What is *A Mind for Numbers* by Barbara Oakley about?

*A Mind for Numbers* provides science-backed strategies to master math, science, and challenging subjects by optimizing learning processes. Barbara Oakley, a former mathphobe turned engineering professor, explains techniques like focused/diffuse thinking, chunking, and combating procrastination. The book emphasizes creativity in problem-solving, with examples from Thomas Edison and Salvador Dalí, and includes exercises to reinforce concepts.

Who should read *A Mind for Numbers*?

This book is ideal for students struggling with STEM subjects, professionals pursuing career changes requiring technical skills, and lifelong learners seeking to improve retention. Oakley’s methods apply to anyone aiming to overcome "math anxiety" or adopt evidence-based learning strategies, with relatable anecdotes from diverse learners.

Is *A Mind for Numbers* worth reading?

Yes—the book condenses neuroscience and cognitive psychology insights into actionable steps, making complex topics accessible. Readers praise its practical advice on spaced repetition, interleaving, and stress management. Though repetitive at times, this intentional design helps cement key ideas.

What are the main concepts in *A Mind for Numbers*?

Key concepts include: - **Focused vs. diffuse thinking**: Alternating intense concentration with relaxed mental states enhances creativity. - **Chunking**: Breaking information into manageable units improves mastery. - **Procrastination hacks**: Techniques like the Pomodoro Method build productive habits.

How does *A Mind for Numbers* help with career changes?

Oakley shares her journey from language studies to engineering, showing how rewiring learning approaches unlocks technical proficiency. The book’s strategies—like deliberate practice and overcoming the "Einstellung effect"—equip career changers to tackle STEM fields systematically.

What famous quotes or analogies are in *A Mind for Numbers*?

Oakley compares problem-solving to sculpting: "You need both the focused chisel and the diffuse sanding tool." She also cites Edison’s creative process, using "vague states of mind" to spark innovation. These metaphors simplify abstract learning principles.

How does *A Mind for Numbers* compare to *Make It Stick* or *Atomic Habits*?

While all three emphasize evidence-based learning, Oakley’s work uniquely targets STEM challenges with specific tactics like mental visualization and error correction. Unlike *Atomic Habits*, it delves into neuroscience behind habit formation in technical contexts.

What are common criticisms of *A Mind for Numbers*?

Some note repetitive structure, though Oakley defends this as reinforcement via spaced repetition. Critics argue certain analogies oversimplify cognitive processes, but most agree the book’s practicality outweighs these issues.

공부하는 독종이 살아남는다

수학 및 과학을 잘하는 법 (대수학에서 낙제했더라도)

바버라 오클리

4.2(21443 Reviews)

공부하는 독종이 살아남는다 개요

숫자와 뇌의 관계를 변화시키세요. 바바라 오클리(Barbara Oakley)의 혁신적인 접근 방식은 메모리 챔피언 넬슨 델리스(Nelson Dellis)가 한계를 뛰어넘을 수 있도록 도왔습니다. 베스트셀러 작가 다니엘 핑크(Daniel Pink)가 왜 이 방법을 "나는 수학 체질이 아니야"라고 생각했던 모든 이들을 위한 궁극의 장애물 타파법이라 부르는지 확인해 보세요.

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1장

Unlocking the Math Mind: How Anyone Can Master Numbers

Have you ever felt your brain freeze at the sight of an equation? You're not alone. Barbara Oakley once hated math so much she couldn't even read an analog clock. Yet this former math-phobe eventually became an engineering professor who studies how our brains learn. Her transformation wasn't magic-it was method. "A Mind for Numbers" has become a global phenomenon, praised by Nobel laureates and embraced by students worldwide. The book has been translated into over 20 languages and forms the foundation for Coursera's "Learning How to Learn," one of the most popular online courses ever created with over 3 million enrollments. Even tech leaders like Bill Gates have recommended it as essential reading for anyone looking to expand their mental capabilities. What makes this book so revolutionary? It reveals that mathematical ability isn't some innate gift-it's a skill anyone can develop with the right approach.

