"Pascal's triangle" may have been discovered by Indians more than two thousand years ago. It reached the Arab-Muslim world and China as early as the 11th century. It did not appear in Europe until the 16th century, when Blaise Pascal began to study it rigorously.
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Although specialists still debate the origins of proof by induction, they often agree that Blaise Pascal's Traité du triangle arithmétique (Treatise on the Arithmetical Triangle) was the first work to set it out explicitly. A guided tour of a landmark in the history of proof.
Mathematical induction is a major tool in mathematical proofs. On at least three occasions, Pascal explicitly uses reasoning that is "almost" mathematical induction, making him one of the method's inventors.
Today, we use "Arabic numerals" to refer to what the Arabs themselves called "Indian numerals." Other numeral systems predated these numerals—the ancestors of our own—and even continued to coexist with them after their introduction.
If you know how to fill in Pascal's triangle, you may be less aware of the treasures it contains. Arithmetic, geometric, combinatorial: it has no shortage of astonishing mathematical properties! And there are undoubtedly many more still to be discovered…
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