Genius at Play: The Curious Mind of John Horton Conway
Authors: Siobhan Roberts, Siobhan Roberts
Overview
Genius at Play is the biography of John Horton Conway, a brilliant and eccentric mathematician known for his groundbreaking contributions to various fields, including game theory, geometry, and number theory. Beyond his remarkable mathematical achievements, the book explores Conway’s playful approach to life and work, his fascination with games and puzzles, and his larger-than-life persona that endeared him to students and colleagues alike.
The book is aimed at a general audience interested in mathematics, science, and the lives of extraordinary individuals. It provides insights into the creative process of a mathematical genius, exploring how Conway’s seemingly “trivial” pursuits often led to profound discoveries.
The book’s playful exploration of Conway’s eccentric life and mind offers a unique perspective on the nature of mathematical creativity, exploring how seemingly childlike games and puzzles can unlock profound insights into complex systems and the universe itself. Conway’s work on games such as “Life” and his invention of the “Surreal Numbers” not only made significant contributions to mathematics but also provided new tools for thinking about computation, infinity, and the nature of reality. Conway’s struggles with “character assassination” stemming from the outsized attention to his “Game of Life” offer a cautionary tale about the potential pitfalls of runaway celebrity, even within the rarified air of the ivory tower.
Genius at Play fits within the genre of scientific biography, offering a lively and engaging portrait of a remarkable individual. The book’s central theme of finding profound connections in seemingly trivial pursuits has relevance to current research in artificial intelligence, especially given the use of game-playing and the study of emergent behavior as strategies for advancing machine learning and building more intelligent systems. The book also raises questions about the interplay between human intelligence and machine intelligence, and about the potential for both collaboration and competition between human mathematicians and their increasingly powerful computing counterparts.
Book Outline
1. Prologue
This prologue introduces John Horton Conway, a brilliant, eccentric mathematician known for his playful approach to work. He views himself as someone who “piddles away reams and reams of time playing games,” yet he holds prestigious positions and has made groundbreaking contributions to various fields of mathematics, including game theory, geometry, and number theory. His most famous creation is the “Game of Life,” which demonstrates how simple rules can generate complex patterns and behaviors, blurring the lines between work and play.
Key concept: “I do have a big ego!” Conway readily admits his ego and often quips, “As I often say, modesty is my only vice. If I weren’t so modest, I’d be perfect.” This sets the stage for his larger-than-life persona, characterized by both brilliance and playfulness.
2. Identity Elements
This chapter describes Conway’s arrival at Cambridge University and his conscious decision to transform himself from a shy, introverted “Mary” to an outgoing, boisterous “Prof.” The backdrop of his youth in Liverpool includes his father’s fascination with science experiments and wordplay, hinting at Conway’s future interests.
Key concept: “Who in the world am I? Ah, that’s the great puzzle.” - Lewis Carroll. This quote reflects Conway’s journey of self-invention and his fascination with identity and transformation, themes woven through his personal and mathematical life.
3. Dazzling New World
This chapter dives into Conway’s childhood during wartime Liverpool, focusing on key memories and family dynamics. It also explores Conway’s selective memory and reliance on anecdotes, sometimes exaggerated, to reconstruct his past. I introduce his sister Joan, ten years his senior, and our shared quest to verify early memories.
Key concept: “As dazzling as first love. I had not imagined there was anything so delicious…” - Bertrand Russell. This quote, referencing Russell’s discovery of Euclid’s geometry, mirrors Conway’s childhood fascination with mathematical concepts and the power of memory.
4. Gymnastics
This chapter takes us on a research trip to England, where Conway is reunited with his daughters and his long-time friend and collaborator, Mike Guy. They revisit Conway’s old haunts, including his high school and family home, but the trip yields little in the way of concrete memories. The focus shifts to Conway’s interactions with his daughters and Guy, providing insights into his personality and social dynamics.
