The history of arithmetic includes the period from the emergence of counting before the formal definition of numbers and arithmetic operations over them by means of a system of axioms. Arithmetic — the science of numbers, their properties and their relations — is one of the main mathematical sciences. It is closely connected with algebra and the theory of numbers. The practical need for counting, elementary measurements and calculations became the reason for the emergence of arithmetic. The first authentic data on arithmetic knowledge are found in the historical monuments of Babylon and Ancient Egypt in the third and second millennia BC. The big contribution to the development of arithmetic was made by the ancient Greek mathematicians, in particular Pythagoreans, who tried to define all regularities of the world in terms of numbers. In the Middle Ages trade and approximate calculations were the main scope of arithmetic. Arithmetic developed first of all in India and the countries of Islam and only then came to Western Europe. In the seventeenth century the needs of astronomy, mechanics, and more difficult commercial calculations put before arithmetic new challenges regarding methods of calculation and gave an impetus to further development. Theoretical justifications of the idea of number are connected first of all with the definition of "natural number" and Peano's axioms formulated in 1889. They were followed by strict definitions of rational, real, negative and complex numbers. Further expansion of the concept of number is possible only if one of the arithmetic laws is rejected. (Wikipedia).
Greek Mathematics: The Beginning of Greek Math & Greek Numerals
Welcome to the History of Greek Mathematics mini-series! This series is a short introduction to Math History as a subject and the some of the important theorems created in ancient Greece. You are watching the first video in the series. If this series interested you check out our blog for
From playlist The History of Greek Mathematics: Math History
Calculus | Math History | N J Wildberger
Calculus has its origins in the work of the ancient Greeks, particularly of Eudoxus and Archimedes, who were interested in volume problems, and to a lesser extent in tangents. In the 17th century the subject was widely expanded and developed in an algebraic way using also the coordinate ge
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Number theory and algebra in Asia (a) | Math History | NJ Wildberger
After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory: Pell's equation, the Chinese rema
From playlist MathHistory: A course in the History of Mathematics
Number systems and Stevin's decimals | Math History | NJ Wildberger
We review some of the development of number systems from the ancient Greeks, followed by the Indian and then Arabic development of our Hindu-Arabic numeral system. Then we focus on the new directions forged by the European mathematicians of the 15th and 16th centuries, culminating in the w
From playlist MathHistory: A course in the History of Mathematics
Teach Astronomy - Newton and Society
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Number theory and algebra in Asia (b) | Math History | NJ Wildberger
After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory (Pell's equation, the Chinese rema
From playlist MathHistory: A course in the History of Mathematics
Algebraic number theory and rings I | Math History | NJ Wildberger
In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include
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Problems with the Calculus | Math History | NJ Wildberger
We discuss some of the controversy and debate generated by the 17th century work on Calculus. Newton and Leibniz's ideas were not universally accepted as making sense, despite the impressive, even spectacular achievements that the new theory was able to demonstrate. In this lecture we di
From playlist MathHistory: A course in the History of Mathematics
What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 2]
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Algebraic number theory and rings II | Math History | NJ Wildberger
In the 19th century, algebraists started to look at extension fields of the rational numbers as new domains for doing arithmetic. In this way the notion of an abstract ring was born, through the more concrete examples of rings of algebraic integers in number fields. Key examples include
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Computer History: Dr. Konrad Zuse, Computer Pioneer and the Z Computers (Z3) (Germany 1935-1945)
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Example: Adding two digit numbers (no carrying) | Arithmetic | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/arithmetic-home/addition-subtraction/add-two-dig-intro/v/adding-whole-numbers-and-applications-1 Adding Whole Numbers and Applications 1 Practice this lesson your
From playlist Addition and subtraction | Arithmetic | Khan Academy
Complex dynamics and arithmetic equidistribution – Laura DeMarco – ICM2018
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Number line 1 | Multiplication and division | Arithmetic | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/multiplication-division/multiplication_fun/e/number_line?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic Watch the next lesson: https://www.khanacademy.org/math/arithmetic/multipl
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The minimum modulus problem for covering systems - Bob Hough
Analysis Seminar Topic: The minimum modulus problem for covering systems Speaker: Bob Hough Affiliation: Member, School of Mathematics Date: Wednesday, May 4 A distinct covering system of congruences is a finite collection of arithmetic progressions to distinct moduli aimodmi, whose u
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Division word problem example 1 | Multiplication and division | Arithmetic | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-word-problems/e/arithmetic_word_problems?utm_source=YT&utm_medium=Desc&utm_campaign=Arithmetic Watch the next lesson: https://www.khanacademy.org/math/a
From playlist Multiplication and division | Arithmetic | Khan Academy
Four Step Recovery Programme for Division by Zero Deniers
Division by zero has been possible since 1957. LINKS: Transmathematica Channel https://youtube.com/channel/UC2ro5bMjox_KhU-UbUvx7jQ Rehab Playlist https://youtube.com/playlist?list=PL2qvIMkhqXu036a0M_TLAryIqjiRO6OKs History of division by zero https://doi.org/10.36285/tm.37 Suppes htt
From playlist Summer of Math Exposition Youtube Videos
Worked example: arithmetic series (recursive formula) | High School Math | Khan Academy
Sal evaluates the sum of the first 650 terms in the sequence defined recursively as {aᵢ=aᵢ₋₁+11, a₁=4}. He does that by finding the 650th term and using the arithmetic series formula (a₁+aₙ)*n/2. Watch the next lesson: https://www.khanacademy.org/math/math-1-2-3/math3/math3-series/math3-a
From playlist Algebra II | High School Math | Khan Academy
Mechanics and curves | Math History | NJ Wildberger
The laws of motion as set out by Newton built upon work of Oresme, Galileo and others on dynamics, and the relations between distance, velocity and acceleration in trajectories. With Newton's laws and the calculus, a whole new arena of practical and theoretical investigations opened up to
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Multiplying: 2 digits times 1 digit | Multiplication and division | Arithmetic | Khan Academy
Let's start by solving a basic multiplication problem. No carrying of numbers in this example! Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/e/multiplication_1.5?utm_source=YT&utm_
From playlist Multiplication and division | Arithmetic | Khan Academy