|
Size: 6258
Comment:
|
Size: 9852
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 38: | Line 38: |
| .p033 . Microsof ATPs, Zaputo, [[ https://www.researchgate.net/publication/220896279_Zap_Automated_Theorem_Proving_for_Software_Analysis | Zap ]], [[https://www.microsoft.com/en-us/research/publication/z3-an-efficient-smt-solver/ | Z3 ]] | .p033 . Microsoft ATPs, Zaputo, [[ https://www.researchgate.net/publication/220896279_Zap_Automated_Theorem_Proving_for_Software_Analysis | Zap ]], [[https://www.microsoft.com/en-us/research/publication/z3-an-efficient-smt-solver/ | Z3 ]] .p033 . [[ https://en.wikipedia.org/wiki/Satisfiability_modulo_theories#Standardization_and_the_SMT-COMP_solver_competition | SMT-COMP ]] .p035 . 2013, de Moura proposes new interactive theorem prover .p036 . [[ https://en.wikipedia.org/wiki/Ramon_Llull | Ramon Llull ]] [[ https://plato.stanford.edu/entries/llull/#FiguQuatPhasTheiFunc | Wheel of 16 divine attributes ]] .p037 . [[ https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz | Leibniz ]] [[ https://en.wikipedia.org/wiki/Characteristica_universalis | characteristica universalis ]] .p037 . [[ https://en.wikipedia.org/wiki/Calculus_ratiocinator | calculus ratiocinator ]] .p038 . Leibniz - Art of Discovery .p040 . [[ https://en.wikipedia.org/wiki/Ernst_Zermelo | Ernst Zermelo ]] [[ https://en.wikipedia.org/wiki/Abraham_Fraenkel | Abraham Fraenkel ]] formal system to express all mathematics as [[ https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory | sets ]] .p041 . ZFC: '''Z'''ermelo-'''F'''raenkel set theory with the [[ https://en.wikipedia.org/wiki/Axiom_of_choice | axiom ]] of '''ch'''oice .p041 . [[ https://en.wikipedia.org/wiki/Bertrand_Russell | Russell ]] and [[ https://en.wikipedia.org/wiki/Alfred_North_Whitehead | Whitehead ]] [[ https://en.wikipedia.org/wiki/Principia_Mathematica | Principia Mathematica ]] 1910-13 [[ Ramified types and the axiom of reducibility | type theory ]] better .p042 . [[ https://en.wikipedia.org/wiki/Satisfiability | satisfiability (SAT) ]] solvers .p043 . [[ https://en.wikipedia.org/wiki/Satisfiability_modulo_theories | Satisfiability Modulo Theories (SMT) ]] .p047 . Interactive Theorem Provers (ITPs): [[ https://en.wikipedia.org/wiki/Rocq | Coq 1989 ]] [[ https://en.wikipedia.org/wiki/Agda_(programming_language) | Agda 1999 ]] [[ https://en.wikipedia.org/wiki/Isabelle_(proof_assistant) | Isabelle 1986 ]] [[ https://en.wikipedia.org/wiki/HOL_Light | HOL Light 1991 ]] .p052 . [[ https://en.wikipedia.org/wiki/Jeremy_Avigad | Jeremy Avigad ]] at [[ https://en.wikipedia.org/wiki/Carnegie_Mellon_University | Carnegie Mellon University ]] .p055 . Grant Passmore at [[ https://www.imandra.ai/about | Imandra AI ]] .p058 . [[ https://fordham.academia.edu/RobertLewis | Rob Lewis ]] .p058 . [[ https://soonhokong.github.io/ | Soonho Kong ]] now at AWS .p058 . [[ https://en.wikipedia.org/wiki/Georges_Gonthier | Georges Gonthier ]] .p059 . [[ https://en.wikipedia.org/wiki/Goldbach%27s_conjecture | Goldbach's conjecture ]] all even numbers greater than two can be written as the sum of two primes .p060 . [[ https://en.wikipedia.org/wiki/Law_of_excluded_middle | law of the excluded middle ]] .p063 . [[ https://en.wikipedia.org/wiki/Lean_(proof_assistant) | Lean ]] helper programs called tactics .p065 . 