Key concept: “What mad pursuit? What struggle to escape?” - John Keats. This captures the playful energy between Conway and long-time collaborator, Mike Guy, and introduces Conway’s daughters, emphasizing the role of collaboration in his life and work.
5. Calculate the Stars
This chapter covers Conway’s early fascination with infinity, drawing on the work of Georg Cantor, who classified infinite numbers. Conway applied his own playful approach to this concept, questioning the infinitude of stars and contemplating the existence of mathematical objects within “an abstract world which . . . has existed throughout eternity.”
Key concept: “In mathematics you don’t understand things. You just get used to them.” - John von Neumann. This quote, expressing Von Neumann’s sentiment about math, highlights Conway’s unique approach, rooted in intuition and a disregard for conventional methods.
6. Nerdish Delights
This chapter describes Conway’s casual attitude toward his formal studies and his penchant for practical jokes and intellectual games, such as creating a water computer named WINNIE and his early explorations of knot theory and flexagons. It also introduces the “John Conway Appreciation Society,” a testament to his popularity among students.
Key concept: “Never let the truth get in the way of a good story, unless you can’t think of anything better.” - Mark Twain. This quote embodies Conway’s approach to storytelling, often blurring the lines between fact and fiction, a tendency I, his biographer, struggled with throughout my research.
7. The Vow
This chapter explores a pivotal moment in Conway’s life during a conference in Moscow in 1966. There, surrounded by mathematicians, Conway formulates “The Vow”: a commitment to stop worrying and pursue his interests freely. This chapter also touches on Conway’s early interest in game theory.
Key concept: “At any moment there is only a fine layer between the ‘trivial’ and the impossible. Mathematical discoveries are made in this layer.” – Andrey Kolmogorov. This quote foreshadows Conway’s discovery of surreal numbers and his ability to find profound connections in seemingly trivial pursuits.
8. Religion
This chapter delves into Conway’s creation of the Game of Life, emphasizing the years of tinkering and rule adjustments that led to its final form. I describe Conway’s “Religion,” a self-imposed rule to see through a Life-form’s fate, which leads to long nights in front of the computer.
Key concept: “Life is far too important to be taken seriously.” - Oscar Wilde. This quote embodies the spirit of Conway’s approach to both life and mathematics, emphasizing his playful yet dedicated pursuits.
9. Criteria of Virtue
This chapter centers on the development of “Life” and the public’s reaction to it. I introduce Martin Gardner, a science writer who popularized the Game of Life in his Scientific American column, causing pandemonium for Conway and sparking his lifelong hatred for the game. This chapter also covers Conway’s personal aversion to the celebrity his simple game generated.
Key concept: Tell all the Truth but tell it slant. Emily Dickinson. This speaks to the challenge of biography and the difficulties in separating truth from embellishment.
10. Character Assassination
This chapter tells the story of the “Look-and-Say Sequence,
Key concept: “Our life is frittered away by detail…Simplify, simplify.” - Henry David Thoreau. This quote captures Conway’s persistent search for simple underlying structures in complex systems and games, and how these pursuits revealed underlying mathematical truths.
11. Snip, Clip, Prune, Lop
This chapter tells the origin story of Conway’s “Surreal Numbers,” a new class of numbers encompassing all numbers, including Cantor’s ordinals and all real numbers.
Key concept: “Time is a game played beautifully by children.” – Heraclitus. This speaks to Conway’s own fascination with seemingly childlike games which yielded surprising mathematical discoveries.
12. Dotto & Company
This chapter describes Conway’s work on the “Atlas of Finite Groups,” a massive collaborative project to document all finite simple groups. It also touches upon Conway’s adventures with Penrose tiles, which offer a different approach to geometry and symmetry.
Key concept: “Symmetry is what we see at a glance.” - Blaise Pascal. This quote captures the core theme of the chapter and book, emphasizing the elegance and underlying significance of symmetry in Conway’s work.
