Mathematics in Ancient Egypt: A Contextual History is a book on ancient Egyptian mathematics by Annette Imhausen. It was published by the Princeton University Press in 2016.
Mathematics in Ancient Egypt: A Contextual History is a book on ancient Egyptian mathematics by Annette Imhausen. It was published by the Princeton University Press in 2016.
The history of ancient Egyptian mathematics covers roughly three thousand years, and as well as sketching the mathematics of this period, the book also provides background material on the culture and society of the period, and the role played by mathematics in society. These aspects of the subject advance the goal of understanding Egyptian mathematics in its cultural context rather than (as in much earlier work on the mathematics of ancient cultures) trying to translate it into modern mathematical ideas and notation. [1] [2] [3] [4] Particular emphases of the book are the elite status of the scribes, the Egyptian class entrusted with mathematical calculations, the practical rather than theoretical approach to mathematics taken by the scribes, [5] and the ways that Egyptian conceptualizations of numbers affected the methods they used to solve mathematical problems. [4]
In keeping with that change in emphasis, the book is ordered by time period rather than by mathematical topics. [3] After an introduction that reviews past studies of the subject and calls for a reassessment of their conclusions, [6] it divides its history into five major eras: prehistoric Egypt and the Early Dynastic Period, the Old Kingdom of Egypt, the Middle Kingdom of Egypt, the New Kingdom of Egypt, and Hellenistic and Roman Egypt. [3] [6] [7]
The topics covered in the book include the Egyptian numbering systems, in both spoken and written (hieroglyphic) form, arithmetic, Egyptian fractions, and systems of measurement, [1] [2] their lunar calendar, calculations of volumes of solids, and word problems involving the measurement of beer and grain. [8] As well, it covers the use of mathematics by the scribes in architectural design and the measurement of land. [7] [9] Although much past effort has gone into questions such as trying to deduce the rules used by the scribes to calculate their tables of representations of fractions of the form 2/n, that sort of mathematical exercise has been avoided here in place of a description of how the Egyptians used these tables and their other mathematical methods in solving practical problems. [9]
Because documents recording Egyptian mathematical knowledge are scarce, much of the book's history comes from other less directly mathematical objects, including the Egyptian architectural accomplishments, their burial goods, and their tax records, administrative writings, and literature. [8] [7] The book also discusses the mathematical problems and their solutions recorded from the small number of surviving mathematical documents including the Rhind papyrus, Lahun Mathematical Papyri, Moscow Mathematical Papyrus, Egyptian Mathematical Leather Roll, [1] [2] Carlsberg papyrus 30 [10] [2] , and the Ostraca Senmut 153 and Turin 57170, [9] placed in context by comparison with other less directly mathematical objects and texts from ancient Egypt, such as Instruction of Amenemope, Papyrus Harris I, Wilbour Papyrus, and Papyrus Anastasi I. [2]
The audience for this book, according to reviewer Kevin Davis, is "mid-way between a specialised and a general readership". [8] Alex Criddle echoes this opinion, suggesting that "those without a special interest in mathematics may find it very dry and hard to understand" but that it should be read by "anyone interested in the history of mathematics, egyptology, or Egyptian culture". [7] Although little specialized knowledge is needed to read this book, readers are expected to understand the basic concepts of modern arithmetic, and to have a general idea of Egyptian geography. [5] Reviewer Victor Pambuccian sees the book as excessively hostile towards the mathematical study of Egyptian mathematics, [9] while reviewer Stephen Chrisomalis sees it as bridging a longstanding gap between historians of the ancient world and historians of mathematics, and sees the book as aimed primarily at specialists in these fields. [4]
Pambuccian faults the book for miscrediting later historians with insights that repeated those of Oswald Spengler, [9] and Chrisomalis takes issue with the book's treatment of hieratic numerals as being equivalent to decimal for the purposes of calculation. [4] Martine Jansen asks for more examples, [11] , and similarly reviewer Joaquim Eurico Anes Duarte Nogueira suggests that more photos and added material on Egyptian games would have made the presentation more appealing. Nogueira also complains that the heavy use of notation based on that of the Egyptians, rather than translation into modern notation, makes the work hard to follow. He adds that although it seems aimed at a popular audience he thinks it will be of more interest to specialists in this area. [1] In contrast, reviewer Glen Van Brummelen writes that the book's "explanations are thorough and generally easy to understand, even for an interested lay person", [3] and reviewer Calvin Johnsma specifically praises the book's efforts to present ancient Egyptian mathematics for what it was rather than converting it into modern forms, avoiding the anachronistic distortions of modern algebraic notation. On the other hand, Johnsma would have preferred to see deeper coverage of the algebraic nature of Egyptian problem-solving techniques, of their changing notions of fractions, and of their geometry. [2]
Although Nogueira calls the book "good, but not excellent", [1] some other reviewers are more positive. Reviewer H. Rindler calls it "an excellent introduction to the current state of knowledge", [12] Davis calls it "head and shoulders above others" on the same topic, [8] and Johnsma calls it "a deeply informed up-to-date contextual history", "masterful", and "highly accessible" to non-experts. [2]
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
Babylonian cuneiform numerals, also used in Assyria and Chaldea, were written in cuneiform, using a wedge-tipped reed stylus to print a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
Liber Abaci is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.
