Numbers or symbols used for counting have existed since man learned to count. Archeologists and historians estimate that numbers were first used around 32,000 years ago. They base this theory on archeological findings such as bones and rocks with marks on them. These may have been counting or tally signs used to keep track of time or quantities of objects, such as food or livestock.

**Simple Systems**

The very first number system must have been a tallying system. Tallying systems have no complex symbols or place values. It is the simplest counting system though not practical for dealing with large quantities of number. Our modern number system has 10 as its base or place value. A place value simplifies number representation and counting.

Another simple number system was the ordinal counting system. It is thought to have started when man began counting with his fingers, each finger standing for a unique number.

**Place Value Systems**

A couple of ancient civilizations invented number systems with place values. The oldest was the Mayan system with 60 at its base, around 3400 BC. The Egyptians invented a 10 base system in 3100 BC. The modern place value system also has 10 as its compression figure. It came from India by way of the Arabs.

**Invention of Number Zero**

The number zero was used by various peoples including the Mayans, Egyptians, Babylonians and Indians. The Egyptians used zero in their accounting records. The Indians referred to zero as “the emptiness.” The inquisitive Greeks were puzzled by this figure and developed many interesting philosophical views on the subject. In fact, occultists and mystics used the number zero to symbolize the nothingness, or void state of things.

**Invention of Negative Numbers**

The Chinese invented numbers in their negative. This is recorded in “The New Chapters on the Art of Mathematics” circa 100 BC. The Greek mathematicians didn’t see the possibility until around the 3rd century AD. By 600 AD, the Indian money lenders were using negatives when computing debts.

Invention of Fraction Numbers

The invention of fractions can be traced to the ancient Egyptians. Their Kahun Papyrus discusses fractions and other mathematical problems. It dates from around 1800 BC. Among the Greeks, the best known mathematical work on the topic is Euclid’s “Elements.”

**Invention of Irrational Numbers**

The Indians knew about fraction numbers, as recorded in their Stananga Sutra. Another text, the Sulba Sutra, expounds on irrational numbers. It dates from 800 to 500 BC. A Greek follower of Pythagoras, Hippasus, is said to have discovered irrationals at the same time. But Pythagoras refused to accept the existence of non-rational numbers and had Hippasus put to death.

**Invention of Modern Numbers**

The Indians also invented the modern number system. It is often called Arabic numerals because it came to Europe through the Arabs. The Persians copied the Indian number system and then passed it on to the Arabs. Then an Italian mathematician named Fibonacci traveled to Algeria to study. When he came back home, he brought the Indian numerals with him. He wrote about the system in his book “Liber Abaci.” This system soon gained wide acceptance throughout Europe. Today it is the number system used in practically the whole world.