Leah's Math Quotes

1:    Calculus as currently taught is, alas, full of inert material . . . The real crisis is that at present [calculus] is badly taught; the syllabus has remained stationary, and modern points of view, especially those having to do with the roles of applications and computing are poorly represented. . .

Peter Lax, Past President of the American Mathematical Society

2:    The facts of mathematics are verified and presented by the axiomatic method. One must guard, however, against confusing the presentation of mathematics with the content of mathematics. An axiomatic presentation of a mathematical fact differs from the fact that is being presented as medicine differs from food. It is true that this particular medicine is necessary to keep mathematicians from self-delusions of the mind. Nonetheless, understanding mathematics means being able to forget the medicine and enjoy the food.

Gian - Carlo Rota

3:    The student needs to develop an understanding, however partial and imperfect, by descriptions rather than definitions, by typical examples rather than grandiose theorems....

Gian - Carlo Rota

4:    Mathematical skills are like any other kind.... If you are learning to play the piano, you usually start by practicing under supervision; you don't begin with theoretical lectures on acoustical vibrations and the internal structure of the instrument. Similarly for mathematical skills.

Ralph Boas

5:    Authors of textbooks need to remember that they are supposed to be addressing students, not the teachers... Contemporary prose style is simpler and more direct than the style of the 19th century- except in textbooks of mathematics. ....I blame the authors of textbooks for not realizing that contemporary students speak a different language.

Ralph Boas

6:    Mathematicians have developed habits of communication that are often dysfunctional. We go through the motions of saying for the record what the students 'ought' to learn while students grapple with the more fundamental issues of learning our language and guessing at our mental models. Books compensate by giving samples of how to solve every type of homework problem. Professors compensate by giving homework and tests that are much easier than the material 'covered' in the course, and then grading the homework and tests on a scale that requires little understanding. We assume the problem is with students rather than communication: that the students either don't have what it takes, or else just don't care.  Outsiders are amazed at this phenomenon, but within the mathematical community, we dismiss it with shrugs.

Bill Thurston

7:    Many conventional academic skills amount to the ability to select and apply. . . procedures rapidly and correctly....[Computer] courseware can concentrate on one skill at a time, in a manner impossible for a textbook and hardly available to the classroom teacher, namely by asking the student to handle only that part of a procedure on which pedagogical stress is to be laid, while other aspects of the same procedure are handled automatically by the computer. . . . This scheme, which combines student interaction with computer assistance, has the merit of focusing attention on the key strategic and conceptual decisions needed to handle a problem. . . This should be of significance to both the strong student . . . and the weak student.

Jacob T. Schwartz

8:    Civilization advances by extending the number of operations we can do without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses and must be made only at decisive moments.

Alfred North Whitehead

9:    Mathematics-speaking machines are about to sweep the campuses....The ready availability of powerful computers will enable students to set new ground rules for college mathematics... Teachers will be forced to change their approach and their assignments. They will no longer be able to teach as they were taught in the pencil and paper era... Undergraduate mathematics will become more like real mathematics . . . By using machines to expedite calculations, students can experience mathematics as it really is - as a tentative, exploratory discipline in which risks and failures yield clues to success. Computers change our perceptions of what is possible and what is valuable. . . Weakness in algebra skills will no longer prevent students students from pursuing studies that require college mathematics . . .

Lynn Arthur Steen, Past President of the Mathematical Association of America

10:    Our teaching does not make full use of that historic event, which is probably the most important event in the history of science, namely, the invention of the decimal system of numeration.

Henri Lebesgue

Math isn't everything...some more great quotes

The greatest pleasure in life is doing what people say you cannot do.
                     - Walter Bagehot

I choose to question you and to answer you with no pretense of authority.
                     - Galileo

I am not a victim.
                     - Lance Armstrong


It is true that a mathematician who is not somewhat of a poet will never be a
perfect mathematician.
                     - K. Weierstrass (Sorry, that one snuck in!)

For one human being to love another: that is perhaps the most difficult of our tasks; 
the ultimate, the last test and proof, the work for which all other work is but preparation. 
 --Rainer Maria Rilke


The problem is not that there are problems. The problem is expecting otherwise
 and thinking that having problems is a problem.
                     - Theodore Rubin


Great spirits have always found violent opposition from mediocrities. The
latter cannot understand it when a man does not thoughtlessly submit to
hereditary prejudices but honestly and courageously uses his intelligence.
                     - Albert Einstein



Nearly all men can stand adversity, but if you want to test a man's character, give him power.
                     - Abraham Lincoln

Truth springs from argument amongst friends.
                     - David Hume


They copied all they could follow
but they couldn't copy my mind
so I left them sweating and stealing
a year and a half behind.
                     - Rudyard Kipling

A mimic is no better than an ass with a load of books on its back.
                     - Kahlil Gibran

If you obey all the rules, you miss all the fun.
                    - Katherine Hepburn

Security is mostly a superstition. It does not exist in nature.... Life is
either a daring adventure or nothing.
                    - Helen Keller 

	 
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