An Egyptian fraction is a finite sum of distinct unit fractions, such as
Ahmes was an ancient Egyptian scribe who lived towards the end of the Fifteenth Dynasty and the beginning of the Eighteenth Dynasty. He transcribed the Rhind Mathematical Papyrus, a work of ancient Egyptian mathematics that dates to approximately 1550 BC; he is the earliest contributor to mathematics whose name is known. He's also the first mathematician to use fractions. Ahmes claimed not to be the writer of the work but rather just the scribe. He claimed the material came from an even older document from around 2000 B.C.
The system of ancient Egyptian numerals was used in Ancient Egypt from around 3000 BCE until the early first millennium CE. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in hieroglyphs. The Egyptians had no concept of a positional notation such as the decimal system. The hieratic form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions. Evidence for Egyptian mathematics is limited to a scarce amount of surviving sources written on papyrus. From these texts it is known that ancient Egyptians understood concepts of geometry, such as determining the surface area and volume of three-dimensional shapes useful for architectural engineering, and algebra, such as the false position method and quadratic equations.
The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It later entered the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today.
In mathematics, ancient Egyptian multiplication, one of two multiplication methods used by scribes, is a systematic method for multiplying two numbers that does not require the multiplication table, only the ability to multiply and divide by 2, and to add. It decomposes one of the multiplicands into a set of numbers of powers of two and then creates a table of doublings of the second multiplicand by every value of the set which is summed up to give result of multiplication.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata, who discovered the sine function. During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics and reaching its modern form with Leonhard Euler (1748).
The Egyptian Mathematical Leather Roll (EMLR) is a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but it was not chemically softened and unrolled until 1927 (Scott, Hall 1927).
The Reisner Papyri date to the reign of Senusret I, who was king of ancient Egypt in the 19th century BCE. The documents were discovered by G.A. Reisner during excavations in 1901–04 in Naga ed-Deir in southern Egypt. A total of four papyrus rolls were found in a wooden coffin in a tomb.
The Akhmim wooden tablets, also known as the Cairo wooden tablets, are two wooden writing tablets from ancient Egypt, solving arithmetical problems. They each measure around 18 by 10 inches and are covered with plaster. The tablets are inscribed on both sides. The hieroglyphic inscriptions on the first tablet include a list of servants, which is followed by a mathematical text. The text is dated to year 38 of an otherwise unnamed king's reign. The general dating to the early Egyptian Middle Kingdom combined with the high regnal year suggests that the tablets may date to the reign of the 12th Dynasty pharaoh Senusret I, c. 1950 BC. The second tablet also lists several servants and contains further mathematical texts.
The Rhind Mathematical Papyrus is one of the best known examples of ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC. The British Museum, where the majority of the papyrus is now kept, acquired it in 1865 along with the Egyptian Mathematical Leather Roll, also owned by Henry Rhind. There are a few small fragments held by the Brooklyn Museum in New York City and an 18 cm (7.1 in) central section is missing. It is one of the two well-known Mathematical Papyri along with the Moscow Mathematical Papyrus. The Rhind Papyrus is larger than the Moscow Mathematical Papyrus, while the latter is older.
A timeline of numerals and arithmetic.
The Lahun Mathematical Papyri is an ancient Egyptian mathematical text. It forms part of the Kahun Papyri, which was discovered at El-Lahun by Flinders Petrie during excavations of a workers' town near the pyramid of the Twelfth Dynasty pharaoh Sesostris II. The Kahun Papyri are a collection of texts including administrative texts, medical texts, veterinarian texts and six fragments devoted to mathematics.
Egyptian geometry refers to geometry as it was developed and used in Ancient Egypt. Their geometry was a necessary outgrowth of surveying to preserve the layout and ownership of farmland, which was flooded annually by the Nile river.
In the history of mathematics, Egyptian algebra, as that term is used in this article, refers to algebra as it was developed and used in ancient Egypt. Ancient Egyptian mathematics as discussed here spans a time period ranging from c. 3000 BCE to c. 300 BCE.
Annette Imhausen is a German historian of mathematics known for her work on Ancient Egyptian mathematics. She is a professor in the Normative Orders Cluster of Excellence at Goethe University Frankfurt.