Math challenges : puzzles, tricks & games

Glen Vecchione e Nina Zottoli

Sterling | 1998 | 98 páginas | pdf |1,6 Mb

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Can quantum operations, recombinant shapes, and concealed distribution actually lead to fun? Sure they can! Just try these optical illusions, mechanical aptitude puzzles, maps and mazes. 

Contents1 Grid & Dot Games
2 Sum of the Parts
3 Vanishing Tricks
4 Stretchy Shapes & Squiggly Lines
5 Mechanical Aptitude
6 Logic Puzzles
7 Amazing Maps & Mazes
8 Fancy Figuring
9 Lewis Carroll, Puzzlemaker
Answers
Index

Tricks, Games, and Puzzles With Matches

Maxey Brooke

Dover Pubns | 1973 | 64 páginas | pdf | 267 kb

online: arvindguptatoys.com

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With a handful of matches you can challenge yourself and your friends to match hundreds of match tricks, games and puzzles. The quipment is simple and can easily be carried with you. The tricks, games and puzzles range from the simple to the advanced. No matter how many match tricks and puzzles you have previously done you are sure to find new twists, new challenges in the puzzles in this collection.
There are classic match problems, problems by foremost puzzlers, and a number of Makey Brooke's own creations. There is match-arithmetic, where you are required to balance equations by removing or adding matches, including a few that require advanced mathematical notation. There are match spellings, match story games, tricks that involve kitchen matches, paper match books and match boxes, and simple mathematical games you can play with matches. A rich selection of match constructions, in which you are required to build, unbuild, or reconstruct squares and other geometrical units by simply moving matches, is made even richer by the inclusion of a special selection from T.R. Dawson's works. The solutions section gives complete information for solving the puzzles plus material on winning games and working the tricks.

Outro livro de Maxey Brooke: 

150 puzzles in crypt-arithmetic. por Maxey Brooke Idioma: Inglês   Editora: New York, Dover Publications [1963]

The Puzzler's Dilemma: From the Lighthouse of Alexandria to Monty Hall, a Fresh Look at Classic Conundrums of Logic, Mathematics, and Life

Derrick Niederman

Perigee Trade | 2012 | 224 páginas | rar - epub | 1,84 Mb

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The Puzzler's Dilemma explores the world of classic logic puzzles, and tells the amazing stories behind them, from the Lighthouse of Alexandria to code-breaking with the Enigma machine. Here are brain teasers that even maths whizzes have never seen explained by a mind as nimble as Derrick Niederman's, author of Number Freak and The New York Times's near-genius crossword setter. "A man is found dead in a room, hanging from a rope with only a puddle of water beneath him: What happened?" Just the thing to get your brain working at full speed!

CONTENTS
1 IN THE BEGINNING
2 KANGAROO PUZZLES
3 THE HUMAN ELEMENT
4 TRY LATERAL THINKING
5 KEEPING IT SIMPLE
6 PARABOLIC PARABLES
7 LITTLE BIG JUMP
8 IT CAN’T BE DONE
9 SOLVED ACCORDING TO DOYLE
10 WHEN INDUCTION GOES BAD
11 YOU ARE HERE: THE SEARCH FOR A FIXED POINT
12 THE FULL MONTY HALL

Be a Number Genius: Flash

Jonathan Hancock e Jon Chapman

Hodder & Stoughton | 2012 | 107 páginas | rar - pdf | 645 Kb

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The books in this bite-sized new series contain no complicated techniques or tricky materials, making them ideal for the busy, the time-pressured or the merely curious. Be A Number Genius is a fun and completely absorbing guide to the magic of numbers, and how to harness their power to improve your professional progress, make better decisions, and solve everyday problems. In just 96 pages you will discover a complete toolkit for how to sharpen your mind and become 100% more mentally acute.

contentsIntroduction 3
1 Mathematical minds: the story so far 12
2 Adding skill, subtracting stress 24
3 Multiply your mind power: divide and conquer 36
4 Bits and pieces 52
5 Shape up your thinking 68
Test yourself now 80
Taking it further 83
Answers 84