2장

The Two Essential Modes of Thinking

Imagine thirteen-year-old chess prodigy Magnus Carlsen playing against legendary grandmaster Garry Kasparov. During their match, Carlsen casually walks away from the board-a move that visibly rattles Kasparov. This seemingly strange behavior reveals something profound about how our brains work, especially when learning technical subjects. Our brains operate in two fundamentally different modes: focused and diffuse. The focused mode is like a powerful, narrow flashlight beam that illuminates a specific area with intense concentration. It's what we use when working through a math problem step-by-step or analyzing the grammar of a foreign language. This mode primarily engages your prefrontal cortex, directing your attention like an octopus extending its tentacles along familiar neural pathways. The diffuse mode, by contrast, is like switching that flashlight to a wide-angle setting. It's a relaxed, big-picture state where your thoughts can wander freely across different areas of your brain, making new connections and seeing broader patterns. This is the mode that activates when you're taking a shower, going for a walk, or drifting off to sleep-precisely when those "aha!" moments often strike. What makes math and science challenging is that humans didn't evolve to naturally process abstract symbols and concepts. Our brains developed to handle concrete threats and opportunities in our environment, not to manipulate equations or understand molecular structures. This is why these subjects often feel like they have "spongier bumpers" in our mental pinball machine-they require more practice to solidify. The key insight is that we need both modes to truly master difficult material. The focused mode helps us absorb the details and work through specific problems, while the diffuse mode helps us understand the bigger picture and make creative connections. The most effective learners know how to toggle between these states, using techniques like the Pomodoro method-25 minutes of intense focus followed by a short break-to engage both modes productively. When you're stuck on a problem, continuing to hammer away at it in focused mode can actually prevent you from finding the solution. This is called the Einstellung effect-where your initial approach blinds you to better alternatives. Instead, deliberately shifting to diffuse mode by taking a walk or switching to another task allows your brain to work on the problem subconsciously, often leading to breakthrough insights when you return.

들리는 모든 단어를 눈으로 확인하세요

공부하는 독종이 살아남는다의 각 단어가 오디오에 맞춰 실시간으로 강조되어 편하게 따라 읽을 수 있습니다.

3장

The Art of Chunking: Building Your Mental Library

Solomon Shereshevsky had a memory so perfect that his boss initially thought he was lazy for not taking notes during assignments. When questioned, Solomon revealed he could recall everything verbatim. Yet this extraordinary ability came with a significant drawback-he struggled to see the big picture because each detail remained so vivid. Unlike Solomon, effective learning requires forming "chunks"-compact packages of information bound together through meaning and practice. Chunking is how we transform scattered bits of information into unified concepts that occupy just one slot in our limited working memory. When a chess master looks at a board, they don't see 32 individual pieces-they see patterns and positions they recognize from thousands of previous games. Similarly, when a mathematician sees the equation E=mc2, they grasp its full meaning and implications in an instant, not as separate symbols. To form a chunk in math or science, you need three key steps. First, focus your full attention on the material without distractions. Multitasking is particularly destructive here-research shows it's like repeatedly pulling up a plant to check its roots, preventing any solid neural connections from forming. Second, understand the basic idea you're trying to chunk. This understanding acts as the glue that binds the information together. Finally, gain context by practicing with varied problems to recognize when to use (or not use) this particular chunk. The most common mistake students make is falling into "illusions of competence"-believing they understand material when they've merely become familiar with it. Highlighting or rereading notes creates a false sense of mastery. Instead, the research is clear: recall practice-forcing yourself to retrieve information from memory-is far more effective. Close your book and explain the concept as if teaching someone else, or solve practice problems without looking at examples. As you build more chunks, you'll find that each new concept becomes easier to learn-what Oakley calls the "Law of Serendipity." Each chunk takes up just one slot in your working memory instead of multiple slots for disconnected facts, freeing up mental space to form new connections. This is why experts can think so much more efficiently in their domain-they're not smarter, they just have a richer library of chunked patterns to draw from. Interleaving-practicing different types of problems rather than focusing on one technique at a time-is crucial for developing true mastery. While it feels more difficult and less satisfying than blocked practice (repeating the same type of problem), research shows it builds more flexible knowledge that transfers better to new situations. It's the difference between learning carpentry by practicing with only a hammer versus learning when to use different tools for different jobs.