2015 Lean 2 .p075 - [[ https://en.wikipedia.org/wiki/Metamath | Metamath ]] proof assistabt .p076 . [[ https://scholar.google.com/citations?user=yaSqFaEAAAAJ&hl=en | Daniel Selsam ]] [[ https://en.wikipedia.org/wiki/David_L._Dill | David Dill ]] .p076 . [[ https://people.ciirc.cvut.cz/~urbanjo3/ | Josef Urban ]] .p079 . [[ https://gebner.org/ | Gabriel Ebner ]] .p080 . [[ | ]] .p088 . [[ | ]] .p095 . [[ | ]] |
| Line 40: | Line 68: |
| .p035 . .p03 . [[ | ]] .p0 . [[ | ]] |
|
| Line 44: | Line 69: |
| .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] .p0 . [[ | ]] . .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p1 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] .p2 . [[ | ]] |
|
| Line 146: | Line 71: |
| .p113 . [[ | ]] .p113 . [[ | ]] .p113 . [[ | ]] .p113 . [[ | ]] .p114 . [[ | ]] .p1 . [[ | ]] .p147 . [[ | ]] .p1 . [[ | ]] .p163 . [[ | ]] .p168 . [[ | ]] .p168 . [[ | ]] .p169 . [[ | ]] .p170 . [[ | ]] .p171 . [[ | ]] .p172 . [[ | ]] .p172 . [[ | ]] .p174 . [[ | ]] .p175 . [[ | ]] .p175 . [[ | ]] .p176 . [[ | ]] .p177 . [[ | ]] .p178 . [[ http://wiki.keithl.com/ProofInCode| ]] .p178 . [[ | ]] .p179 . [[ | ]] .p180 . [[ | ]] .p181 . [[ | ]] .p183 . [[ | ]] .p184 . [[ | ]] .p184 . [[ | ]] .p185 . [[ | ]] .p185 . [[ | ]] .p185 . [[ | ]] .p186 . [[ | ]] .p187 . [[ | ]] .p187 . [[ | ]] .p188 . [[ | ]] .p188 . [[ | ]] .p188 . [[ | ]] .p188 . [[ | ]] .p189 . [[ | ]] .p189 . [[ | ]] .p190 . [[ | ]] .p190 . [[ | ]] .p191 . [[ | ]] .p191 . [[ | ]] .p192 . [[ | ]] .p196 . [[ | ]] .p198 . [[ | ]] |
|
| Line 148: | Line 126: |
| .p200 . [[ | ]] .p200 . [[ | ]] .p207 . [[ | ]] .p209 . [[ | ]] .p210 . [[ | ]] .p211 . [[ | ]] .p212 . [[ | ]] .p213 . [[ | ]] .p213 . [[ | ]] .p214 . [[ | ]] .p217 . [[ | ]] .p217 . [[ | ]] .p219 . [[ | ]] .p220 . [[ | ]] .p221 . [[ | ]] .p221 . [[ | ]] .p222 . [[ | ]] .p222 . [[ | ]] .p223 . [[ | ]] .p223 . [[ | ]] .p223 . [[ | ]] .p225 . [[ | ]] .p225 . [[ | ]] .p229 . [[ | ]] .p229 . [[ | ]] .p229 . [[ | ]] .p230 . [[ | ]] .p231 . [[ | ]] .p231 . [[ | ]] .p232 . [[ | ]] .p232 . [[ | ]] .p235 . [[ | ]] .p235 . [[ | ]] .p236 . [[ | ]] .p237 . [[ | ]] .p238 . [[ | ]] .p239 . [[ | ]] .p240 . [[ | ]] .p241 . [[ | ]] .p241 . [[ | ]] .p242 . [[ | ]] .p242 . [[ | ]] .p242 . [[ | ]] .p243 . [[ | ]] .p243 . [[ | ]] .p243 . [[ | ]] .p244 . [[ | ]] .p244 . [[ | ]] .p246 . [[ | ]] .p247 . [[ | ]] .p247 . [[ | ]] .p248 . [[ | ]] .p248 . [[ | ]] .p249 . [[ | ]] .p250 . [[ | ]] .p250 . [[ | ]] .p250 . [[ | ]] .p251 . [[ | ]] .p252 . [[ | ]] .p252 . [[ | ]] .p253 . [[ | ]] .p254 . [[ | ]] .p255 . [[ | ]] .p257 . A Lean Proof for the Infinitude of Primes |