Mike Byster

Harmony | 2014 | 368 páginas | rar - epub | 2,7 Mb

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An uncommon guide for accomplishing more every day by engaging the unique skill of forgetting, from the creator of the award-winning memory training system Brainetics
Is it possible that the answer to becoming a more efficient and effective thinker is learning how to forget? Yes! Mike Byster will show you how mastering this extraordinary technique—forgetting unnecessary information, sifting through brain clutter, and focusing on only important nuggets of data—will change the quality of your work and life balance forever.
Using the six tools in The Power of Forgetting, you’ll learn how to be a more agile thinker and productive individual. You will overcome the staggering volume of daily distractions that lead to to brain fog, an inability to concentrate, lack of creativity, stress, anxiety, nervousness, angst, worry, dread, and even depression. By training your brain with Byster’s exclusive quizzes and games, you’ll develop the critical skills to become more successful in all that you do, each and every day.

Satan, Cantor, And Infinity and Other Mind-Boggling Puzzles

Raymond M. Smullyan 

 Knopf | 1992 | 284 páginas | rar - epub | 2,1 Mb

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The author of What Is the Name of This Book? presents a compilation of more than two hundred challenging new logic puzzles--ranging from simple brainteasers to complex mathematical paradoxes

Contents
PART I • LOGICAL SORCERY
  1   The Lie Detective
  2   When I Was a Boy
  3   The Abduction of Annabelle
  4   How Kazir Won His Wife
  5   A Plague of Lies
  6   On the Other Hand
  7   The Island of Partial Silence
PART II • PUZZLES AND METAPUZZLES
 8   Memories of the Sorcerer’s Uncle
 9   The Planet Og
10   Metapuzzles
PART III • SELF-REPRODUCING ROBOTS
11   The Island of Robots
12   The Quaint System of Professor Quincy
13   From the Ridiculous to the Simple
PART IV • GÖDELIAN PUZZLES
14   Self-Reference and Cross-Reference
15   The Sorcerer’s Miniature Gödelian Language
PART V • HOW CAN THESE THINGS BE?
16   Something to Think About!
17   Of Time and Change
PART VI • A JOURNEY INTO INFINITY
18   What Is Infinity?
19   Cantor’s Fundamental Discovery
20   But Some Paradoxes Arise!
21   Resolutions
22   The Continuum Problem
PART VII • HYPERGAME, PARADOXES, AND A STORY
23   Hypergame
24   Paradoxical?

25   Satan, Cantor, and Infinity

A lifetime of puzzles : a collection of puzzles in honor of Martin Gardner's 90th birthday

Erik D. Demaine, Martin L. Demaine e Tom Rodgers

A K Peters/CRC Press | 2008 | 338 páginas | rar - pdf | 6,2 Mb

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Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

ContentsPreface ix
I CastaSpell 1
Martin Gardner and His Influence on Magic 3
Christopher Morgan
Martin Gardner—Encore! 15
Prof. M. O’Snart
Low-Down Triple Dealing 29
Colm Mulcahy
Products of Universal Cycles 35
Persi Diaconis and Ron Graham
II In Hindsight 57
Tangram: TheWorld’s First Puzzle Craze 59
Jerry Slocum
De Viribus Quantitatis by Luca Pacioli: The First Recreational Mathematics Book 77
David Singmaster
Magic and Card Tricks in Luca Paciolo’s De Viribus Quantitatis 123
Vanni Bossi
III Move It 131
Railway Mazes 133
Roger Penrose
Mechanical Mazes 149
M. Oskar van Deventer
Insanity Puzzles: Instant and On-the-Spot 157
Rik van Grol
The Adventures of Ant Alice 177
Peter Winkler
IV Fitting In 187
Simplicity 189
Stewart Coffin
Extreme Puzzles 195
Frans de Vreugd
Satterfield’s Tomb 221
David A. Klarner and Wade Satterfield,
edited by Thane E. Plambeck
Computer-Assisted Seashell Mosaics 233
Ken Knowlton
V Speak to Me 243
Memories and Inconsistencies 245
Raymond Smullyan
A Bouquet for Gardner 253
Jeremiah Farrell and Thomas Rodgers
NetWords: A Fascinating New Pencil-Paper Game 265
Mamikon Mnatsakanian, Gwen Roberts, and Martin Gardner
TheWizard Is Always In 273
James Randi
VI Making Arrangements 277
Symmetric Graphs in Mathematical Puzzles 279
Ed Pegg Jr
Martin Gardner and Ticktacktoe 293
Solomon W. Golomb
Scheduling Tennis Doubles Competitions 303
Dick Hess
When MultiplicationMixes Up Digits 313
David Wolfe
Magic, Antimagic, and Talisman Squares 319
Rodolfo Kurchan
Rectangle Arithmetic: Another Slant on Fractions 327
Bill Gosper
About the Authors 345

