This 3,700-Year-Old Babylonian Clay Tablet Just Changed The History of Maths

The Babylonians developed trigonometry 1,500 years before the Greeks and were using a sophisticated method of mathematics which could change how we calculate today, which makes it a 3,700-year-old clay tablet.

The tablet, known as Plimpton 332, was discovered in the early 1900s in Southern Iraq by the American archaeologist and diplomat Edgar Banks, who was the inspiration for Indiana Jones.

The true meaning of the tablet has eluded experts until now but new research by the University of New South Wales, Australia, has shown it is the world’s oldest and most accurate trigonometric table, which was probably used by ancient architects to construct temples, palaces, and canals.

However, unlike today’s trigonometry, Babylonian mathematics used a base 60, or sexagesimal system, rather than the 10 which is used today. Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate.

“Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles,” said Dr. Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science.

“It is a fascinating mathematical work that demonstrates undoubted genius.

The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.

“This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3000 years, but it has possible practical applications in surveying, computer graphics, and education.

“This is a rare example of the ancient world teaching us something new.”

The Greek astronomer Hipparchus, who lived around 120BC, has long been regarded as the father of trigonometry, with his ‘table of chords’ on a circle considered the oldest trigonometric table.

A trigonometric table allows a user to determine two unknown ratios of a right-angled triangle using just one known ratio. But the tablet is far older than Hipparchus, demonstrating that the Babylonians were already well advanced in complex mathematics far earlier.

The tablet, which is thought to have come from the ancient Sumerian city of Larsa, has been dated to between 1822 and 1762 BC. It is now in the Rare Book and Manuscript Library at Columbia University in New York.

“Plimpton 322 predates Hipparchus by more than 1000 years,” says Dr. Wildberger.

“It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.

“A treasure-trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us.”

The 15 rows on the tablet describe a sequence of 15 right-angle triangles, which are steadily decreasing in inclination.

The left-hand edge of the tablet is broken but the researchers believe that there were originally six columns and that the tablet was meant to be completed with 38 rows.

“Plimpton 322 was a powerful tool that could have been used for surveying fields or making architectural calculations to build palaces, temples or step pyramids,” added Dr. Mansfield.

The new study is published in Historia Mathematica, the official journal of the International Commission on the History of Mathematics.

Ancient Assyrian rock carvings in Iraq show a procession of gods riding mythical animals

Ancient Assyrian reliefs of a king in a procession of gods and goddesses riding on animals and mythical creatures have been uncovered by archaeologists.

The Assyrian carvings are nearly 3,000 years old and were discovered late last year by Italian and Iraqi archaeologists excavating in the district of Faida, south of Duhok city, about 300 miles (480 kilometers) north of Baghdad, in the region of Kurdistan in northern Iraq.

Dr. Daniele Morandi Bonacossi, from the Italian University of Udine and with the help of archaeologists from the Department of Antiquities, is responsible for the land of Nineveh Archeological Project.

According to the university’s excavation chief at Faida, with the exception of the carvings at the archaeological site of Khinnis discovered near the city of Mosul in 1845, there exists “no other” comparable Assyrian rock art.

Dating back about 2,800 years ago, the story of Assyrian King Sargon II on both sides of a procession of the seven major Assyrian gods and goddesses was cut off from the rocks in relief over an ancient irrigation canal in a time of expanding in the Assyrian Empire.

All gods and goddesses are riding animals and mythical creatures, including horses, bulls, lions, and dragons, each facing the direction that the water once flowed under them into the ancient canal.

According to an article in Live Science, Dr. Morandi Bonacossi said the carving feature: the sun god Shamash on a horse and the moon god Sin is on the back of a horned lion. Furthermore, the god of wisdom is mounted on a dragon, while the weather god is on a horned lion and a bull.

Ishtar, the goddess of love and war sits on a lion and Ashur, the chief Assyrian god, is perched upon a dragon and a horned lion, while his wife Mullissu sits on a decorated throne supported by a lion.

The famous Assyrian king Sargon ruled from 722 BC until 705 BC and according to the Hebrew Bible, he invaded and defeated the  Kingdom of Israel. It was under his rule that the canal had been built for local irrigation.

His son and successor, Sennacherib, ruled until 681 BC and rebuilt the ancient city of Nineveh alongside the Tigris River, on the outskirts of modern Mosul. He integrated his father’s canal into a much more expansive irrigation network that transformed the Assyrian Empire into an agricultural giant.

In a National Geographic article about the new discovery, Hassan Ahmed Qasim Duhok from the Directorate of Antiquities said the carvings were first seen in 1973 by a British team who noted the tops of three stone panels but tensions between Kurds and the Baathist regime in Baghdad prevented further work.

Then, in 2012, Dr. Morandi Bonacossi identified six more reliefs but all archaeological work was abandoned in 2014 when ISIS captured nearby Mosul. However, a full scientific excavation resumed in 2017 after the terrorist organization was finally driven out of the region.

You would think such an incredible discovery would more than satisfy archaeologists, but it only seems to have peeked their exploratory natures, as they now suspect more might lie beneath. Dr. Morandi Bonacossi told Live Science that the 4-mile-long (6.5 km) canal, which once carried water to farmland in the Faida district during the eighth century BC, had been filled in a long time ago.

However, the archaeologist says it’s “highly probable” that more reliefs and maybe monumental celebratory cuneiform inscriptions are still buried under the soil debris that filled the canal, waiting to be uncovered.

The Faida archaeological site has traditionally been the focus of vandalism and looting caused by rapid and urban expansion, including the construction of a modern aqueduct nearby, which now threatens the site, according to Dr. Morandi Bonacoss.

