Modern mathematics has spread into some interesting and incredibly useful areas of contemporary life. Highway engineers utilize optimization techniques and linear algebra to analyze traffic patterns and decrease travel time for commuters. Airlines, hotels, and Broadway theaters (and of course some retailers) use complex mathematical models, so complicated that just computer applications can sometimes solve them, to set prices to a dynamic basis. Physicists use group theory and tensor analysis to address the puzzles of sub-atomic particles. There are many other instances, from data being used by the Census Bureau and study companies to predict market trends, to partial differential equations used by brokerage houses to invent models of in which the market is going.

**Origins of Mathematics**

But where did mathematics originate from? How did it get started, and how complex (or simple) were its beginnings in the ancient world?

While arithmetic in certain type (counting) has been with us since people banded together in primitive tribal bands 35,000 years ago, formal math couldn’t start until writing was invented. This event happened around 3200 BCE in the Fertile Crescent (especially Mesopotamia, close to the ancient city of Sumer); some governments think it was independently invented in ancient Egypt around the exact same time, in addition to at China 1200 BCE. The ancient Egyptians may have made important contributions too.

For instance, the”Moscow mathematical papyrus” (so called because it’s held in a Moscow museum and dates back to 1850 BCE) contains an issue analyzing the dimensions of a truncated pyramid. While the hieroglyphic excuse would look like another Egyptian manuscript to modern eyes, the diagram accompanying it would be readily recognizable in any modern algebra class.

So what’s the link between math and writing, and why was it essential for the growth of writing to precede the development of a mathematics that could go beyond counting and simple arithmetic?

Aside from the relative permanence of writing and the ability to transmit information from 1 generation to another, writing is distinguished from other representational representational systems (e.g., cave art, or temple decorations) from the fact that its symbols (letters) are not associated with their significance, but instead reflect sounds or other phonemes because the abstract building blocks of speech. This development moves writing outside short-hand pictorial representations, so that the story is told by putting together abstract letters to form words, and not by recounting a story in images.

Likewise, mathematics Couldn’t get started until the starts of a symbolic language to represent basic mathematical theories was developed. Arithmetic started roughly in precisely the exact same time as writing started, around 4000 BCE from the Fertile Crescent (in what is now modern Iran), and initially was established solely on counting techniques. By way of instance, arithmetic at the time may be used to signify that 4 apples also 5 apples yields 9 apples.

Mathematics as we know it today, where math symbols take on subjective significance beyond simple enumeration and arithmetic, did not really have its infancy before the time of the ancient Greeks (eighth century BCE). The Pythagorean theorem (sixth century BCE), that says that the amount of the squares of the 2 legs of a ideal triangle is equal to the square of the hypotenuse, is usually thought to be the most ancient mathematical formula to go beyond simple arithmetic and geometry. The Greeks are also credited with being the first to develop deductive logic, a sort of justification fundamental to mathematics, whereby one can prove a theorem or announcement to always be accurate.

Again, while the text could be incomprehensible to anybody now who didn’t read ancient Greek, the diagrams in the fragment pictured below are all easily familiar to any college (or higher school) algebra student. Here is a fragment of Euclid’s”Elements” found at Oxyrhynchus (in Egypt) and dating to roughly 100 CE.

**Ancient Greek Contributions to Mathematics**

What exactly are some of the contributions of early Greek mathematicians to the mathematics we use now?

A key Greek contributor, Pythagoras (570 BCE to 495 BCE) is the developer of the Pythagorean Theorem, and made significant contributions to spiritual philosophy and basic doctrine as well as mathematics. Indeed, some scholars assert that the ancient Greeks considered mathematics for a technical form of pure philosophy rather than a separate branch of research at all.

Another early Greek philosopher, Thales, used geometry to address real world problems like the height of buildings (along with the pyramids), and also the distance between ships and the coastline. Plato (428/427 BCE — 348/347 BCE) made significant contributions by assessing the distinction between data and assumptions, as did Euclid (c. 300 BCE), who bolstered the mathematical rigor of proofs by introducing the explicit theories of significance, axiom, theorem, and proof.

Archimedes (c.287–212 BC) described the surface area and volume of a world and functioned with infinite series, as well as contributing to the analysis of physics with the principle of buoyancy and the production of the Archimedes screw, which could transfer water from one place to another (such as raising it against the pull of gravity).

**Chinese and Indian Contributions to Mathematics
**

Important contributions to ancient math were made by the Chinese, the Indians, and the Muslims, though the Muslims functioned largely in the eighth century CE and afterwards, so that they are regarded as more modern than ancient times. The Chinese and Indian cultures, however, flourished roughly contemporaneously with the ancient Greeks.

Chinese mathematics, in particular, is so different in its approach and formulas, that scholars generally agree it was developed independently. The Chinese are credited with developing a decimal positional notation system (so that forces of 10, 100, 1000 etc are distinguished from each other), many different geometrical theorems, and mathematical proofs such as the Pythagorean Theorem and Gaussian elimination, a method used in modern day Linear Algebra to manipulate matrices using row reduction.

Unlike ancient Greek math, Chinese mathematics continued to grow well beyond ancient times, so that, for example, in the 13^{th} century CE, Zu Chongzhi calculated the value of pi to seven decimal places and Chu Shih-chieh devised a way of solving higher order algebraic equations).

The Indian culture for mathematics prospered somewhat later (eighth century BCE to next century CE), also included calculations to the square root of 2, a statement (but not proof) of the Pythagorean Theorem, and astronomical treatises from the fourth and fifth centuries CE involving various trigonometric proofs.

Certainly, the mathematics that we use today is the accumulative knowledge of a fantastic many people, extending back in time over three thousand decades and over a number of distinct cultures situated across the world.