13. Optional Probability Fields
This chapter details how Conway treated the early years at Princeton as a new game, exploring how much he could get away with before he was sacked. He continued his quirky routines from Cambridge including turning lectures into playful explorations of mathematical concepts like “How to Stare at a Brick Wall.”
Key concept: “Whatever is not forbidden is permitted.” – Friedrich Schiller. This quote summarizes the spirit behind Conway’s mathematical creativity, encouraging exploration of all that is not explicitly disallowed.
14. Character Assassination
This chapter covers Conway’s playful yet profound exploration of mathematical concepts and his fascination with games, puzzles, and wordplay. It delves into his love for the Lexicode Theorem, a demonstration of his unique approach to mathematical reasoning.
Key concept: “Knowing is not enough; we must apply.” - Goethe. This quote emphasizes the importance of application and engagement with knowledge, a defining aspect of Conway’s approach.
15. Lustration
This chapter focuses on Conway’s struggles with giving talks after his suicide attempt. He finds it hard to concentrate and worries about the quality of his lectures, demonstrating a rare vulnerability beneath his usual confidence.
Key concept: I was taught that the way of progress was neither swift nor easy. – Marie Curie. This quote serves as a foil against Conway’s working style which tends to be swift and easy, at least on the surface.
16. Take It As Axiomatic
This chapter explores Conway’s engagement with young mathematicians at math camps, where he shares his passion for puzzles, games, and the joy of mathematical exploration. It highlights his dedication to nurturing young talent and his unique ability to make complex concepts accessible.
Key concept: “Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.” Albert Einstein. This quote speaks to the difficulty of comprehending infinity and our never-ending capacity to underestimate it. It also introduces Conway’s penchant for working with mathematically-minded youngsters.
17. Humpty Dumpty’s Prerogative
This final chapter brings us back to the Free Will Theorem, with Conway continuing to question the validity of the proof and engaging in discussions with colleagues and students about its philosophical implications. It touches upon Conway’s personal struggles and his ongoing pursuit of mathematical understanding.
Key concept: “What is mind? No matter. What is matter? Never mind.” - Lady Frances Russell. This quote summarizes Conway’s view on metaphysics and his general tendency to ‘shelve it.’, and instead focus on the knowable.
18. Epilogue
This epilogue reflects on the challenges of writing Conway’s biography and captures a final conversation with him, in which he contemplates his retirement, his legacy, and the enduring power of mathematics.
Key concept: “When the hurly-burly’s done, when the battle’s lost and won.” William Shakespeare. This captures the long and winding path of Conway’s life and career, and the bittersweet ending of his quest for mathematical knowledge and understanding.
Essential Questions
1. What were John Horton Conway’s most significant mathematical contributions, and what unifying themes connect his work?
Conway’s most notable contributions include the “Game of Life,” the discovery of surreal numbers, and work on the classification of finite simple groups. “Life,” a cellular automaton, shows how simple rules can generate complex behavior. Surreal numbers expand our understanding of infinity, challenging established notions. His work on finite simple groups contributed to the monumental “Atlas of Finite Groups.” These seemingly disparate areas share a common thread: his genius for finding order and structure in complex systems, driven by a sense of playfulness and a love for “trivial” pursuits that often lead to unexpected and profound mathematical insights.
2. How did Conway’s unique approach to mathematical exploration differ from conventional methods, and how did it contribute to his discoveries?
Conway’s method was often one of playful exploration. He tinkered with games and puzzles, using them as tools for thinking. This approach challenged the conventional image of a mathematician toiling away with rigorous proofs and abstract concepts. His focus was on finding simple, elegant explanations and solutions, even for the most complex problems. This playful approach was not merely a matter of style; it allowed him to see connections and possibilities that others missed, leading to original and often unexpected discoveries. This emphasis on simplicity and elegance also made his work more accessible to a broader audience, as evidenced by the widespread popularity of “Life.”
