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.

Lois Lane knows that Superman can fly, but she doesn't know that Clark Kent can fly even though Superman equals Clark Kent. The substitution of one for the other can't be made. Similarly, former President Reagan may have believed, as the apocryphal story has it, that Copenhagen is in Norway, but even though Copenhagen equals the capital of Denmark, it can't be concluded by substitution that Reagan believed that the capital of Denmark is in Norway. https://abcnews.go.com/Technology/WhosCounting/story?id=711316&page=1 (as of 2021-08-12)

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".

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.

• I cannot recommend him too highly nor say enough good things about him.
• There is no other student of mine with whom I can adequately compare him.
• His thesis is the sort of work you don't expect to see nowadays and in it he has clearly demonstrated his complete capabilities.
• The amount of material he knows will surprise you.
• You will indeed be fortunate if you can get him to work for you.

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.