Number

Numbers help us do many things.

We use them to count groups of things. We use them to measure how big things are. They can also be labels for things, like a phone number.

Long ago, people used marks on bones to count. Some bones are very old. They might have tracked days or animals.

We use symbols to write numbers. We call these symbols numerals. Most people use the same symbols today. These are the Hindu-Arabic numerals.

Zero is a very special number. It can stand for nothing. It also helps us show place in a number.

Math lets us work with many kinds of numbers. We can add or take away. This helps us solve puzzles.

Numbers help us count, measure, and label things.

We use them to see how many items are in a group. We also use them as labels, like for a phone number.

Long ago, people used marks on bones to count. These might be the Ishango bone or the Lebombo bone.

People may have used them to track days or animals. Later, the Babylonians used a system based on sixty. The Egyptians used a system based on ten.

We use symbols to write numbers. These symbols are called numerals. Most people today use Hindu-Arabic numerals. These use ten digits to show any number. The symbol for zero was very important for this system. Ancient Indian mathematicians helped develop zero around 500 AD.

Math uses many kinds of numbers. We have natural numbers like 1, 2, and 3. We have negative numbers, which can show debts. We also have rational numbers, which are like fractions. These are ways to show parts of a whole.

The Maya people used a system with dots and bars.

Numbers are special objects used to count, measure, and label the world.

We use them to see how many things are in a group. We also use them as labels, like for a phone numbers. Numbers can also be used for ordering, such as with serial numbers. There is a difference between a number and a numeral. A number is the idea of the amount itself. A numeral is the symbol we write down to show that number. For example, "eleven" is a number word. The symbol "11" is a numeral. We use numeral systems to keep things organized. The most common one is the Hindu-Arabic system. This system uses ten digits to show any non-negative integer.

Math uses many different kinds of numbers to solve problems. Natural numbers are the simplest, like 1, 2, and 3. Rational numbers are like fractions, which show parts of a whole.

We also use negative numbers to show things like debt. Real numbers include things like pi or the square root of 2.

Some even more advanced ideas are called complex numbers. We use arithmetic to work with these numbers. This includes adding, subtracting, multiplying, and dividing. People also use exponentiation to grow numbers quickly. Studying these properties is called number theory.

People have been using numbers for a very long time.

Some very old bones have marks cut into them. The Lebombo bone is about 43,000 years old. The Ishango bone is between 22,000 and 30,000 years old. Historians think these might be tally marks for counting. They might have tracked days or the number of animals. These early systems did not have place value. This made it hard to show very large numbers. Later, the Mesopotamians used a base 60 system around 3400 BC. The Egyptians used a base 10 system by 3100 BC.

One of the most important ideas is the number zero.

For a long time, people used zero just as a placeholder. The Indian mathematician Brahmagupta was a pioneer here. In his work from AD 628, he treated zero as a real number. He wrote rules for adding and subtracting zero. He even discussed dividing by zero. The concept spread to China and the Islamic world. It reached Europe around the year 1000. The Maya people also used a placeholder symbol for zero. They used a shell glyph by 38 BC.

Numbers help us understand how the universe works.

We can use them to find the area of a circle. The Babylonians even had an estimate for pi long ago. Their clay tablets showed a value of 3.125. This was a very early approximation of pi. We see numbers in patterns and in the shapes of objects. They help us build things and keep records. From counting snacks to launching rockets, numbers are everywhere. They turn the world into something we can measure and understand.

A number is a mathematical object used to count, measure, and label.

Numbers allow us to quantify the world around us. We use them to determine the size of a collection, known as a cardinal number. We also use them for ordering, such as with serial numbers, or for coding, such as with ISBNs. While people often use the terms interchangeably, a number is different from a numeral. A numeral is the specific symbol used to represent a number. For example, "eleven" is a number word, while "11" is the corresponding numeral. To represent any number efficiently, we use a numeral system. The most common is the Hindu-Arabic system, a decimal system using ten digits. This system can display any non-negative integer through organized combinations of symbols.

Mathematics has expanded the concept of numbers over many centuries. The most basic are natural numbers, such as 1, 2, and 3. Mathematicians also use rational numbers, which are fractions representing parts of a whole. Real numbers include values like pi (π) or the square root of 2.

Beyond these are complex numbers, which extend real numbers by using the square root of -1, represented as *i*.

We perform calculations with these objects using arithmetic operations. These include addition, subtraction, multiplication, division, and exponentiation. The study of these properties is called arithmetic or number theory.

Humanity's relationship with numbers began with very simple tools.

Archaeologists have found bones with marks cut into them, which may be tally marks. The Lebombo bone dates to about 43,000 years ago. The Ishango bone is estimated to be between 22,000 and 30,000 years old. These marks might have recorded lunar cycles or animal quantities. Tallying systems are the first abstract numeral systems, though they lack place value. This limitation makes it difficult to represent very large numbers. Later, the Mesopotamians developed a base 60, or sexagesimal, system around 3400 BC. The Egyptians used a base 10 system starting around 3100 BC.

One of the most significant shifts in math was the treatment of zero.

Initially, zero served only as a placeholder in place-value systems. The Babylonians and Egyptians used zero in this way. In the New World, the Olmec people used a shell glyph as a placeholder by 38 BC. The Maya later developed zero as a cardinal number in their base 20 system.

In the Old World, the Indian mathematician Brahmagupta formulated the concept of zero as a number in AD 628. He treated zero as an integer and established rules for its use. He discussed how zero interacts with positive and negative numbers. He even addressed the operation of division by zero.

Negative numbers also represent a major conceptual development. As early as 100–50 BC, mathematicians in China recognized negative numbers. They used red and black rods to denote positive and negative coefficients. In India, negative numbers were used during the 600s to represent debts. European mathematicians resisted this idea for a long time. Even in the 18th century, many ignored negative results as meaningless. René Descartes referred to them as "false roots" when they appeared in algebraic polynomials. It was not until the 17th century that the concept gained broader acceptance in Europe.

Rational and irrational numbers provide even more precision. Rational numbers include fractions, which the Ancient Egyptians used in texts like the Rhind Mathematical Papyrus. These texts show how to derive areas using fractional notation. Irrational numbers, such as the square root of 2, cannot be expressed as simple fractions. Interestingly, the Babylonians showed they could approximate these values as early as 1800 BCE. Their clay tablet, YBC 7289, shows an approximation of the square root of 2 with great accuracy. This demonstrates that humans have been seeking precise numerical values for millennia.

Today, the concept of numbers continues to grow through algebraic structures. In the 19th century, mathematicians developed systems that share properties with numbers. Some of these, like p-adic or hypercomplex numbers, are explicitly called numbers. Others are categorized differently based on mathematical convention. These structures extend our ability to model complex systems. From ancient tally marks to modern algebraic theory, numbers remain the fundamental language of measurement and logic.