Apparently the Babylonians invented integral calculus.

https://www.scientificamerican.com/article/babylonians-tracked-jupiter-with-fancy-math-tablet-reveals/

>"It sounds minute for a layperson, but this geometry is of a very special kind that is not found anywhere else, for instance, in ancient Greek astronomy," Ossendrijver said. "It is an application in astronomy that was totally new. Thus far everybody thought Babylonian scholars only computed with numbers."

>The tablet has long been in the collection at the British Museum in London, and it was likely created in Babylon (located in modern-day Iraq) between 350 and 50 B.C. Ossendrijver recently deciphered the text, and he described his discovery in an article that's featured on the cover of the journal Science this week.

>From his office at Humboldt University here in Berlin, which is decorated with posters of both the Ishtar Gate and the Antikythera mechanism(thought to be the world's oldest known computer), he explained that the tablet plots the apparent decreasing velocity of Jupiter from the planet's first appearance along the horizon, to 60 days later, and then 120 days later. If drawn on a graph, this relationship is represented in the shape of two conjoined trapezoids. The area of each trapezoid describes Jupiter's total displacement (measured in degrees) along the ecliptic, or the path of the sun.

>Ancient Greek mathematicians and astronomers were using geometry around the same time, but only to make calculations involving real, 3D space, such as using circles torepresent the orbits of planets around Earth. Students of math might take it for granted today, but the abstract use of geometry was, until now, unheard of at the time.

>Current textbooks on the history of math say this invention took place around A.D. 1350.

https://www.scientificamerican.com/article/babylonians-tracked-jupiter-with-fancy-math-tablet-reveals/

>"It sounds minute for a layperson, but this geometry is of a very special kind that is not found anywhere else, for instance, in ancient Greek astronomy," Ossendrijver said. "It is an application in astronomy that was totally new. Thus far everybody thought Babylonian scholars only computed with numbers."

>The tablet has long been in the collection at the British Museum in London, and it was likely created in Babylon (located in modern-day Iraq) between 350 and 50 B.C. Ossendrijver recently deciphered the text, and he described his discovery in an article that's featured on the cover of the journal Science this week.

>From his office at Humboldt University here in Berlin, which is decorated with posters of both the Ishtar Gate and the Antikythera mechanism(thought to be the world's oldest known computer), he explained that the tablet plots the apparent decreasing velocity of Jupiter from the planet's first appearance along the horizon, to 60 days later, and then 120 days later. If drawn on a graph, this relationship is represented in the shape of two conjoined trapezoids. The area of each trapezoid describes Jupiter's total displacement (measured in degrees) along the ecliptic, or the path of the sun.

>Ancient Greek mathematicians and astronomers were using geometry around the same time, but only to make calculations involving real, 3D space, such as using circles torepresent the orbits of planets around Earth. Students of math might take it for granted today, but the abstract use of geometry was, until now, unheard of at the time.

>Current textbooks on the history of math say this invention took place around A.D. 1350.