Effective thinking

Effective Thinking Through Mathematics,这大抵是这二十多年来我听过的最好的课程了,为期九周,今天终于完成。


  • Understand Deeply,理解问题

    Don’t face complex issues head-on; first understand simple ideas deeply. Clear the clutter and expose what is really important. Be brutally honest about what you know and don’t know. Then see what’s missing, identify the gaps, and fill them in. Let go of bias, prejudice, and preconceived notion. There are degrees to understanding (it’s not just a yes-or-no proposition) and you can always heighten yours. Rock-solid understanding is the foundation for success.


  • Make Mistakes,试错

    Fail to succeed. Intentionally get it wrong to inevitably get it even more right. Mistakes are great teachers - they highlight unforeseen opportunities and holes in your understanding. They also show you which way to turn next, and they ignite your imagination.


  • Raise Questions,提问

    Constantly create questions to clarify and extend your understanding. What’s the real question? Working on the wrong questions can waste a lifetime. Ideas are in the air - the right questions will bring them out and help you see connections that otherwise would have been invisible.


  • Follow the Flow of Ideas,点子流

    Look back to see where ideas came from and then look ahead to discover where those ideas may lead. A new idea is a beginning, not an end. Ideas are rare - milk them. Following the consequences of small ideas can result in big payoffs.


  • The Quintessential Element,跳出定势

    The unchanging element is change - by mastering the first four elements, you can change the way you think and learn. You can always improve, grow, and extract more out of your education, yourself, and the way you live your life. Change is the universal constant that allows you to get the most out of living and learning.

    唯一不变的就是变化。熟练掌握上述 4 点之后,还要持续总结、改进、提高。突破定势,走向成功!

课程中通过在数学方面的多个例子,演示了如何利用这五大原则去解决“不可能的难题”,启发非常大。后面我希望能在编程领域通过 leetcode 题库等方式,训练自己的思维方式,以期提升自己解决未知难题的能力。