4장

Taming the Procrastination Zombie

When you think about doing math, your brain actually experiences pain. Neuroimaging studies show that for math-anxious people, merely anticipating a math problem activates the same brain regions involved in physical pain. This explains why procrastination is particularly damaging for learning technical subjects-your brain is literally trying to protect you from discomfort. Procrastination follows a predictable pattern: you face a challenging task, your brain registers discomfort, you shift attention to something more pleasant, and you feel temporary relief. This cycle creates a habit loop that becomes increasingly automatic-what Oakley calls your "procrastination zombie." Like arsenic poisoning that begins with small doses, procrastination starts with avoiding just one uncomfortable task but gradually becomes a harmful pattern affecting multiple areas of life. The key insight is that the anticipation of doing math causes more suffering than actually doing it. Once you begin working, the pain centers in your brain typically quiet down. This means the solution isn't trying to summon more willpower (which is limited) but changing how you respond to the initial discomfort. To overcome procrastination, focus on process rather than product. Process means concentrating on putting in a specific amount of time (like 25 minutes) rather than completing an assignment (the product). Products trigger pain that causes procrastination, while processes can be followed mindlessly by your "zombie" brain systems. The Pomodoro technique-setting a timer for 25 minutes of focused work followed by a short break-is particularly effective because it makes the process concrete and manageable. Identify your procrastination cues-location, time, feelings, reactions to people, or preceding events-and develop specific plans to handle them. Create new routines like going to a special study location or developing a pre-study ritual that signals to your brain it's time to focus. Ensure your rewards are meaningful and immediate, whether it's a brief social media check, a snack, or simply the satisfaction of crossing an item off your list. The most effective approach combines the planner-journal system with the concept of "eating your frogs first"-tackling your most difficult tasks early in the day when your willpower is strongest. Write your tasks the night before to engage your subconscious, keep your daily list manageable (about six items), and set a specific quitting time to maintain work-life balance. Even highly successful academics maintain this discipline, recognizing that constant work leads to diminishing returns and eventual burnout.

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5장

Memory Magic: Unlocking Your Visual Superpowers

Joshua Foer was a journalist with an average memory who eventually became a U.S. Memory Championship finalist. How? By tapping into the brain's extraordinary visual and spatial memory systems-evolutionary gifts from our ancestors who needed to remember hunting routes and food locations. While we struggle to remember abstract concepts or lists, our brains effortlessly absorb thousands of visual details about new places we visit. Memory champions exploit this natural ability through techniques like the "memory palace," where you mentally place vivid images representing concepts at specific locations in a familiar setting. Later, you can "walk" through this space to retrieve the information in order. For example, to remember the mineral hardness scale (talc, gypsum, calcite, fluorite, apatite, orthoclase, quartz, topaz, corundum, diamond), you might imagine walking through your home and seeing a talking piece of talc on your doormat, a gypsum statue crying on your hall table, a calcite crystal on your kitchen counter, and so on. This technique works because it transforms abstract information into concrete, spatial representations that your brain is naturally equipped to handle. Creating memorable visual metaphors is equally powerful. When learning about electrical current, visualize water flowing through pipes. For algebraic equations, imagine being the variable x trying to escape from operations performed on you. These visualizations connect new ideas to existing neural structures, providing physical understanding of abstract concepts and helping break through mental blocks when you're stuck. The key is making these images bizarre, multisensory, and emotionally engaging. The funnier or more outrageous the image, the more likely you'll remember it. For instance, to remember that f=ma (force equals mass times acceleration), picture a flying (f) mule (m) accelerating (a) through the air. The more senses you engage-smell, touch, sound-the more neural hooks you build for easier recall. Spaced repetition complements these techniques by working with your brain's natural forgetting curve. Instead of cramming all at once, briefly review material at increasing intervals-perhaps an hour after first learning it, then a day later, then a week later. This approach signals to your brain that the information is important enough to retain long-term. Research shows students using these memory techniques outperform those who don't, transforming novices into semi-experts much faster. The memorization process itself becomes creative, building unexpected connections as you internalize ideas. With practice, creating vivid images becomes faster and easier, simultaneously deepening your understanding of the material.

