Mathematics: Is God Silent? / Edition 2

Mathematics: Is God Silent? / Edition 2

by James Duane Nickel

ISBN-10: 187999822X

ISBN-13: 9781879998223

Pub. Date: 01/28/2001

Publisher: Ross House Books

This book revolutionizes the prevailing understanding and teaching of math. This book is a must for all upper-level christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject which cannot be taught…  See more details below


This book revolutionizes the prevailing understanding and teaching of math. This book is a must for all upper-level christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject which cannot be taught from a distinctively biblical perspective.

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Ross House Books
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Table of Contents

The Details Insideix
List of Figuresxiv
Preface to the First Editionxix
Preface to the Second Editionxxi
Chapter Summariesxxiv
Part IMathematics in History1
1Does it Really Matter?3
1.1Case closed ... or is it?4
1.2Penetrating Declarations4
1.3Laying Foundations5
1.4Worldview and Presuppositions5
1.5The Components of a Worldview7
1.6The Biblical Worldview8
Questions for Review, Further Research, and Discussion10
2From Adam to Christ11
2.2Early Civilizations14
2.3Classical Greece16
2.4Reason and Nature Alone16
2.5Hebrew Revelation17
2.6Revelation Rejected19
2.7The Ionian School19
2.7.1The Six Propositions of Thales20
2.8The Rise and Fall of Pythagoras21
2.9Heraclitus, the Obscure24
2.10The Eleatic School25
2.11Geometry to the Rescue27
2.12Pluralistic Metaphysics27
2.13The Ideal World of Plato29
2.14Aristotelian Metaphysics32
2.15The "Elements of Euclid"34
2.15.1Euclid's Five Axioms and Five Postulates35
2.15.2Applied Geometry36
2.15.3Geometry and Latitude38
2.16Accomplishments in Alexandria38
2.16.1Eratosthenes Measures the Circumference of the Earth41
2.16.2The Sieve of Eratosthenes43
2.16.3Rudimentary Trigonometric Ratios46
2.16.4Finding the Height of a Tree47
2.16.5What Happens if a Mountain Gets in the Way?48
2.16.6Calculating the Radius of the Earth49
2.16.7Determining the Distance Between any Two Points on the Earth50
2.16.8Determining the Distance from the Earth to the Moon51
2.16.9Determining the Radius of the Moon51
2.17Sovereign God at Work52
2.18Sandy Foundations52
Questions for Review, Further Research, and Discussion54
3From Christ to Wycliffe57
3.1Ptolemaic Theory57
3.2Pragmatic Rome59
3.3The Advent of Christ60
3.4Jerusalem Confronts Athens62
3.5The Bishop of Hippo64
3.6The Essence of the Conflict66
3.7Eventual Compromise66
3.7.1The Seven Liberal Arts67
3.8Mathematicians of the Early Christian Era68
3.9The Dark Ages?71
3.10The Medieval Industrial Revolution73
3.10.1Three-Field Farming75
3.11The Status of Mathematics and Science79
3.12Muslim and Byzantine Input83
3.13The University85
3.14The Scholastics at Oxford86
3.15A Champion of Aristotle88
3.16Forerunners of Innovative Thoughts89
3.17The Role of Scripture94
3.18The Morning Star96
Questions for Review, Further Research, and Discussion97
4From Wycliffe to Euler99
4.1Medieval Recap99
4.2Modern Heritage101
4.3Ingredients in the Mix of the Scientific Revolution102
4.4The Catalyst: Nature's New Perspective104
4.5Two Indispensable Tools of Applied Mathematics107
4.5.1Symbolic Algebra107
4.6.1Nicholaus Copernicus112
4.6.2Francis Bacon113
4.6.3Johannes Kepler114's Three Laws of Planetary Motion116
4.6.4Galileo Galilei118 Proof of Heliocentrism121
4.6.5Isaac Newton122's Three Laws of Motion124's Law of Universal Gravitation126
4.6.6Gottfried Wilhelm Leibniz128
4.7Biblical Theology: The Match that Lit the Fire129