3. How did Conway’s struggle with the unexpected and unwanted fame brought about by the “Game of Life” reveal tensions between public perception and his own self-perception as a mathematician?
Conway’s struggle with the fame generated by “Life” highlights the complexities of celebrity, even in the realm of mathematics. While he was proud of its creation, he resented the way it overshadowed his other, more substantial contributions. He viewed “Life” as a “trivial” pursuit compared to his other work, and yet it was “Life” that captured the public imagination and led to his widespread recognition. This struggle reveals a tension between the desire for recognition and the need to preserve one’s own sense of identity and intellectual priorities.
4. What was the significance of Conway’s “vow,” and how did it shape his life and career?
Conway’s “vow” was a turning point, enabling him to fully embrace his unconventional methods and passions. By prioritizing his interests and letting go of self-doubt and guilt, he entered a period of extraordinary productivity, resulting in discoveries such as surreal numbers. The “vow” highlights the importance of intellectual freedom and pursuing one’s passions without constraint.
5. How can Conway’s life and work, as depicted in the book, inspire and inform research and development in AI and related fields?
The book’s focus on Conway’s unconventional approach, his creative process, and his embrace of playful exploration is not only biographical but also offers valuable insights for those interested in AI development. Conway’s intuitive approach, his ability to connect seemingly disparate areas of mathematics, and his focus on simplicity and elegance are qualities that could inspire innovative solutions in the field of AI. His use of games and simulations as tools for thinking could also inform the development of new AI algorithms and systems, while his insights into infinity and computation might inspire research into artificial life and new models of computation. His story encourages interdisciplinary thinking and out-of-the-box problem-solving, highlighting the potential for playful experimentation to lead to breakthroughs. His “vow” to pursue his passions serves as a reminder that intellectual freedom is crucial for progress and discovery, suggesting that AI research might benefit from a more exploratory and less constrained approach.
1. What were John Horton Conway’s most significant mathematical contributions, and what unifying themes connect his work?
Conway’s most notable contributions include the “Game of Life,” the discovery of surreal numbers, and work on the classification of finite simple groups. “Life,” a cellular automaton, shows how simple rules can generate complex behavior. Surreal numbers expand our understanding of infinity, challenging established notions. His work on finite simple groups contributed to the monumental “Atlas of Finite Groups.” These seemingly disparate areas share a common thread: his genius for finding order and structure in complex systems, driven by a sense of playfulness and a love for “trivial” pursuits that often lead to unexpected and profound mathematical insights.
2. How did Conway’s unique approach to mathematical exploration differ from conventional methods, and how did it contribute to his discoveries?
Conway’s method was often one of playful exploration. He tinkered with games and puzzles, using them as tools for thinking. This approach challenged the conventional image of a mathematician toiling away with rigorous proofs and abstract concepts. His focus was on finding simple, elegant explanations and solutions, even for the most complex problems. This playful approach was not merely a matter of style; it allowed him to see connections and possibilities that others missed, leading to original and often unexpected discoveries. This emphasis on simplicity and elegance also made his work more accessible to a broader audience, as evidenced by the widespread popularity of “Life.”
3. How did Conway’s struggle with the unexpected and unwanted fame brought about by the “Game of Life” reveal tensions between public perception and his own self-perception as a mathematician?
Conway’s struggle with the fame generated by “Life” highlights the complexities of celebrity, even in the realm of mathematics. While he was proud of its creation, he resented the way it overshadowed his other, more substantial contributions. He viewed “Life” as a “trivial” pursuit compared to his other work, and yet it was “Life” that captured the public imagination and led to his widespread recognition. This struggle reveals a tension between the desire for recognition and the need to preserve one’s own sense of identity and intellectual priorities.