6장

Beyond Natural Talent: Developing Mathematical Intuition

Magnus Carlsen's extraordinary chess abilities might seem like pure genius, but they actually stem from his vast mental library of chess patterns developed through years of practice. Elite chess players typically spend a decade mastering thousands of pattern chunks that allow rapid recognition of game situations. This pattern recognition, not raw intelligence, is what enables their seemingly magical intuition. While intelligence certainly matters-smarter people often have larger working memories-it can sometimes hinder creativity. A superb working memory can hold thoughts so tightly that new ideas can't break through (the Einstellung effect). Research shows that intelligent people sometimes overthink simple problems, missing obvious solutions while getting lost in complexity. Meanwhile, those with smaller working memories may struggle initially but can more easily generate creative combinations by drawing from different brain regions. Santiago Ramon y Cajal, the father of modern neuroscience, believed anyone could "sculpt their brain" through persistent practice and flexible thinking. Despite his troubled youth and academic struggles, Cajal developed a unique approach to studying brain cells: he would prepare microscope slides each morning, spend hours viewing cells, then draw from memory what he'd seen, comparing his drawings to the actual slides and redrawing until he captured the essence of the entire collection. This process of "deep chunking" allowed Cajal to abstract key patterns that helped others see what was essential. Once we create such neural chunks, we can transfer them to new domains-explaining why concepts in math and science often have analogies to things we already know, and why people skilled in these fields can often apply their thinking to areas like finance or business. Learning math and science resembles mastering sports. In baseball, repetition creates muscle memory so your body responds automatically to a single thought rather than recalling complex steps. Similarly, once you understand why you do something in math, you don't need to reexplain the how each time. With practice across varied problems, your mind constructs patterns of meaning rather than simply accepting what others tell you. As you develop expertise, you'll begin to perform tasks automatically without conscious awareness of every detail. You'll make complex decisions rapidly by shutting down conscious analytical systems and relying on well-trained intuition from deeply ingrained chunks. At some point, consciously analyzing why you do what you do just interrupts flow and leads to worse decisions.

들리는 모든 단어를 눈으로 확인하세요

공부하는 독종이 살아남는다의 각 단어가 오디오에 맞춰 실시간으로 강조되어 편하게 따라 읽을 수 있습니다.

7장

Test-Taking Mastery: Turning Anxiety into Advantage

Testing itself is an extraordinarily powerful learning experience-you'll retain and learn far more from an hour of testing than an hour of studying the same material. The concentrated mental focus required during tests strengthens neural connections and reveals gaps in your understanding that might otherwise remain hidden. Research shows that students who regularly self-test retain up to 50% more information compared to those who merely review materials. This testing effect is particularly powerful when combined with immediate feedback and error correction. The counterintuitive "hard-start-jump-to-easy" approach is particularly effective for math and science exams. Start with the hardest problem but pull away within minutes if you get stuck. This loads the difficult problem in mind then switches attention away, allowing your diffuse mode to begin working on it subconsciously while you complete easier problems. For example, in calculus, you might briefly examine a complex integration problem, then move to simpler derivatives while your brain processes the harder concept. This approach ensures you make progress on every problem, helps avoid getting stuck in wrong approaches, and uses your brain more efficiently. Studies show students using this technique complete 20% more problems correctly compared to traditional linear approaches. Test anxiety produces physical symptoms like sweaty palms and racing heart due to stress chemicals like cortisol. Research shows that reinterpreting these symptoms positively ("I'm excited!" rather than "I'm afraid!") significantly improves performance. Elite athletes and performers use this same technique, viewing pre-performance jitters as beneficial energy rather than harmful anxiety. For panicky test-takers, deep breathing helps-relax your stomach, place your hand on it, and draw a deep breath, allowing your chest to expand outward. This sends oxygen to critical brain areas, signaling all is well. Practice this breathing technique regularly before the test to make it automatic during high-stress moments. When checking your work, deliberately shift between focused and diffuse modes. The focused mode helps you execute calculations accurately, while the diffuse mode provides a big-picture perspective to catch conceptual errors. Consider starting from the back and working forward for a fresh perspective, asking "Does this really make sense?" Verify work using different approaches when possible, watching for simple errors like missed minus signs or calculation mistakes. For mathematical problems, try plugging answers back into equations or estimating reasonable ranges for answers. In essay questions, read your responses aloud to catch awkward phrasing or logical gaps. Sleep is perhaps the most important factor in test preparation. Without adequate rest, other preparation becomes meaningless. Sleep deprivation before exams can sabotage even well-prepared students by impairing working memory and higher cognitive functions. Research demonstrates that students who sleep 8 hours before an exam score an average of 15% higher than those who pull all-nighters. The brain requires sleep to consolidate learning and strengthen neural pathways formed during study. One hour of study with a well-rested brain is more effective than three hours with a tired one. Establish a consistent sleep schedule at least a week before important exams, aiming for 7-9 hours of quality rest each night.