The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs by Raymond M. Smullyan

Raymond M. Smullyan

Dover Publications | 2013 | 288 páginas | rar - epub | 557 kb

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These brand-new recreational logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.
The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.

TABLE OF CONTENTS
Part I—Puzzles, Paradoxes, Infinity and other Curiosities
Chapter I A Chatty Personal Introduction
Chapter II Some Curious Adventures
Chapter III The Strange Island of Musica
Chapter IV Four Metapuzzles
Chapter V Certified Knights and Knaves
Chapter VI Paradoxical?
Chapter VII Infinity and Induction
Chapter VIII Introducing Self-Reference
Chapter IX Fixed Point Puzzles
Chapter X Some Curious Systems
Chapter XI How to Stump a Decision Machine
Chapter XII Some Additional Gödelian Puzzles
Part II—Provability, Truth and the Undecidable
Chapter XIII Truth and Provability
Chapter XIV Syntactic Incompleteness Theorems
Chapter XV Provability in Stages
Chapter XVI Formal Systems and Recursion
Chapter XVII Incompleteness and Undecidability
Chapter XVIII First-Order Arithmetic
Chapter XIX Arithmetic Truth Is Not Formalizable
Chapter XX The Incompleteness of Peano Arithmetic

Las matematicas de Oz, Gimnasia mental mas alla del limite

Clifford Pickover e Richard Ley

Almuzara Estudios S A | 2007 | 408 páginas | pdf | 18,3 Mb

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Coja un lápiz. Relájese. Después despegue en un viaje alucinante hasta la última frontera de las matemáticas, la mente y el significado, mientras el aclamado autor Dr. Clifford Pickover, Dorotea y el Dr. Oz exploran algunos de los más extraños y peculiares caminos de aquellos obsesionados con los números.

Les jeux mathematiques d'Eureka

Eureka (Marie Berrondo)

Dunod | 1979 | 187 páginas | djvu | 2,6 Mb

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Marie Berrondo, qui a choisi le pseudonyme d'Eurêka, propose 253 récréations suivies de solutions détaillées. Les problèmes touchent aux probabilités, à la logique, aux relations entre vitesses, distance et temps, à la géométrie et à l'arithmétique.

Math en jeux, niveau 4e 3e : 200 jeux pour aimer les maths

Xuan Quang-Bui, Marie Berrondo-Agrell

Bordas | 1990 | 161 páginas | djvu | 5 Mb

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Oui, les Mathématiques peuvent être amusantes et l'on se passionnera à essayer de résoudre ces problèmes parfois bien comiques. Quel moyen plus agréable pour progresser en Mathématiques - et les aimer - lorsqu'on est en 4e ou en 3e, puisque ces jeux relèvent tous du niveau de ces classes ! Pleins d'humour, ces casse-tête sont classés selon leur difficulté et entièrement corrigés. Ils demandent, pour être résolus, astuce, bon sens et logique. Egayés de dessins pleins de malice, ils permettent de développer ingéniosité et capacité de raisonnement.

