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

2010
*
Lecture Notes in Computer Science
*

. . . or even serious, but misguided "provers"

doi:10.1007/978-3-642-15582-6_27
fatcat:ujjfgqjrcjeszcuqvjhbvsd66m
*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 ...##
###
Why Markets Crash and What Law Can Do about It

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*? ...

##
###
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?

2014
*
ILAR journal
*

The vast majority

doi:10.1093/ilar/ilu047
pmid:25541546
pmcid:PMC4342719
fatcat:oqyjenn2yjdndnx3htv2oayqge
*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. ...##
###
Educación financiera: ¿por qué la necesitamos?
[chapter]

Financial education: why do we need it?

2021
*
ESTRATEGIA NACIONAL DE EDUCACIÓN FINANCIERA (ENEF) En búsqueda de un Brasil mejor
*

Financial education: why do we need it?

Financial citizenship entails an individual's ability

doi:10.52343/riemmaeditora.978-65-00-16994-2.1
fatcat:dwfyhhsglnbx7fx7ol3unqywa4
*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*? ...##
###
Why do we Still Believe in Newton's Law ? Facts, Myths and Methods in Gravitational Physics
[article]

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. ...

##
###
Mathematical Proof Between Generations
[article]

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. ...

##
###
Proof assistants: History, ideas and future

2009
*
Sadhana (Bangalore)
*

In this paper I will discuss the fundamental ideas behind

doi:10.1007/s12046-009-0001-5
fatcat:nnrgwwfdxjhqnfdoye7s4665su
*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.' ...##
###
Proof script pragmatics in IMPS
[chapter]

1994
*
Lecture Notes in Computer Science
*

This paper introduces the imps

doi:10.1007/3-540-58156-1_25
fatcat:hu3gcvyfwzadxor364di5fm3ny
*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*. ...##
###
Prove-It: A Proof Assistant for Organizing and Verifying General Mathematical Knowledge
[article]

2020
*
arXiv
*
pre-print

Prove-

arXiv:2012.10987v2
fatcat:7qcog2ba7fez5hnszkvq5itady
*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 ...##
###
MACHINE-ASSISTED PROOFS

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. ...

##
###
Towards the animation of proofs – testing proofs by examples

2002
*
Theoretical Computer Science
*

Logically,

doi:10.1016/s0304-3975(00)00350-9
fatcat:lhtwroijgza4xmjfsh5lyox7qi
*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. ...##
###
Proof, Message and Certificate
[chapter]

2012
*
Lecture Notes in Computer Science
*

We claim that

doi:10.1007/978-3-642-31374-5_2
fatcat:momn5n67sfem3bt2styrau2cbe
*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. ...##
###
Mathematical Method and Proof

2006
*
Synthese
*

This view fails

doi:10.1007/s11229-005-4064-5
fatcat:4ienrswtvzbetaw74oxyu7omzi
*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*. ...##
###
Universality of Proofs (Dagstuhl Seminar 16421)

2017
*
Dagstuhl Reports
*

The seminar was motivated by the fact that

doi:10.4230/dagrep.6.10.75
dblp:journals/dagstuhl-reports/DowekDPR16
fatcat:5isaoju43faxfdxb3tx7xoi7py
*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 ...##
###
Towards a Comprehensive Conception of Mathematical Proof

2018
*
Journal of Education and Learning (EduLearn)
*

Hence,

doi:10.11591/edulearn.v12i4.9557
fatcat:cpcceev3wzehdfo3lcccvni3im
*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 ...
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