8장

Renaissance Learning: Balancing Independence and Collaboration

Charles Darwin, despite being a poor student who failed medical school, became one of history's most influential figures by learning independently as a ship's naturalist aboard the HMS Beagle. His five-year voyage allowed him to observe, collect specimens, and develop theories free from academic constraints. Learning on your own provides a unique path to mastery, revealing the three-dimensional reality of subjects beyond what any single teacher or book can provide. This independent exploration allows you to discover connections others might miss and develop your own intellectual framework, much as Darwin did in formulating his theory of evolution. When facing criticism, maintain a cool dispassion that helps you focus on learning while tuning out those who seek to undercut you. As Santiago Ramon y Cajal, the father of modern neuroscience, warned, achievement inevitably attracts criticism. The greater your success, the more others may attack your efforts out of their own insecurity or resistance to new ideas. Darwin himself faced intense opposition when publishing "On the Origin of Species," but remained focused on evidence rather than emotional reactions. Use failures as learning opportunities to improve your approach rather than evidence of innate limitation. Each setback provides valuable data about what doesn't work and how to adjust your strategy. Working with others provides an essential complement to independent learning. Even brilliant minds like Niels Bohr needed someone like Richard Feynman who wasn't intimidated and would challenge flawed thinking. Study partners serve as external "diffuse mode" thinkers who spot your blind spots and catch errors your own brain might miss. The most productive study groups allow for constructive criticism rather than overly polite interactions. Consider how the Manhattan Project succeeded through intense collaboration between diverse minds, each bringing unique perspectives and challenging assumptions. The right hemisphere helps us step back and put our work into perspective, enabling "aha!" insights and reality checks. This big-picture thinking complements the left hemisphere's detailed, sequential processing. When you rush through problems without checking your work, you're essentially refusing to use parts of your brain. Rechecking allows for interaction between hemispheres, taking advantage of each one's abilities - the left's analytical precision and the right's holistic understanding. Good learners always verify that their work makes sense rather than playing "equation sheet bingo." This verification process might involve asking questions like "Does this answer seem reasonable?" or "What other approaches could validate this solution?" Scientists like Einstein regularly used thought experiments and visual imagery to check their mathematical calculations, engaging both hemispheres in the process.