4. What was the significance of Conway’s “vow,” and how did it shape his life and career?
Conway’s “vow” was a turning point, enabling him to fully embrace his unconventional methods and passions. By prioritizing his interests and letting go of self-doubt and guilt, he entered a period of extraordinary productivity, resulting in discoveries such as surreal numbers. The “vow” highlights the importance of intellectual freedom and pursuing one’s passions without constraint.
5. How can Conway’s life and work, as depicted in the book, inspire and inform research and development in AI and related fields?
The book’s focus on Conway’s unconventional approach, his creative process, and his embrace of playful exploration is not only biographical but also offers valuable insights for those interested in AI development. Conway’s intuitive approach, his ability to connect seemingly disparate areas of mathematics, and his focus on simplicity and elegance are qualities that could inspire innovative solutions in the field of AI. His use of games and simulations as tools for thinking could also inform the development of new AI algorithms and systems, while his insights into infinity and computation might inspire research into artificial life and new models of computation. His story encourages interdisciplinary thinking and out-of-the-box problem-solving, highlighting the potential for playful experimentation to lead to breakthroughs. His “vow” to pursue his passions serves as a reminder that intellectual freedom is crucial for progress and discovery, suggesting that AI research might benefit from a more exploratory and less constrained approach.
Key Takeaways
1. The Power of Simplicity and Elegance
Conway consistently sought simple rules and elegant explanations, even when dealing with complex mathematical concepts. He believed that true understanding came from reducing a problem to its essence, and his discoveries of “Life” and surreal numbers demonstrate how simplicity can be the key to unlocking complex behaviors and new mathematical landscapes.
Practical Application:
In AI research, focusing on simplicity and elegance can be valuable when designing algorithms, models, and user interfaces. A simple, intuitive design can be more efficient, scalable, and user-friendly, leading to wider adoption and impact.
2. The Value of Playful Exploration
Conway’s playful approach, using games and puzzles as tools for thought, allowed him to see connections that others missed. He viewed mathematics as a game to be played, not a problem to be solved, and this playful approach was essential to his creative process.
Practical Application:
In product design, promoting playfulness and experimentation can lead to innovative solutions and user engagement. Creating interactive prototypes, incorporating game-like elements, and encouraging user feedback can foster a sense of play and lead to unexpected discoveries.
3. The Importance of Collaboration
Conway often collaborated with colleagues and students, using their insights and expertise to refine and develop his ideas. While he sometimes struggled with the collaborative process, he recognized its importance and the benefits of shared intellectual exploration.
Practical Application:
Collaboration and communication are crucial in any professional environment, especially in fields like AI where interdisciplinary collaboration is essential.
4. Balancing Focus and Distraction
Conway’s personal challenges with organization and information management highlight the need for balance between focused work and diffuse thinking. While he thrived on the unstructured environment of the common room, his inability to keep track of papers and emails also hindered his progress at times.
Practical Application:
Finding ways to manage information overload and distractions is crucial for productivity and effectiveness. Techniques like timeboxing, prioritization, and dedicated focus time can help individuals regain control of their attention and time.
5. The Power of Mentorship
Conway nurtured young talent, providing guidance and encouragement to students who were often drawn to his unconventional style and open-door approach. While he claimed to have “never taught anyone anything,” he made a significant impact on many young mathematicians’ careers.
Practical Application:
Mentoring is an important aspect of leadership, especially in fast-moving fields like AI where experience and knowledge transfer are valuable. Conway’s story shows that mentoring is not just about instruction, but also inspiration and supporting individual talent. He may have often disavowed his role in mentoring, but he made a major impact on his students’ work.
1. The Power of Simplicity and Elegance
Conway consistently sought simple rules and elegant explanations, even when dealing with complex mathematical concepts. He believed that true understanding came from reducing a problem to its essence, and his discoveries of “Life” and surreal numbers demonstrate how simplicity can be the key to unlocking complex behaviors and new mathematical landscapes.
Practical Application:
In AI research, focusing on simplicity and elegance can be valuable when designing algorithms, models, and user interfaces. A simple, intuitive design can be more efficient, scalable, and user-friendly, leading to wider adoption and impact.