4.8The Reformation and Modern Science130
4.9Why Europe?138
4.9.3The Muslim World142
4.9.4One Viable Birth143
4.10Two Key Recognitions144
4.11Sovereign God at Work146
4.12The Bernoulli Family147
4.13The Incredible Euler149
Questions for Review, Further Research, and Discussion151
5From Euler to Godel153
5.1Reason Contra Revelation153
5.2Cartesian Geometry155
5.2.1The Cartesian Coordinate System156
5.3Cartesian Philosophy - Mathematics Absolutized158
5.4The "Fruits" of Success161
5.5Twentieth Century Ramifications162
5.6"I have no need of this hypothesis"166
5.7Philosophical Tomfoolery167
5.8"I serve the laws of nature"172
5.9Mathematical Idolatry?174
5.10The Idol Falls175
5.11Implications and Insights179
5.11.1Plurality of Geometries180
5.13Infinity Strikes Again182
5.13.1An ode to infinity184
5.14Divergent Schools186
5.15The Hiroshima of Mathematics190
5.16True Foundations192
Questions for Review, Further Research, and Discussion194
6Why Does Mathematics Work?195
6.1The Myth of Neutrality195
6.2The State of the Art199
6.2.1Preestablished Harmony199
6.2.2"The Footprint is Our Own"202
6.3A Quantum Leap204
6.4A Deeper Look into Morris Kline205
6.5The Confessions of a Nobel Prize Winner207
6.5.1The Structure of the Atom in Quantum Mechanics208
6.6More Miracles, Mystery, and Wonder208
6.7The Real Issue211
6.8The Wonders of Creation211
6.8.1The Mathematics of the Honeycomb212
6.8.2The Path of Light Through a Water Droplet215
6.9Guiltily Blind217
6.10Mathematics: Metaphysical and Epistemological Reality219
6.11The Unifying Factor221
Questions for Review, Further Research, and Discussion226
Part IIHow Should We Then Teach?227
7.1The Biblical Worldview and Mathematics229
7.2Three Christian Approaches to Mathematics Education234
7.3Four Curriculum Objectives234
7.4The Wonders of God's Creation236
7.4.1Music, Trigonometry, and Wave Motion237 Octave Frequencies237 Mathematical Harmony of Music237
7.4.2The Fibonacci Sequence240 Genealogy of the Male Bee242 Fascinating Mathematical Properties of [phi] (phi)246
7.4.4Conic Sections250
7.4.7Congruence, Similarity, Symmetry, etc.251
7.4.8Trigonometry and the Heavenly Expanse251
7.5The "One and the Many"251
7.5.1The Problem251
7.5.2The Solution in the Ontological Trinity253
7.5.3The Solution Applied255
7.6The Attributes of the Living God258
7.6.1Infinite, Eternal, and Triune258
7.6.2Sovereign, Almighty, and Faithful259
7.6.6Everywhere Present262
7.6.8Orderly, Precise, and Just263
7.7Subdue the Earth263
7.7.3Exponents and Logarithms266
7.7.4Mathematical Modeling268
7.7.5Conic Sections269
7.7.8Trigonometry273 Motion of a Bob on a Spring273
7.7.9Algebraic equations and functions275
7.7.10Complex and Imaginary numbers275
7.7.12The Divine Proportion276
7.7.15Linear Programming277
7.7.16The Calculus277
7.8Disciple all Nations277
Questions for Review, Further Research, and Discussion279
8Pedagogy and Resources281
8.1Weakness in Modern Mathematics Instruction282
8.2Biblical Motivation283
8.3Teacher Preparation285
8.4Teaching Principles286
8.4.2Integration and History289
8.4.3Induction and Deduction291
8.4.4Knowledge, Understanding, and Wisdom292
8.5Annotated Resources293
8.5.1Worldview Analysis294
8.5.2Christian Resources295
8.5.4Creational Studies and Dominion Mandate Applications299
8.5.5Mental Mathematics300
8.5.6General Introduction301
Questions for Review, Further Research, and Discussion308
From Adam to Christ311
From Christ to Wycliffe312
From Wycliffe to Euler316
From Euler to Godel321
After Godel329
Scripture Index361
General Index363
About the Author409

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