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The video discusses the origins of mathematics and its development over time. It highlights the work of early mathematicians and the importance of the new languages of algebra and numbers developed in Asia.

**00:00:00**The video discusses how mathematics began with the need to make sense of patterns in the natural world. The most basic concepts of mathematics, space and quantity, are hard-wired into human brains and are essential for everyday life. The video discusses how the Egyptians developed a decimal system motivated by the 10 fingers on our hands.**00:05:00**The sign for one was a stroke, 10, a heel bone, 100, a coil of rope, and 1,000, a Lotus plant. How much is this T-shirt? Er, 25. 25!Yes!So that would be 2 knee bones and 5 strokes. So you're not gonna charge me anything up here? Here, one million! One million? My God! This one million. One million, yeah, that's pretty big! The hieroglyphs are beautiful, but the Egyptian number system was fundamentally flawed. They had no concept of a place value, so one stroke could only represent one unit, not 100 or 1,000. Despite the drawback of this number system, the Egyptians were brilliant problem solvers. We know this because of the few records that have survived. The Egyptian scribes used sheets of papyrus to record their mathematical discoveries. This delicate material made from reeds decayed over time and many secrets perished with it. But there's one revealing document that has survived. The Rhind Mathematical Papyrus is the most important document we have today for Egyptian mathematics. We get a good overview of what types of problems the Egyptians would have dealt with in their mathematics. We also get explicitly stated how multiplications and**00:10:00**The ancient Egyptians developed notation which recorded new numbers. One of the earliest representations of fractions came from a hieroglyph which had great mystical significance. The Eye of Horus is one of the earliest representations of a geometric series, and it appears at a number of points in the Rhind Papyrus. The Egyptians applied their knowledge to understanding shapes that they encountered day-to-day, including the circle. Their calculation of the area of the circle was very accurate, and depended on seeing how the shape of the circle could be approximated by shapes that the Egyptians already understood. The Rhind Papyrus states that a circular field with a diameter of nine units is close in area to a square with sides of eight. This relationship was discovered through the ancient game of mancala.**00:15:00**The video discusses the mathematical brilliance of ancient Egyptians and Babylonians. The Egyptians were able to generate beautiful methods in mathematics, while the Babylonians were able to develop calculus.**00:20:00**The Babylonians were a very successful empire due to their mastery of mathematics. They developed a number system using their fingers, which was very useful for arithmetic, and their system recognised place value. They also developed a geometrical textbook which shows their interest in practical problems.**00:25:00**The Babylonians were a very advanced civilization in the ancient world, and their mathematics was very sophisticated. They had a system of numbers, measurement, and calculation that was in perfect harmony with their system of angular measurement. They developed a new symbol for big numbers, and this led to the invention of zero. They were also avid game-players, and their love of mathematics led to the development of algebra.**00:30:00**This video introduces the Babylonians and their use of mathematics. The Babylonians are recognized as one of the first cultures to use symmetrical mathematical shapes to make dice, but there is more heated debates about whether they might also have been the first to discover the secrets of another important shape - the right-angled triangle. This tablet, Plimpton 322, is believed to show the Babylonians could well have known the principle regarding right-angled triangles, that the square on the diagonal is the sum of the squares on the sides, and known it centuries before the Greeks claimed it. This small school exercise tablet is nearly 4,000 years old and reveals just what the Babylonians did know about right-angled triangles. It uses a principle of Pythagoras' theorem to find the value of an astounding new number - the square root of two. This information has far-reaching implications, as the Babylonians knew something of Pythagoras' theorem 1,000 years before Pythagoras and the square root of two is what we now call an irrational number, which means that it doesn't end after the decimal point.**00:35:00**The Babylonians were a very skilled in mathematics and were pioneers in developing a deductive system for mathematics. When their imperial power declined, so did their intellectual vigour. The Greeks, who had invaded Mesopotamia, took the best from the Babylonians and developed their own mathematical prowess. Their greatest innovation was the power of proof, which allowed them to prove the validity of mathematical theorems and theories. Pythagoras, who founded a school in Samos in the sixth century BC, is a controversial figure because he left no written records of his work. However, there is evidence that there were schools of Pythagoreans and that they were involved in the politics of their cities. One feature that makes the Pythagoreans unique is that they included women.**00:40:00**Pythagoras is credited with the discovery of the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. This theorem illustrates one of the characteristic themes of Greek mathematics - the appeal to beautiful arguments in geometry rather than a reliance on number. However, the theorem and Pythagoras' world view did not fit well with the Babylonian understanding of mathematics, which included irrational numbers. Later Greek commentators tell the story of how Pythagoras swore his sect to secrecy, but Hippasus let slip the discovery and was promptly drowned for his attempts to broadcast their research. However, these mathematical discoveries could not be easily suppressed and schools of philosophy and science flourished all over Greece, built on these foundations. The most famous of these was the Academy, which was founded by Plato.**00:45:00**The video discusses the history of mathematics and its origins in Ancient Greece. Euclid is credited with creating one of the most important texts in mathematics, The Elements. The video also discusses the influence of Alexandria on mathematics and the rise of Archimedes as a mathematician.**00:50:00**The video recounts the history of mathematics, from the ancient Greeks to Hypatia. Archimedes is particularly celebrated for his contributions to mathematics, weapons of mass destruction, and calculating the volumes of solid objects. However, his dedication to mathematics led to his death at the hands of a Christian mob. Hypatia, although not as well-known, was a brilliant mathematician and teacher. Her death signalled the end of the Greek mathematical tradition in Alexandria.**00:55:00**The video discusses the history of mathematics and the development of different languages used to describe mathematics. It highlights the importance of the work of early mathematicians and discusses the importance of the new language of algebra and numbers developed in Asia.

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