Mathematical Byways in Ayling, Beeling, and Ceiling

Hugh ApSimon

Oxford University Press | 1991 | 11 páginas | pdf | 1,1 Mb

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Unique and highly original, Mathematical Byways is a work of recreational mathematics, a collection of ingenious problems, their even more ingenious solutions, and extensions of the problems--left unsolved here--to further stretch the mind of the reader. The problems are set within the framework of three villages--Ayling, Beeling, and Ceiling--their inhabitants, and the relationships (spacial and social) between them.The problems can be solved with little formal mathematical knowledge, although most require considerable thought and mental dexterity, and solutions are all clearly expounded in non-technical language. Stimulating and unusual, this book proves what Hugh ApSimon has known all along: mathematics can be fun!

Dr. Crypton and His Problems: Mind Benders from Science Digest

 Dr. Crypton
 St Martins Pr | 1982 | 191 páginas | djvu | 1,7 Mb
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" The mysterious Dr. Crypton (presumably a friend  of Superman except that he has a superbrain instead  of a superbody) has assembled a super collection of puzzles and curiosities involving mathematics, words, and anything at all that lends itself to logical  and creative thinking. A delightful book to read and ponder. " 
-Martin Gardner

Contents 
Acknowledgments vii
Questions by Isaac Asimov ix
1. An Enigmatic Evening with Microwave Cornbread 1
2. The Intragalactic Cabaret 14
3. The Case of the Fatal Forfex 23
4. Palindromes: No Lemons! No Melon! 31
5. Sleight of Mind in Katmandu 42
6. Shockley: Sperm Hustler Offers Compatible  Kinky Ladies Einsteinish Young 50
7. Zeno of Elea: The First Paradoxologist 57
8. The Well-Hung Natives and Twenty-three  Other Conundrums 67
9. The Logistics of Armchair Ornithology 115
10. Lora Does a Mobius Strip 121
11. The BANG and Other Phrenetic Phrases 143
12. How's Your Resistance? (There's No Place like Ohm) 148
14. Triskaidekaphobia 151
15. Freud and the Number 23 158
16. The Puzzles of Nympholepts: Lewis Carroll and
Vladimir Nabokov 165
17. The Talk of the Town 178 

Conned Again, Watson!, Cautionary Tales of Logic, Math, and Probability

 Colin Bruce

Perseus Publishing | 2000 | 290 páginas | pdf | 1,4 Mb

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In these cautionary tales of greedy gamblers, reckless businessmen, and ruthless con men, Sherlock Holmes uses his deep understanding of probability, statistics, decision theory, and game theory to solve crimes and protect the innocent.

Contents

Preface vii

Acknowledgments ix

1 The Case of the Unfortunate Businessman 1

2 The Case of the Gambling Nobleman 19

3 The Case of the Surprise Heir 45

4 The Case of the Ancient Mariner 65

5 The Case of the Unmarked Graves 85

6 The Case of the Martian Invasion 115

7 Three Cases of Unfair Preferment 141

8 The Execution of Andrews l6l

9 Three Cases of Relative Honor 181

10 The Case of the Poor Observer 207

11 The Case of the Perfect Accountant 225

12 Three Cases of Good Intentions 247

Afterword 275

Mathematics Galore!, The First Five Years of the St. Mark’s Institute of Mathematics

 (Classroom Resource Materials)

James Tanton 

Mathematical Association of America | 2012 | 289 | pdf | 3,3 Mb

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Mathematics Galore! Showcases some of the best activities and student outcomes of the St. Mark s Institute of Mathematics and invites you to engage the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. See some great mathematics explained and proved via natural and accessible means.

Based on 26 essays ( newsletters ) and eight additional pieces,Mathematics Galore! offers a large sample of mathematical tidbits and treasures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within.

