Learn Mathematics for Its Value

The following is an extended quotation from a book by Edward Barbeau.

Inspired by the article of Underwood Dudley, Is Mathematics Beautiful? (CMJ 28 (1997), 360-364), Elizabeth Berman Appelbaum of Shawnee Mission, KS, has a few comments on some more textbook examples of "real world" problems.

Problem. Jack Glover wishes to add enough 50% antifreeze solution to 16 gallons of a 5% antifreeze solution to obtain a 20% antifreeze solution. How much of the 50% solution should he add?

Comment by EBA: I just talked to an employee at a service station. He did this kind of problem in mathematics classes, but on the job nobody does it this way. They test antifreeze in the car for the temperature at which it provides protection. Then they add enough antifreeze to get to the desired temperature.

While many people use some mathematics in their jobs, Dr. Appelbaum feels that mathematics should nonetheless be taught primarily for its own sake. Applications are fine if they are simple and appealing; otherwise they should be left to an applied course. She sees the current emphasis on applications as a response to anti-intellectualism among students. When students ask what good the mathematics is, she suspects that the students are really saying that they cannot understand the subject and so hope that it is no good. She has often met people who are glad that they studied mathematics, or wish that they had studied more, but never anyone who said that they were sorry to have learned mathematics.


  1. E. J. Barbeau, Mathematical Fallacies, Flaws, and Flimflam, MAA, 2000


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