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## Stubborn Mathematicians

Following up on last week's MathLint, the entire idea of negative numbers has had a rough history.

Consider the question: Is there a number x that will make the equation 4x + 20 = 0 true?

In his text Arithmetica, the great mathematician Diophantus of Alexandria (ca. 275) called such a question "absurd." He did not know about (or accept) the idea of negative numbers.

Yet previous to this time, negative numbers were in common use in China. Red counting rods stood for positive numbers and black counting rods represented negative numbers (note, reversal of today's language of "going into the red").

In 1225, the Italian mathematician Fibonacci faced a similar equation and said: "I will show this question cannot be solved unless it be conceded that a man might be in debt."

As late as 1759, Francis Maseres, an English mathematician, suggested that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". His conclusion: negative numbers were nonsensical.

Even in the 18th century, when solving equations, mathematicians tended to ignore any negative roots, assuming they were "false" roots and therefore meaningless.

Gradually, the stubborn mathematicians gave in; a gradual move was being made to accept both positive and negative numbers (and/or roots).

If you think this story was interesting, investigate the histories of either irrational numbers or imaginary numbers. Mathematicians can be so stubborn!