RECENT INVENTION IN MATHEMATICS

 RECENT INNOVATIONS IN MATHEMATICS

1. Binary logic (George Boole)

Boole was interested in developing a mathematical representation of the “laws of thought,” which led to using symbols (such as x) to stand for concepts (such as Irish mathematicians). He hit a snag when he realized that his system required x times x to be equal to x. That requirement pretty much rules out most of mathematics, but Boole noticed that x squared does equal x for two numbers: 0 and 1. In 1854 he wrote a whole book based on doing logic with 0s and 1s — a book that was well-known to the founders of modern computer languages.

2. Decimal fractions (Simon Stevin, Abu’l Hasan Al-Uqlidisi)

Stevin introduced the idea of decimal fractions to a European audience in a pamphlet published in 1585, promising to teach “how all Computations that are met in Business may be performed by Integers alone without the aid of Fractions.” He thought his decimal fraction approach would be of value not only to merchants but also to astrologers, surveyors and measurers of tapestry. But long before Stevin, the basic idea of decimals had been applied in limited contexts. In the mid-10th century, al-Uqlidisi, in Damascus, wrote a treatise on Arabic (Hindu) numerals in which he dealt with decimal fractions, although historians differ on whether he understood them thoroughly or not.

3. Zero and 3. Negative numbers (Brahmagupta)

Brahmagupta, a seventh-century Hindu astronomer, was not the first to discuss negative numbers, but he was the first to make sense of them. It’s not a coincidence that he also had to figure out the concept of zero to make negative numbers make sense. Zero was not just nothingness, but a meaningful number, the number you get by subtracting a number from itself. “Zero was not just a placeholder,” writes Joseph Mazur in his new book Enlightening Symbols. “For what may have been the first time ever, there was a number to represent nothing.”

4. Calculus (Isaac Newton, Gottfried Leibniz)

You know the story — Newton gets all the credit, even though Leibniz invented calculus at about the same time, and with more convenient notation (still used today). In any event, calculus made all sorts of science possible that couldn’t have happened without its calculational powers. Today everything from architecture and astronomy to neuroscience and thermodynamics depends on calculus.

5. Arabic numerals

Did you ever wonder why the Romans didn’t do much creative quantitative science? Try doing a complicated calculation with their numerals. Great advances in Western European science followed the introduction of Arabic numerals by the Italian mathematician Fibonacci in the early 13th century. He learned them from conducting business in Africa and the Middle East. Of course, they should really be called Hindu numerals because the Arabs got them from the Hindus. In any case, mathematics would be stuck in the dark ages without such versatile numerals.