The Proof in the Code
How a Truth Machine Is Transforming Math and AI
Kevin Harnett . 2026 . 510.2856 HAR . Beaverton Library (book not stamped)
p003 . Leo de Moura started Lean project in 2013
p004 . Kevin Buzzard Patrick Massot Johan Commelin Mario Carneiro
p009 . Tom Hales b1958 1999 Princeton Institute for Advanced Study
p009 . Langlands Program
p010 . John Conway 1982 lecture at Cambridge University
p010 . Kepler Conjecture 1611 sphere packing density around 74% for both square and hexagonal base
p011 . Hales proves conjecture 1993-4, 300 pages in Annals of Mathematics "3GB worth of computer calculations"??
p012 . in 1900 David Hilbert 23 most important open problems in mathematics includes Kepler Conjecture
p014 . László Fejes Tóth Regular Figures
- p015 . Hales 1760 cases of ball arrangement, cluster of Sun workstations
- p016 . early 1998 eliminated all but fifty arrangements, 30 in spring, 19 in June, down to one by July 4
p019 . Mathematics, Form and Function by Saunders Mac Lane (indexed "Mac Lane")
- p019 . Four years later, peer reviews barely started
p020 . ITP Interactive Theorem Prover aka Proof Assistant
- p021 . Writing formal language ITP proof takes orders of magnitude longer than by hand
p023 . Mechanically checkable form Flyspeck Project
p023 . Dense Sphere Packings: A Blueprint for Formal Proofs 286 page book
p025 . Microsoft Research Leo de Moura born 1971 Rio de Janeiro
p027 . March 1989 Pontifical Catholic University of Rio de Janeiro
- p027 . internship at Semantic Designs (est 1993? 2026 dead link) in Austin Texas
- p028 . Math objective, but problem importance is subjective
p028 . SRI 1946 now SRI International
- p029 . LATEX, Siri
- p029 . 2001 Symbolic Analysis Laboratory . SAL
- p030 trace expressed as formula for all conditions that result in bad state???
p030 . Yices SMT solver
p030 . Automated theorem proving ATP
p031 . Microsoft Research Thomas Ball
- p032 . de Moura joins Microsoft in August 2006
p033 . SMT-COMP
- p035 . 2013, de Moura proposes new interactive theorem prover
p037 . calculus ratiocinator
- p038 . Leibniz - Art of Discovery
p040 . Ernst Zermelo Abraham Fraenkel formal system to express all mathematics as sets
p041 . ZFC: Zermelo-Fraenkel set theory with the axiom of choice
p041 . Russell and Whitehead Principia Mathematica 1910-13 type theory better
p042 . satisfiability (SAT) solvers
p047 . Interactive Theorem Provers (ITPs): Coq 1989 Agda 1999 Isabelle 1986 HOL Light 1991
p052 . Jeremy Avigad at Carnegie Mellon University
p055 . Grant Passmore at Imandra AI
p058 . Rob Lewis
p058 . Soonho Kong now at AWS
p058 . Georges Gonthier
p059 . Goldbach's conjecture all even numbers greater than two can be written as the sum of two primes
p060 . law of the excluded middle
p063 . Lean helper programs called tactics
- p065 . 2015 Lean 2
p075 - Metamath proof assistabt
p076 . Daniel Selsam David Dill
p076 . Josef Urban
p079 . Gabriel Ebner
- p257 . A Lean Proof for the Infinitude of Primes