However, Faida is currently undergoing a major salvage and restoration project, and a new archaeological park is being created nearby, which will help protect the site from further incursions. 

The First City in Recorded History

It is the oldest city in ancient Mesopotamia. It was located in the southern region of Sumeria (now Warka, Iraq) to the northeast of the Euphrates River. Uruk was an ancient city of Sumer and Babylon at one time.

The ruins of what once used to be the great city of Uruk show thousands of clay tablets that indeed it was a religious and scientific center. The oldest texts of the world were written here, according to Archeology Magazine.

A series of wedge-shaped symbols pressed into wet clay using reeds was developed around 3200 B.C. The writing system is known as cuniform. By Sumerian scribes in Uruk.

The combination of shapes represented different sounds, so the system could thus be adopted by scribes who spoke different languages. The script was used by multiple cultures for around 3,000 years.

Uruk is also well known as the city of Gilgamesh. The mythological Sumerian hero-king was made famous in the modern world with the discovery of a collection of stories — known as the “Epic of Gilgamesh” — in 1853. The 12 cuneiform tablets on which the stories were written were discovered by archaeologist Hormuzd Rassam at the site of the Royal Library of Ashurbanipal.

According to Professor John Maier of the State University of New York College at Brockport, “Ancient writings point to the existence of an actual, historical person we now call Gilgamesh. He lived, according to our best estimate, about 2600 B.C.”

It is also believed that Uruk is the biblical city of Erech, the second city of the kingdom of Nimrod in Shinar (Genesis 10:10). Archaeologists distinguish nine different periods in the rise of the city from a simple settlement to the first urban center of the world.

The foundations of the first settlements on the site date somewhere around 5000 B.C., the Eridu period. According to the Sumerian King List (an ancient stone tablet which lists all the kings of Sumer, in Sumerian language), Uruk was founded by King Enmerkar around 4500 B.C. This was during the Ubaid period (5000–4100 B.C.)

After 4000 B.C., Uruk rose from small, agricultural villages to a significantly larger and more complex center. This has been attributed partly to a period of climatic change; the area saw less rainfall and so people living in the hills migrated to the river valley of the ancient Euphrates. The course of the Euphrates has since shifted, an important factor in the decline of the city.

Nestled in the lush and fertile river valley, the population of Uruk continued to grow throughout the Early Uruk period (4000–3500 B.C.), Middle Uruk period (3800–3400 B.C.) and Late Uruk period (3500–3100 B.C.). Farming and irrigation techniques were refined, providing a surplus of food for the community.

By around 3200 B.C., the city of Uruk was the largest settlement in southern Mesopotamia, and probably in the world. It was an urban center with a full-time bureaucracy, stratified society, and a formal military. It was also a major hub of trade and administration.

The organization of Uruk in this period set the blueprint for cities ever since. There is evidence of social hierarchies and coercive political structures that would be familiar to most of us today. Clay tablets containing a “standard professions list” have been found, listing around 100 professions. As the city became more affluent, those at the top sought ways to display their wealth and power. Luxury goods were acquired by conquest or trade with lands as far as the Egyptian Nile Delta.

Uruk was a city of extraordinary architecture and works of art. The remains of monumental mud-brick buildings, the walls of which were decorated with mosaics of painted clay cones, pressed into the mud plaster — a technique known as clay cone mosaic — have been excavated. The most impressive creations discovered to date of this Sumerian craft are the two large temple complexes in the heart of Uruk.

One was dedicated to Anu, the god of the sky, and the other, known as the Mosaic Temple of Uruk, to Inanna (or Ishtar), the goddess of love, procreation, and war. There was a clear division of the city into the Anu and Eanna Districts.

Another famous piece of artwork, “The Lady of Uruk,” or the Mask of Warka, was discovered in 1939 by the German Archaeological Institute in Uruk. Dating from 3100 B.C., it is most likely that the mask was part of a much larger work from one of the temples and it is considered to represent of Inanna. The marble sculpture is one of the earliest representations of the human face.

To this day, the mask is the most significant artifact found on the site, and it is part of the collection of National Museum of Iraq in Baghdad. It is also called “The Sumerian Mona Lisa.” Uruk continued to expand and, as the center of luxurious materials and possessions, it demanded greater protection.

Although it was traditionally believed that the great wall of Uruk was built by King Gilgamesh himself, as it is written in the Epic of Gilgamesh, it was possibly created during the reign of King Eannutum who established the first empire in Uruk during the Jemdet Nasr Period (3100-2900 B.C.) By the time the wall was raised, it protected an area of 2.32 square miles and a population of almost 80,000.

During the Early Dynastic period (2900–2350 B.C.), Mesopotamia was governed by city-states whose rulers gradually grew in importance and power. Starting circa 2004 B.C. the struggles between the Sumerians in Babylonia and the Elamites from Elam, the Pre-Iranian civilization rose to serious national conflicts.

Uruk was still a prominent center during this time but suffered severely. There are recollections about the conflicts in the Gilgamesh epic. Sometime after 2000 B.C., Uruk lost importance, but it wasn’t abandoned.

The city remained inhabited throughout the Seleucid (312–63 B.C.) and Parthian (227 B.C.–224 A.D.) periods. The last people living there left Uruk after the Islamic contest of Persia in 633–638 A.D. The remains of probably the oldest city in the world laid buried until 1850 when archaeologist William Loftus led the first excavations on the site and identified the city as “Erech, the second city of Nimrod.”