Contents
Introduction;
Newsletters and commentaries;
1. Arctangents;
2. Benford's Law;
3. Braids;
4. CLIP Theory;
5. Dots and dashes;
6. Factor trees;
7. Folding fractions and conics;
8. Folding patterns and dragons;
9. Folding and pouring;
10. Fractions;
11. Integer triangles;
12. Lattice polygons;
13. Layered tilings;
14. The middle of a triangle;
15. Partitions;
16. Personalized polynomials;
17. Playing with Pi;
18. Pythagoras's Theorem;
19. On reflection;
20. Repunits and primes;
21. The Stern-Brocot Tree;
22. Tessellations;
23. Theon's ladder and squangular numbers;
24. Tilings and theorems;
25. The Tower of Hanoi;
26. Weird multiplication;
Appendices:
1. Numbers that are the sum of two squares;
2. Pick's theorem;
3. The Mobius function;
4. The Borsuk-Ulam theorem;
5. Galilean ratios;
6. A candy-sharing game;
7. Bending Buffon's needle;
8. On separating dots;
Indexes:
1. Index of terms;
2. Index of topics;
3. Classic theorems proved.

Outros livros do mesmo autor:

Encyclopedia of mathematics por James Stuart Tanton Idioma: Inglês   Editora: New York : Facts on File, ©2005.

Solve this : math activities for students and clubs por James Stuart Tanton Idioma: Inglês   Editora: Washington, D.C. : Mathematical Association of America, 2001.

Caliban's Problem Book: Mathematical, Inferential and Cryptographic Puzzles

Hubert C. Phillips

 Dover Publications | 1961 | 191 páginas | djvu | 1,4 Mb

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150 Puzzles in Crypt-Arithmetic

Maxey Brooke

Dover | 1963 | 77 páginas | pdf | 1,1 Mb

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Eureka! Math Fun From Many Angles

David Lewis

Perigee Trade | 1955 | 199 páginas | pdf | 4,8 Mb

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Presents a variety of puzzles, problems, and paradoxes that test the reader's skills in logic and knowledge of mathematics

Contents

Fun and Games

1. Twisted Topology

2. A Bag of Tricks and Treats

3. A Score of Games

4. The Magic's There

5. Rubiquity

Nifty Numerics

6. Palindromesemordnilap

7. A Pole Vaulter

8. A Timely Switch

Fallacies and Logic

9. If This Is Not a Chapter, My Name Is Raymond Smullyan

10. Thrice Befuddled

11. Better Mixed-Up Than Lost

And Even Dissection of Solids

12. Archimedes Anderson and the Case of the Sinister Plot 93

13. How to Dissect a Square and Other Marvels of Modern Biology 96

14. Geometer's Heaven 105

15. Hole in the Sphere 108

16. Convexstasy 110

17. Great Unsolved Problems 113

18. Out of This World 115

Photons Are Light Matter, Too

19. Archimedes Anderson and the Gambling Candidate 119

20. Once Upon a Time. . . 122

21. A Problem Fly 123

22. The Leading Series of Pisa 124

23. The Early Something Catches the Whatever 127

Shortcuts

24. A Speedier System of Solving 129

25. A Letter Home 135

26. In Which We Are Initiated Into the Secret

Society of Square Root Solvers

27. Heads and Legs

28. Noble Bases

29. A Division in Ancient Rye

30. Getting at the Root of the Problem

31. Or is it 32? Remumbt:r Nembers

Neat Numbers

32. Prime Time 151

33. A Sense of Balance 159

34. Perfect Numbers and Some Not-So-Perfect Numbers 161

Cranium Crackers and Cheese: Problems to Munch On

35. Classy Problems 165

36. LEITERS + DIGITS = FRUSTRATION 174

FUNdamental Ratios

37. Expand Your Mind

38. E? Ah!

39. A Section of Gold

40. A Bundled-Up Buyer

41. A Piece of Pi

Bibliography

Ball of Confusion: Puzzles, Problems and Perplexing Posers

Johnny Ball

Icon Books |  2012 | 254 páginas | rar - epub |2,4 Mb

link (password: matav)

From how to cheat in a coin toss to why it is that some parts of a high speed train travelling at 125 mph are actually going backwards, Ball of Confusion is designed to twist your brain into enjoyable knots of empuzzlement—from puzzles solved in a twinkling of an eye to some that will knit your brow for hours.

