How to solve it

book 32: How to solve it

  • July NJ, 2019

Regardless of what is my current status of career development, being a borderline mathematician is my last pride and light.  In order to avoid the story beginning as “Once, i studied mathematics …” , I am keeping working on math problems, even some simple algebraic problems. After all, the only way to understand math by is by doing maths. At least, I m reading maths books.

Without the loss of generality, How to solve it concluded a 4-Step-Method to solve a problem.

  1. Preview: Get acquaintance with the problem( background knowledge) 
  2. Planning: Make a Plan for solving the problem
  3. Solving: Carry out the plan to solve the problem
  4. Review: Check the answers, think about is there another way to solve the problem?

Then i thought this 4-step method is ubiquitous, it can be used anywhere anytime, in music, workout or life planning. I think I used the 4-step method partially in my previous academical years. What I am missing is 1. Preview and 4. Review. Now I really think Review is crucial in learning, or I m just repeating my mistakes again and again. I didn’t get any worse, but I won’t get any better without the Review Step. 

Music 🎧🎼:

  1. Listen to Recordings, be familiar with the flow of movement
  2. Study the music, make a plan for fingering and bow distribution
  3. Carry out the bow distribution and expression
  4. Analyze the self-recording, what could be improved and don’t forget to applaud for the part we did good!

I enjoy the author’s philosophy, celebrate the tiniest successes! If we can’t figure out a hard problem, (1/x)sin(x) is continuous, can we proof sin(x) is continuous first? 
At last, the fervent wish counts, too! most of times, I quit thinking and copied others solution besides I m not confident enough, I didn’t think one problem mattered.  One problem after another, qualify ends up to be my Waterloo. Luckily, we have the expression: 卷土重来未可知。


🌱Sparkling Lines:

You may experience the tension and enjoy the triumph of discovery

a taste for mental work and leave their imprint on mind & character for a lifetime

a great amibition

deeper curisority, a desire to understand the ways and means, the motive and procedures of solutions

in satu nascendi

a plan of the solution, carrying out the plan looking back check the argument 

To understand mathematics means to be able to do mathematics


draw figures

this idea may emerge gradually

seeing and proving

use of all relvent data variation of the data, symmetry, analogy

what i can gain by doing so?

analogy : a sort of similarity

individual thinking! that’s important

Auxillary elements

Intelligent readear think the motive behind each step

nevertheless you should be greatful for all new ideas

it is safe riding at 2 anchors

Exploit your sucess

going back to the definition is an important operation of mind

you settle down to work seriously 

you throw your whole personality if there is a great promis

if your promise is set, you stick to it, you seek for little success

carrying out your plan of the solution at each step,can you see clearly each step is correct?

could you solve a part of the problem?

always use your own brains first

proves to prove vs problems to find analogy, gereralization, specialization, decomposing, recombing

Solve the part of the problem?

Keep the Ball Rolling

Rules of Style:
Control yourself, when you have 2 things to say, say first one then the other. not both at the same time

clearly expressible signs

less difficult, less ambitious, special, auxiliary problem as a stepping stone in solving the more difficult , more amibitious, general, original problems

Past ages regarded a sudden good idea as an inspiration, a gift of the gods. You must deserve such a gift by work, or at least a feverent wish!

mathematician should discover his likes and dislikes, his taste, his own line.

Choose the problems which are in his line mediate upon their solution , and invent new problems.

He must concentrate upon the problem,he must earnestly to obtain its solution

The open secret to a real success is to throw your whole personality into your problem

Intelligent readers/listeners
1.present step is correct
2.See the purpose of present step

Geometry is the art of correct reasoning on incorrect figures

Diligence is the mother of good luck
Perseverance kills the game

An oak is not felled at one stroke, if at first, you dont succeed, try, try again

we must do as we may if we can’t do as we would

what a fool does at last, a wise man does at first.

Many years ago, when Huang finished his Ph.D, he told me , 知之不如好知,好知不如乐知。

就是说对知识永远有好奇心和开心。 后来他的女儿叫 怡知 寓意为希望她有乐观学习知识的态度,我好喜欢这个名字。也好喜欢那些学数学的日子!

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