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John Allen Paulos
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1. John Allen Paulos
John Allen Paulos (American mathematics professor) is an American mathematics professor at Temple University in Philadelphia, PA. He has published many books having to do with the subject of mathematical literacy and, in particular, the dangers of mathematical illiteracy.

2. Equals for equals
A historical example of not being able to substitute equals for equals is that of Ronald Reagan making comments on Denmark and Norway. From his ABC News "Whose Counting" commentary entitled "Math in Narratives" by mathematician John Paulos on May 3, 2007 (from May 1, 2005), we have the following.

3. Engineer, mathematician, and psychologist
The difference between engineers and mathematicians can, perhaps, be understood by way of the following story (modified from Paulos, J. (1991). Beyond innumeracy. New York: Vintage Books., p. 81.).

A psychologist is questioning a mathematician and a engineer in the same room. To the engineer, the psychologist asks, "There is a fire on the stove and a glass of water on the table. What do you do?". To which the engineer, without hesitation, replies, "I would take the glass of water on the table and use it to dowse the fire on the stove". The psychologist then asked the mathematician, "The glass of water is now on the window sill. What would you do?". To which the mathematician, without hesitation, replies, "I would take the glass of water on the window sill and move it to the table and in that manner reduce the problem to the previously solved problem".

4. Paragraph of recommendation
Here is a paragraph of recommendation.

To whom it may concern: You wrote to ask me for my opinion of John, who has applied for a position in your department. Source: Paulos, J. (1995). A mathematician reads the newspaper. New York: Basic Books., p. 43.

That is, while (many) computer languages are designed to be unambiguous, natural language is inherently ambiguous.


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