Boost Logic, Math Thinking & Reasoning: Gödel Insights

Boost your critical thinking, reasoning, and decision-making through puzzles, Gödel’s theorems, and real-world logic

What you'll learn

• Develop sharper logical reasoning skills by solving puzzles, probability problems, and illustrative examples from game-theory scenarios step by step.
• Understand the structure and limits of formal reasoning, including paradoxes and self-referential problems that lead to Gödel’s incompleteness theorems.
• Analyze decision-making under uncertainty using classic problems like the Prisoner’s Dilemma and the Monty Hall scenario.
• Identify where and why AI systems like ChatGPT can make reasoning mistakes, and what that reveals about both AI and human thinking.
• Connect abstract logic to practical contexts, including psychology, artificial intelligence, and even personal health and habits.
• Explore the evolution of intelligence and reasoning, understanding how health, experience, and perspective influence clear thinking.
• Combine structured reasoning and intuition to solve problems, correctly interpret probabilities, and avoid common mistakes in conditional reasoning

Requirements

• No prior knowledge of formal logic or Gödel’s theorems is required.
• A curiosity for puzzles, problem-solving, and critical thinking will help you get the most out of the course.
• Basic familiarity with high-school level mathematics (algebra, probability) is helpful
• A willingness to think deeply, reflect, and engage with challenging questions.
• Recommended: pen and paper for working through puzzles and the lectures. Don't be afraid to stop the videos and think.

Description

This course is initially built around a carefully selected set of puzzles from Martin Gardner’s My Best Mathematical and Logic Puzzles. The problems are presented with clear, step-by-step reasoning, diagrams, and quizzes to challenge and engage you.

But this is far more than a puzzle course. Through these problems, and especially in later sections, we reflect on the very structure of logical thinking, when intuition fails, how formal reasoning helps, and how paradoxes expose the limits of thought. These discussions naturally lead to Gödel’s incompleteness theorems, inspired in part by the works of Torkel Franzén, Raymond Smullyan, and sections on Gödel from Ananyo Bhattacharya’s The Man from the Future: The Visionary Life of John von Neumann.

Rather than covering logic in a purely symbolic or formal way, this course takes you on a journey guided by intuition, sometimes moving to higher levels of abstraction. Some puzzles are more accessible, while others are more subtle, but the main objective is to show different facets of reasoning (from intuitive reasoning to more rigorous reasoning in some cases), and from mathematics to philosophy, artificial intelligence, and decision-making.

Along the way, you will discover how understanding the limits of logic can help you evaluate information, avoid common reasoning traps, and even see where advanced AI systems like ChatGPT can make mistakes.

Some sections are academic in nature, but others provide practical insights useful for professionals and leaders who want to think clearly, solve problems under uncertainty, and make smarter decisions. Although the course does not focus explicitly on business examples, it teaches transferable thinking skills directly applicable in professional contexts, which is why I chose the Business category. However, the course benefits anyone seeking to sharpen logical thinking and decision-making, regardless of their professional background

In this course, you will explore classic logic and probability puzzles, including the Prisoner’s Dilemma and Monty Hall scenarios, to strengthen your decision-making under uncertainty, weigh risks effectively, and anticipate outcomes in both personal and professional contexts.

Topics include:

• Logic puzzles, probability challenges, and elements of game theory
• Gödel’s completeness vs. incompleteness theorems explained clearly (with varying levels of abstraction and from different perspectives)
• Links between logic, quantum systems, psychology, AI, and human intelligence
• How intelligence, health, and compromise influence clear thinking
• Practical perspectives for viewing life events and learning from them

Who this course is for:

• Professionals and leaders seeking sharper decision-making skills, structured reasoning, and practical problem-solving strategies.
• Students of mathematics, computer science, or engineering who want to explore logic and reasoning beyond the classroom.
• AI and tech enthusiasts interested in understanding where artificial intelligence still makes logical mistakes.
• Anyone preparing for competitive exams, IQ tests, or interviews where strong logical thinking and problem-solving are key.
• Thinkers, strategists, and problem-solvers who enjoy connecting abstract theory, like Gödel’s theorems, to practical insights.