof

Zakaria Ndemo, David. J. Mtetwa, Fred Zindi
2018 Journal of Education and Learning (EduLearn)  
Hence, it is suggested in this paper that current research could also focus on mechanisms that promote an analytic conceptions of mathematical proof that are comprehensive enough to allow students to engage  ...  There is overwhelming evidence that students face serious challenges in learning mathematical proof. Studies have found that students possess a superficial understanding of mathematical proof.  ...  We also express our appreciation of the tremendous support by Library Staff at BUSE and University of Zimbabwe in assisting us with access to data bases from which we obtained relevant literature ideas  ... 
doi:10.11591/edulearn.v12i4.9557 fatcat:cpcceev3wzehdfo3lcccvni3im
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