2. The Value of Playful Exploration
Conway’s playful approach, using games and puzzles as tools for thought, allowed him to see connections that others missed. He viewed mathematics as a game to be played, not a problem to be solved, and this playful approach was essential to his creative process.
Practical Application:
In product design, promoting playfulness and experimentation can lead to innovative solutions and user engagement. Creating interactive prototypes, incorporating game-like elements, and encouraging user feedback can foster a sense of play and lead to unexpected discoveries.
3. The Importance of Collaboration
Conway often collaborated with colleagues and students, using their insights and expertise to refine and develop his ideas. While he sometimes struggled with the collaborative process, he recognized its importance and the benefits of shared intellectual exploration.
Practical Application:
Collaboration and communication are crucial in any professional environment, especially in fields like AI where interdisciplinary collaboration is essential.
4. Balancing Focus and Distraction
Conway’s personal challenges with organization and information management highlight the need for balance between focused work and diffuse thinking. While he thrived on the unstructured environment of the common room, his inability to keep track of papers and emails also hindered his progress at times.
Practical Application:
Finding ways to manage information overload and distractions is crucial for productivity and effectiveness. Techniques like timeboxing, prioritization, and dedicated focus time can help individuals regain control of their attention and time.
5. The Power of Mentorship
Conway nurtured young talent, providing guidance and encouragement to students who were often drawn to his unconventional style and open-door approach. While he claimed to have “never taught anyone anything,” he made a significant impact on many young mathematicians’ careers.
Practical Application:
Mentoring is an important aspect of leadership, especially in fast-moving fields like AI where experience and knowledge transfer are valuable. Conway’s story shows that mentoring is not just about instruction, but also inspiration and supporting individual talent. He may have often disavowed his role in mentoring, but he made a major impact on his students’ work.
Suggested Deep Dive
Chapter: Religion
Conway’s invention of the Game of Life is one of his most widely known achievements, and it has become a significant influence in computer science, artificial life research, and the study of complex systems. A deeper dive into this chapter provides context for the public reception of this discovery which ultimately lead to Conway’s “character assassination.” It also offers a fascinating exploration of Conway’s unorthodox working process, illustrating the evolution of “Life” from an idea to a fully realized system that continues to capture the imagination.
Memorable Quotes
Prologue. 13
I do have a big ego!
Criteria of Virtue. 25
There is this abstract world which in some strange sense has existed throughout eternity.
Calculate the Stars. 79
You can’t push a cat in a direction it doesn’t want to go. You can’t push a number either.
The Vow. 128
Before, everything I touched turned to nothing. Now I was Midas, and everything I touched turned to gold.
Religion. 140
It’s not God’s game!
Prologue. 13
I do have a big ego!
Criteria of Virtue. 25
There is this abstract world which in some strange sense has existed throughout eternity.
Calculate the Stars. 79
You can’t push a cat in a direction it doesn’t want to go. You can’t push a number either.
The Vow. 128
Before, everything I touched turned to nothing. Now I was Midas, and everything I touched turned to gold.
Religion. 140
It’s not God’s game!
Comparative Analysis
Genius at Play stands out for its intimate portrayal of a mathematician’s life, offering a rare glimpse into the mind and creative process of a mathematical genius. Unlike more conventional biographies that focus solely on achievements, Roberts delves into Conway’s eccentricities, his playful approach to work, and his deep fascination with games. This intimate lens allows her to explore a recurring theme in Conway’s work: the surprising connections between seemingly trivial pursuits and profound mathematical discoveries. In contrast to books like Marcus du Sautoy’s Symmetry, which explores the broader cultural and historical context of symmetry, Roberts focuses on Conway’s personal relationship with the concept, highlighting how it underpins his idiosyncratic approaches and original results. Similarly, while books like Stephen Wolfram’s A New Kind of Science offer grand visions of computation and the universe, Roberts emphasizes the power of Conway’s simple, intuitive approaches and how his fascination with simple systems like “Life” belied the complexity they generate. Conway’s story, as told by Roberts, provides a counterpoint to the notion of laborious, highly technical approaches to mathematics, demonstrating the power of playfulness and curiosity in unlocking profound insights.