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9장

The Paradoxical Nature of Learning

Richard Feynman, the Nobel Prize-winning physicist, developed his safecracking skills during the Manhattan Project years while his wife was gravely ill in a New Mexico hospital. His methodical approach to cracking safes containing nuclear secrets reveals the paradoxical nature of learning: sometimes our desperate desire to solve problems immediately actually prevents solutions. Feynman discovered that stepping back, observing patterns, and allowing time for insight often proved more effective than brute-force attempts. Learning involves many apparent contradictions that challenge our intuitive assumptions. Intense focus helps solve complex problems yet can simultaneously block fresh approaches when we become too fixated. Success provides validation and confidence, but failure often teaches more profound lessons about process and understanding. Persistence is crucial for mastery, yet misplaced persistence in unproductive directions leads to frustration and blocked learning. Understanding these paradoxes allows us to work with our brain's natural tendencies rather than against them, much like a sailor working with the wind rather than fighting it. The ten rules of good studying distill these insights into practical applications: Use active recall after reading instead of passive highlighting, forcing your brain to retrieve information; test yourself constantly with flash cards, embracing the productive difficulty of self-testing; chunk problems by practicing until solutions come to mind automatically, like a pianist's fluid movements; space repetition across days like an athlete training for peak performance; alternate different problem-solving techniques during practice to build flexible understanding; take strategic breaks when frustrated to let your diffuse mode work in the background; use explanatory questioning and simple analogies to deepen comprehension; focus intensely for 25-minute sessions with small rewards after completion; tackle the hardest tasks earliest when mental energy is fresh; and create vivid mental contrast between your current position and future aspirations to maintain motivation through challenges. Conversely, the ten rules of bad studying highlight common mistakes that waste time and energy: Passive rereading without actively recalling main ideas, creating an illusion of learning; excessive highlighting that becomes a substitute for understanding; merely glancing at solutions without working through problems step-by-step; last-minute cramming instead of distributed practice over time; repeatedly solving familiar problem types that don't stretch understanding; allowing study groups to lose focus and become social gatherings; skipping assigned reading before attempting problems; avoiding asking for help when genuinely confused; studying while constantly checking phones or social media; and sacrificing sleep for study time, which undermines memory consolidation. The key to reshaping your brain is patient persistence - working with your brain's strengths and weaknesses like a skilled gardener rather than forcing growth. By understanding our brain's default settings - its natural learning mechanisms involving focused and diffuse modes, memory consolidation during sleep, and the importance of spaced practice - we can unlock our potential, just as Feynman discovered the locksmith's secret was knowing manufacturers' default settings. Whether you're currently struggling with math and science or already excel in these subjects, these evidence-based techniques will help you learn more deeply and effectively, transforming not just what you know, but how you think and approach new challenges.

★★★★★

공부하는 독종이 살아남는다 완독을 축하합니다

100만 명 이상의 학습자가 사랑합니다

“23일째 매일 사용하고 있어요. 이제 제 일상의 한 부분이 되었습니다.”

jayallen

공부하는 독종이 살아남는다의 핵심 주제

focused and diffuse thinking
chunking information
illusions of competence
recall practice
overcoming procrastination

공부하는 독종이 살아남는다의 명언

Mathematical ability isn't some innate gift-it's a skill anyone can develop.
Humans didn't evolve to naturally process abstract symbols and concepts.
Multitasking is particularly destructive here.
The anticipation of doing math causes more suffering than actually doing it.
Focus on process rather than product.

공부하는 독종이 살아남는다의 등장인물

Barbara OakleyAuthor and engineering professor
Magnus CarlsenChess prodigy used as a case study for thinking
Garry KasparovLegendary chess grandmaster
Solomon ShereshevskyMan with a perfect memory used as a case study

저자 소개

베스트셀러 *수학의 즐거움: 수학과 과학을 잘하기 위한 뇌과학의 비밀(A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra))*의 저자인 바바라 오클리(Barbara Oakley)는 뇌과학 기반 학습 전략 분야에서 세계적으로 인정받는 전문가입니다.

오클랜드 대학교의 공학 석좌 교수인 오클리는 군 복무와 소련 저인망 어선의 통역 업무를 거쳐 전기 공학자가 되었습니다. 이러한 여정은 학습의 장벽을 극복하는 그녀의 연구에 큰 영감을 주었습니다.

뉴욕 타임스에서 찬사를 받은 그녀의 저서는 인지 과학과 까다로운 과목을 마스터하기 위한 실용적인 기법을 결합하고 있으며, 언어학자이자 STEM 전문가로서의 독특한 관점을 반영하고 있습니다. 오클리의 획기적인 코세라(Coursera) 강의인 *학습법 배우기(Learning How to Learn)*는 전 세계적으로 300만 명 이상의 학생이 수강했으며, 그녀의 연구는 *월스트리트 저널(Wall Street Journal)*과 *미국 국립과학원 회보(Proceedings of the National Academy of Sciences)*에 소개되기도 했습니다.

그녀는 학술 선집인 *병적 이타주의(Pathological Altruism)*를 공동 편집했으며, 회고록인 *개털: 러시아 저인망 어선에서의 이야기(Hair of the Dog: Tales from Aboard a Russian Trawler)*를 집필했습니다. 교육계의 노벨상이라 불리는 맥그로 상(McGraw Prize)을 수상한 오클리의 학습법은 하버드 대학교에서 가르치고 있으며 포춘 500대 기업에서도 활용되고 있습니다. 수학의 즐거움은 100만 부 이상 판매되었으며 전 세계 STEM 프로그램의 필독서로 자리 잡았습니다.

