The History of Zero
In today's modern mathematics, we have become accustomed to zero as a number. It's hard to believe that most ancient number systems didn't include zero. The Mayan civilization may have been among the first to have a symbol for zero. The Mayas flourished in the Yucatan peninsula of Mexico about 1300 years ago. They used the as a placeholder, in a vertical place-value system. It is considered one of their cultures greatest achievements.
The ancient Egyptians, Romans, and Greeks alike had no symbol for zero. In Greek geometry, zero and irrational numbers were impossible. The Greeks made great strides in mathematics, but it was all done with a number system without zero. The Greek astronomer Ptolemy (ca. A.D. 150) was the first to write a zero at the end of a number. For this he used a circular symbol.
In ancient Babylonian history there was no use of the zero. In the later Babylonian or during the Seleucid period a special symbol, which was also used as a separation mark between sentences, came into use for a zero. There's a definite possibility that the Babylonians used this mark for a zero within a number, as early as the end of the eighth century B.C. Up until the time of Aristotle, there seems to be no evidence that the Babylonians ever regarded zero as a number. Aristotle discussed division by zero in connection with speed through a vacuum.
Throughout the Dark Ages, Western mathematics was held back by the Roman's traditional numbering system. The first to think differently was Leonardo Fibonacci. He was a merchant's son, born in the Italian city-state Pisa, late in the twelfth century. In Pisa, he studied the work of Euclid and other Greek mathematicians. When he was still a boy, he moved to the Muslim city of Bugia, in North Africa. There he examined leather and furs before they were shipped back to Pisa. Leonardo got an education in Arabic culture as he traveled around the Mediterranean to Constantinople, Egypt and Syria. He recognized that the Hindu-Arabic numerals, the numerals we use today, were superior to the Roman numerals he had grown up with in the West.
In the sixth century, mathematicians in India developed a place-value system. They introduced the concept of zero to keep their symbols in their proper places. In the seventh century, Hindu scholars introduced to Islam the ideas of zero and place-value. These ideas spread rapidly throughout the Arabic world. Six centuries later, Fibonacci was so impressed with the ease of Hindu-Arabic numerals that he wrote a book entitled Liber abaci.
The Pisan local merchants, the trading class, ignored Fibonacci's book. They were wallowing in prosperity and did not want to be bothered with giving up Roman numerals and adopting a zero. Ferbonacci's mathematician friends liked the new number system and slowly over time gave up the Roman numerals. By the fifteenth century, the numerals were showing up on coins and gravestones. Western mathematics had emerged from the Dark Ages, and was flourishing into a new number system with a zero, the Hindu-Arabic numerals. The immediate advances in mathematics after that time are proof of the importance of, the zero.
In today's modern mathematics, we have become accustomed to zero as a number. It's hard to believe that most ancient number systems didn't include zero. The Mayan civilization may have been among the first to have a symbol for zero. The Mayas flourished in the Yucatan peninsula of Mexico about 1300 years ago. They used the as a placeholder, in a vertical place-value system. It is considered one of their cultures greatest achievements.
The ancient Egyptians, Romans, and Greeks alike had no symbol for zero. In Greek geometry, zero and irrational numbers were impossible. The Greeks made great strides in mathematics, but it was all done with a number system without zero. The Greek astronomer Ptolemy (ca. A.D. 150) was the first to write a zero at the end of a number. For this he used a circular symbol.
In ancient Babylonian history there was no use of the zero. In the later Babylonian or during the Seleucid period a special symbol, which was also used as a separation mark between sentences, came into use for a zero. There's a definite possibility that the Babylonians used this mark for a zero within a number, as early as the end of the eighth century B.C. Up until the time of Aristotle, there seems to be no evidence that the Babylonians ever regarded zero as a number. Aristotle discussed division by zero in connection with speed through a vacuum.
Throughout the Dark Ages, Western mathematics was held back by the Roman's traditional numbering system. The first to think differently was Leonardo Fibonacci. He was a merchant's son, born in the Italian city-state Pisa, late in the twelfth century. In Pisa, he studied the work of Euclid and other Greek mathematicians. When he was still a boy, he moved to the Muslim city of Bugia, in North Africa. There he examined leather and furs before they were shipped back to Pisa. Leonardo got an education in Arabic culture as he traveled around the Mediterranean to Constantinople, Egypt and Syria. He recognized that the Hindu-Arabic numerals, the numerals we use today, were superior to the Roman numerals he had grown up with in the West.
In the sixth century, mathematicians in India developed a place-value system. They introduced the concept of zero to keep their symbols in their proper places. In the seventh century, Hindu scholars introduced to Islam the ideas of zero and place-value. These ideas spread rapidly throughout the Arabic world. Six centuries later, Fibonacci was so impressed with the ease of Hindu-Arabic numerals that he wrote a book entitled Liber abaci.
The Pisan local merchants, the trading class, ignored Fibonacci's book. They were wallowing in prosperity and did not want to be bothered with giving up Roman numerals and adopting a zero. Ferbonacci's mathematician friends liked the new number system and slowly over time gave up the Roman numerals. By the fifteenth century, the numerals were showing up on coins and gravestones. Western mathematics had emerged from the Dark Ages, and was flourishing into a new number system with a zero, the Hindu-Arabic numerals. The immediate advances in mathematics after that time are proof of the importance of, the zero.