quotes

think geometrically, prove algebraically
---John Tate

Whenever I meet in LA Place with the words "Thus it plainly appears," I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears.
---Bowditch's Memoir of Nathaniel Bowditch

From a practical point of view, it is a wast of time to try to write on the board all the definitions and proofs. They are in the text.
---Fraleigh's A First Course in Abstract Algebra

In summary, on your first reading of a section, I suggest you concentrate on what information the section gives, and on gaining a real understanding of it. If you do not understand what the statement of a theorem means, it will probably be meaningless for you to read the proof. 
---Fraleigh's A First Course in Abstract Algebra

The cookbook system. We have discussed the advantages of proofs but we certainly did not advocate that all proofs should be given "in extenso." On the contrary, there are cases in which it is scarcely possible to do so; an important case is the teaching of the differential and integral calculus to students of engineering.

If the calculus is presented according to modern standards of rigor, it demands proofs of a certain degree of difficulty and subtlety ("epsilon-proofs"). But engineers study the calculus in view of its application and have neither enough time nor enough training or interest to struggle through long proofs or to appreciate subtleties. Thus, there is a strong temptation to cut out all the proofs. Doing so, however, we reduce the calculus to the level of the cookbook.

The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. The cookbook may serve its purpose perfectly. In fact, it need not have any sort of logical or mnemo-technic system since recipes are written or printed and not retained in memory.
---Polya's How to Solve it

I personally don't like hard exercises very much; why spend time on them rather than on doing research?
---Eisenbud's Commutative Algebra

Any Ph. D. student interested in Abelian Group Theory should solve all the exercises in our collection.
---Exercises in Abelian Group Theory

一個數學家的嘆息那本書中有很多很棒的話，還沒放上來。

Gallian裡面有一些語錄也還沒放上來。

Dropbox/List/Quotes.txt中也有一些話還沒放上來。