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학습 계획

Math

This plan is essential for anyone looking to bridge the gap between basic arithmetic and high-level abstract reasoning. It is ideal for students, professionals, or lifelong learners who want to master logical problem-solving and the universal principles of mathematics.

5 h 33 m•4 섹션

학습 계획

The Psychology of Everyday Mind Tricks

In an era of digital manipulation and complex social dynamics, understanding the hidden forces of the mind is essential for clear thinking. This plan is ideal for professionals and social navigators looking to sharpen their influence, emotional intelligence, and critical thinking skills.

2 h 18 m•3 섹션

학습 계획

The Architecture of Mathematical Thought

This plan bridges the gap between abstract philosophy and practical application, offering a deep dive into the structures that govern logic and reality. It is ideal for thinkers, analysts, and problem-solvers looking to sharpen their decision-making and modeling skills.

1 h 30 m•3 섹션

학습 계획

Mathematics

This comprehensive path bridges the gap between basic arithmetic and the advanced theories that define our physical reality. It is ideal for students, professionals, or lifelong learners seeking to sharpen their analytical intuition and master the universal language of logic.

3 h 46 m•4 섹션

학습 계획

The Polymath's Blueprint for Deep Focus

This plan is designed for lifelong learners and professionals who need to master complex subjects in an era of constant interruption. It provides a strategic framework for anyone looking to bridge multiple disciplines by optimizing their neurological and organizational systems for elite performance.

1 h 30 m•3 섹션

학습 계획

Outperform my math rival in speed and skill

This plan is designed for competitive students and math enthusiasts who want to bridge the gap between competence and mastery. It combines mechanical speed with psychological resilience to ensure you remain calm and accurate during high-stakes academic rivalries.

3 h 36 m•3 섹션

학습 계획

Rewire Your Mind for Mastery

This plan is designed for lifelong learners and professionals seeking a cognitive edge in a rapidly changing world. By combining neuroscience, metacognition, and social psychology, it provides a comprehensive toolkit for personal and professional evolution.

1 h 30 m•3 섹션

샌프란시스코에서 컬럼비아 대학교 동문들이 만들었습니다

LOVED BY

1,000,000+ curious minds.

4.7

avg rating

1M+ learners

"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

@Moemenn

"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

@Chloe, Solo founder, LA

117

"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

@Raaaaaachelw

"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

@Matt, YC alum

108

"Reading used to feel like a chore. Now it’s just part of my lifestyle."

@Erin, Investment Banking Associate , NYC

254

"Feels effortless compared to reading. I’ve finished 6 books this month already."

@djmikemoore

"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

@Pitiful

4.5K

"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

@SofiaP

"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

@Jaded_Falcon

201

"It is great for me to learn something from the book without reading it."

@OojasSalunke

"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

@Leo, Law Student, UPenn

483

"Makes me feel smarter every time before going to work"

@Cashflowbubu

웹에서 BeFreed가 어떻게 논의되고 있는지 더 보기

샌프란시스코에서 컬럼비아 대학교 동문들이 만들었습니다

LOVED BY

1,000,000+ curious minds.

4.7

avg rating

1M+ learners

"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

@Moemenn

"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

@Chloe, Solo founder, LA

117

"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

@Raaaaaachelw

"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

@Matt, YC alum

108

"Reading used to feel like a chore. Now it’s just part of my lifestyle."

@Erin, Investment Banking Associate , NYC

254

"Feels effortless compared to reading. I’ve finished 6 books this month already."

@djmikemoore

"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

@Pitiful

4.5K

"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

@SofiaP

"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

@Jaded_Falcon

201

"It is great for me to learn something from the book without reading it."

@OojasSalunke

"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

@Leo, Law Student, UPenn

483

"Makes me feel smarter every time before going to work"

@Cashflowbubu

"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

@Moemenn

"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

@Chloe, Solo founder, LA

117

"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

@Raaaaaachelw

"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

@Matt, YC alum

108

"Reading used to feel like a chore. Now it’s just part of my lifestyle."

@Erin, Investment Banking Associate , NYC

254

"Feels effortless compared to reading. I’ve finished 6 books this month already."