Contents

How Ball of Confusion was born …

Introduction

1: Kitchen Capers and Domestic Problems

2: ‘I Can Hear You Thinking’ Puzzles

3: Any Number of Puzzles – About Numbers

4: Easy Peasy Puzzles and Catchy Watchy Questions

5: Geometric Shape and Angle Puzzles

6: Dear Old Faves from Days Gone By

7: Even More Thoughtful Thinking Puzzles

8: Party Puzzles and Tricks to Show Off With

Answers

Bibliography

Outros livros do mesmo autor:

Why pi? por Johnny Ball Livro : Público juvenil Idioma: Inglês   Editora: New York, N.Y. : DK Pub., 2009.

Think of a number por Johnny Ball Público juvenil Idioma: Inglês   Editora: London : Dorling Kindersley, 2005.

Games and Mathematics: Subtle Connections

David Wells

 Cambridge University Press |  2012 | 258 páginas | rar - pdf |1 Mb

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The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Contents
PART I: Mathematical recreations and abstract games
Introduction; Everyday puzzles;
1 Recreations from Euler to Lucas;
Euler and the Bridges of Königsberg; Euler and knight tours; Lucas and mathematical recreations; Lucass game of solitaire calculation;
2 Four abstract games;
From Dudeneys puzzle to Golombs Game; Nine Mens Morris; Hex; Chess; Go;
3 Mathematics and games: mysterious connections;
Games and mathematics can be analysed in the head; Can you -look ahead'?; A novel kind of object; They are abstract. They are difficultRules; Hidden structures forced by the rules; Argument and proof; Certainty, error and truth; Players make mistakes; Reasoning, imagination and intuition; The power of analogy; Simplicity, elegance and beauty; Science and games: lets go exploring;
4 Why chess is not mathematics;
Competition; Asking questions about; Metamathematics and game-like mathematics; Changing conceptions of problem solving; Creating new concepts and new objects; Increasing abstraction; Finding common structures; The interaction between mathematics and sciences;
5 Proving versus checking.
The limitations of mathematical recreationsAbstract games and checking solutions; How do you `prove' that 11 is prime?; Is `5 is prime' a coincidence?; Proof versus checking; Structure, pattern and representation; Arbitrariness and un-manageability; Near the boundary;
PART II: Mathematics: game-like, scientific and perceptual
Introduction;
6 Game-like mathematics;
Introduction; Tactics and strategy; Sums of cubes and a hidden connection; A masterpiece by Euler;
7 Euclid and the rules of his geometrical game;
Cevas theorem; Simsons line; The parabola and its geometrical properties. Dandelins spheres
8 New concepts and new objects;
Creating new objects; Does it exist?; The force of circumstance; Infinity and infinite series; Calculus and the idea of a tangent; What is the shape of a parabola?;
9 Convergent and divergent series;
The pioneers; The harmonic series diverges; Weird objects and mysterious situations; A practical use for divergent series;
10 Mathematics becomes game-like; Eulers relation for polyhedra;
The invention-discovery of groups; Atiyah and MacLane disagree; Mathematics and geography;
11 Mathematics as science;
Introduction. Triangle geometry: the Euler line of a triangleModern geometry of the triangle; The Seven-Circle Theorem, and other New Theorems;
12 Numbers and sequences;
The sums of squares; Easy questions, easy answers; The prime numbers; Prime pairs; The limits of conjecture; A Polya conjecture and refutation; The limitations of experiment; Proof versus intuition;
13 Computers and mathematics;
Hofstadter on good problems; Computers and mathematical proof; Computers and 'proof'; Finally: formulae and yet more formulae;
14 Mathematics and the sciences;
Scientists abstract.