Reflection
Genius at Play is more than just a biography of a quirky mathematician; it’s a story about the nature of creativity, the pursuit of knowledge, and the often blurry lines between work and play. Conway’s playful approach to mathematics reminds us that even complex ideas often have simple underlying structures. While Conway may have been a “professional nonunderstander,” as he jokingly calls himself, his pursuit of understanding led to breakthroughs that continue to shape how we think about computation, infinity, and the nature of reality.
Roberts’s writing style is engaging and accessible, even when delving into complex concepts. However, her personal relationship with Conway, both as a biographer and friend, also raises questions about objectivity and bias. Her book, like her subject, also occasionally blurs the lines between fact and fiction, highlighting the slipperiness of memory and raising skeptical questions about some of the more outlandish anecdotes. Nonetheless, her portrayal of Conway’s struggles with fame, his battles with depression, and his persistent pursuit of knowledge humanizes a brilliant mind and reveals a complex individual.
By placing Conway’s life and work in the context of broader scientific and philosophical debates, particularly around artificial intelligence, Roberts invites us to consider the role of play, intuition, and the human element in the pursuit of knowledge and the ongoing quest to understand the universe. It is a book not only about a life lived in numbers but a testament to the power of curiosity, the joy of exploration, and the profound insights that come from playing at the edge of the unknown.
Flashcards
What is the Game of Life?
A mathematical game invented by Conway where simple rules lead to complex, unpredictable behavior.
What are Surreal Numbers?
A new class of numbers invented by Conway that extends beyond real numbers to encompass infinitesimals and various forms of infinity.
What is the order of a group?
The order of a group is the total number of its symmetries.
What does ‘sporadic’ mean in the context of group theory?
A mathematical term used to describe groups that do not belong to any known families, such as the Monster group.
What is the Doomsday Rule?
An algorithm invented by Conway for quickly determining the day of the week for any given date.
What are Penrose tiles?
Nonperiodic tiling patterns of the plane discovered by Roger Penrose.
What is Domineering?
A game played on a Go board, used by Conway to explore game theory concepts and the properties of games.
What is the “Laziness Doctrine”?
Conway’s playful approach to mathematics and his tendency to prioritize his own intellectual curiosity and enjoyment over traditional academic pursuits.
What is the “speed limit theorem”?
The principle in cellular automaton theory, including Conway’s Game of Life, that information cannot propagate faster than a certain speed, creating a bounding “box.”
What is the Game of Life?
A mathematical game invented by Conway where simple rules lead to complex, unpredictable behavior.
What are Surreal Numbers?
A new class of numbers invented by Conway that extends beyond real numbers to encompass infinitesimals and various forms of infinity.
What is the order of a group?
The order of a group is the total number of its symmetries.
What does ‘sporadic’ mean in the context of group theory?
A mathematical term used to describe groups that do not belong to any known families, such as the Monster group.
What is the Doomsday Rule?
An algorithm invented by Conway for quickly determining the day of the week for any given date.
What are Penrose tiles?
Nonperiodic tiling patterns of the plane discovered by Roger Penrose.
What is Domineering?
A game played on a Go board, used by Conway to explore game theory concepts and the properties of games.
What is the “Laziness Doctrine”?
Conway’s playful approach to mathematics and his tendency to prioritize his own intellectual curiosity and enjoyment over traditional academic pursuits.
What is the “speed limit theorem”?
The principle in cellular automaton theory, including Conway’s Game of Life, that information cannot propagate faster than a certain speed, creating a bounding “box.”