@djmikemoore

"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

@Pitiful

4.5K

"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

@SofiaP

"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

@Jaded_Falcon

201

"It is great for me to learn something from the book without reading it."

@OojasSalunke

"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

@Leo, Law Student, UPenn

483

"Makes me feel smarter every time before going to work"

@Cashflowbubu

"Instead of endless scrolling, I just hit play on BeFreed. It saves me so much time."

@Moemenn

"I never knew where to start with nonfiction—BeFreed’s book lists turned into podcasts gave me a clear path."

@Chloe, Solo founder, LA

117

"Perfect balance between learning and entertainment. Finished ‘Thinking, Fast and Slow’ on my commute this week."

@Raaaaaachelw

"Crazy how much I learned while walking the dog. BeFreed = small habits → big gains."

@Matt, YC alum

108

"Reading used to feel like a chore. Now it’s just part of my lifestyle."

@Erin, Investment Banking Associate , NYC

254

"Feels effortless compared to reading. I’ve finished 6 books this month already."

@djmikemoore

"BeFreed turned my guilty doomscrolling into something that feels productive and inspiring."

@Pitiful

4.5K

"BeFreed turned my commute into learning time. 20-min podcasts are perfect for finishing books I never had time for."

@SofiaP

"BeFreed replaced my podcast queue. Imagine Spotify for books — that’s it. 🙌"

@Jaded_Falcon

201

"It is great for me to learn something from the book without reading it."

@OojasSalunke

"The themed book list podcasts help me connect ideas across authors—like a guided audio journey."

@Leo, Law Student, UPenn

483

"Makes me feel smarter every time before going to work"

@Cashflowbubu

웹에서 BeFreed가 어떻게 논의되고 있는지 더 보기

지금 바로 학습 여정을 시작하세요

9장

공부하는 독종이 살아남는다

개요공부하는 독종이 살아남는다 개요

한 권의 책, 다양한 듣기 방식.

Unlocking the Math Mind: How Anyone Can Master Numbers

The Two Essential Modes of Thinking

들리는 모든 단어를 눈으로 확인하세요

The Art of Chunking: Building Your Mental Library

Taming the Procrastination Zombie

공부하는 독종이 살아남는다에서 더 많은 것을 얻으세요

Memory Magic: Unlocking Your Visual Superpowers

Beyond Natural Talent: Developing Mathematical Intuition

들리는 모든 단어를 눈으로 확인하세요

Test-Taking Mastery: Turning Anxiety into Advantage

Renaissance Learning: Balancing Independence and Collaboration

공부하는 독종이 살아남는다에서 더 많은 것을 얻으세요

The Paradoxical Nature of Learning

공부하는 독종이 살아남는다 완독을 축하합니다

공부하는 독종이 살아남는다의 핵심 주제

공부하는 독종이 살아남는다의 명언

공부하는 독종이 살아남는다의 등장인물

저자 소개

공부하는 독종이 살아남는다 요약 다운로드

다른 사용자들도 좋아한 책

이 책에 대한 FAQ

What is A Mind for Numbers by Barbara Oakley about?

Who should read A Mind for Numbers?

Is A Mind for Numbers worth reading?

What are the main concepts in A Mind for Numbers?

더 알아보기

1,000,000+ curious minds.

1,000,000+ curious minds.

한 권의 책, 다양한 듣기 방식.

Unlocking the Math Mind: How Anyone Can Master Numbers

The Two Essential Modes of Thinking

들리는 모든 단어를 눈으로 확인하세요

The Art of Chunking: Building Your Mental Library

Taming the Procrastination Zombie

공부하는 독종이 살아남는다에서 더 많은 것을 얻으세요

Memory Magic: Unlocking Your Visual Superpowers

Beyond Natural Talent: Developing Mathematical Intuition

들리는 모든 단어를 눈으로 확인하세요

Test-Taking Mastery: Turning Anxiety into Advantage

Renaissance Learning: Balancing Independence and Collaboration

공부하는 독종이 살아남는다에서 더 많은 것을 얻으세요

The Paradoxical Nature of Learning

공부하는 독종이 살아남는다 완독을 축하합니다

다른 사용자들도 좋아한 책

더 알아보기

공부하는 독종이 살아남는다 개요