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Aug 1, 2023 08:42 PM
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How to apply mathematical thinkings in our life?
 
Mathematical thinking is a powerful tool, and not some hocus pocus 🎩. It extends beyond ordinary, everyday thinking, deepening our understanding and connection with our surroundings. The essence of mathematics is not confined to solving problems, but rather, it illuminates insights, uncovers connections, and presents explanatory narratives 🌉. Regardless of the complexity, delving deeper into any aspect of your life, will reveal more intricate patterns and lessons.
The primary purpose of mathematics is to convey ideas and concepts with exactness 🎯. The act of reducing a problem to its fundamentals can illuminate your daily life, providing clarity and insight that otherwise might have remained obscured.
Applying mathematical thinking to your daily life requires a few key ingredients: experimentation, a willingness to fail, and proactive deconstruction. In addition, it's important to maintain a bird's eye view on the situation, apply abstraction, formulate a plan of action, and proceed accordingly 🌳.
Another powerful tool in our mathematical arsenal is the use of narrative or analogy. Math is a myriad of shades, not merely black and white 🎨. A compelling narrative allows us to comprehend an abstract mathematical problem in a practical manner, transforming a solution from a mere numeric answer into a tangible concept. However, beware of misleading narratives that suggest unnecessary solutions, like seeking a precise solution when an approximation would suffice.
The real magic lies in crafting a good story, and often, these narratives are born out of seemingly 'dumb' questions. Remember, there's no such thing as a 'dumb' question in mathematics, the 'dumber' the question, the greater the potential insight 🎣. Make ample use of analogies wherever possible, like equating a double negative to running a store or comparing salt density in the ocean to conducting a poll. This interplay between intuition and rigor will make you feel smarter, better equipped to tackle life's complexities.
When it comes to mathematical thinking, failure is not the end, but a beginning 🏁. Avoid pointing fingers in the face of failure; instead, treat it as a clue towards the correct answer. Determine what doesn't work and why, keeping in mind that persistence and patience are the keys 🔑.
Everyone hits a roadblock at some point. If you aren't, then perhaps it's time to step up the challenge. When you're stuck, tap into your resources and remember, experience often trumps energy. Sometimes, letting go of the problem, even for a short while, allows you to return with fresh eyes and uncover something previously unseen 👀. Constantly expose yourself to challenges, remember that stakes are low and that you can always start over. The objective is to derive pleasure from the process rather than merely solving the problem swiftly and efficiently.
So take the leap and unravel life's intricate patterns with the lens of mathematical thinking, making everyday a journey of discovery and enlightenment. 🌟
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Copy Terence’s style to approach problems in mathematical thinkings and first principles. If you want to copy his knowledge, then best of luck to you!
 

📎 Bullet points from the interview

  1. Mathematical thinking is actually an extension of ordinary, everyday thinking. It’s not magic 🎩.
    1. The more you think about your surroundings, the clearer it becomes that everything is connected.
    2. Math is not just about solving problems. It’s about gaining insights, finding connections ,and explanations.
    3. The deeper you dive into anything in your life, the more you will discover and learn.
    4. The purpose of mathematics, ultimately, is to communicate ideas and concepts with precision.
    5. Even in your day-to-day life, stripping down a problem to its bare essentials can provide clarify and insight that you wouldn’t have had before.
  1. Practical mathematical thinking requires:
    1. experimentation
    2. a willingness to fail
    3. proactive deconstruction
    4. remember sometimes to zoom out, apply, abstraction, choose a plan of action, then act accordingly. Keep an eye on the big picture.
  1. Framing a problem with a narrative or an analogy can make a huge difference.
    1. Math is not black and white.
    2. A good narrative allows you to understand an abstract mathematical problem in a practical way. It can help you see the solution as more than just a numerical answer.
    3. A bad narrative, however, can , make you think that you need a solution that is not actually necessary, such as a precise solution to a problem that might require only an approximate answer.
    4. the key is to tell a good story
    5. good stories come from dumb questions
    6. the dumber the question is, the better the question is
    7. use analogies whenever possible, the analogy between negative-negative and running a store
    8. salt density of ocean and the polling
    9. doing back and forth with intuitions and rigor makes you feel smarter
  1. Don’t be afraid to fail.
    1. Try to avoid blaming a failure on yourself or others.
    2. Remember that failure is often what provides us the clues to a correct answer.
    3. Figure out what does not work and why
    4. Persistence is key. Stay patient- it’s all part of the process.
  1. Everyone gets stuck. If you are not hitting roadblocks, you are not challenging yourself.
    1. Tap into all your other resources if you get stuck.
    2. Experience often trumps energy.
    3. Finally, sometimes you need to learn to let your problems go, wait for a bit, and return with fresh eyes, so you can see something you didn’t see before.
    4. Expose yourself to challenges, stakes are low and start over. The goal is to enjoy it intend of solving it quickly and efficiently.
 
 
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