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Course: Algebra 1>Unit 1

Lesson 1: Overview and history of algebra

Origins of algebra

Where did the word "Algebra" and its underlying ideas come from? Algebra, a key branch of mathematics, has a rich history. The term 'algebra' comes from an Arabic word meaning 'restoration' or 'completion'. Significant contributions to algebra were made by Diophantus in Greece, Brahmagupta in India, and al-Khwarizmi in Baghdad, who is often credited with giving algebra its name. Created by Sal Khan.

Want to join the conversation?

• At , how does a person or group of people discover/invent a new type of math like Algebra? How did Newton invent calculus? Are there people doing research today creating new math to understand the universe?
• How did Newton invent calculus?

Well, Newton was describing the orbits of planets around the sun, and mentioned that he suspected the orbits were not perfectly circular, but elliptical. A friend colleague of his was unfazed by his assertions.

"Prove it" said the colleague.

And Newton shut himself up for two three days trying to come up with a mathematical proof for his theory. He had to invent calculus to do so. Which he did :)
• Why is algebra so important?
• Algebra is important because it is one of the largest, broadest and most relevant type of mathematics today. For an example, we would not be able to have landed on the moon if not for algebra. We would need to substitute unknowns (variables) in place of the information or data we do not have such as the perfect speed of shuttle/spaceship or another variable. Using algebra, constants and what we know for fact, we were able to solve for those variables and launch into space, which was deemed impossible as early as 1000 B.C.
• What is the difference between Greek letters and Roman letters?
• For the most part, Roman letters are the same letters we use today ( A, B, C, etc.). In contrast, the Ancient Greeks used a different alphabet with different letters and symbols (for instance, when you hear words like "alpha", "beta", and "gamma" you are hearing the names of certain letters in the Greek alphabet). However, the Roman civilization was influenced in a lot of ways by Ancient Greece and, because of that, there were a lot of similarities between the two cultures. As just one example, several of the Roman letters (such as "a" & "b") look a lot like the Greek letters (in this case, "alpha" & "beta").

In math, you often come across both Roman and Greek letters. For example, when dealing with triangles, you often see the triangle's angles symbolized by Greek letters ("theta" and "phi" are the most commonly used) whereas the sides of the triangle most often have Roman letters for names (such as "a", "b", & "c").

Hope this helps!
• Why is algebra used in our daily lives even if we don't want it to be?
• The same reason why the alphabet is used in our daily lives.
The same reason why you ride in/drive a vehicle every day.
The same reason why we eat with forks instead of our hands.
The same reason why you usually don't say your middle name.
The same reason why the numbers on the keyboard I'm typing on are in the order 1 2 3 4 5 6 7 8 9 0.
The same reason why we store our toothbrushes in the bathroom.
Et cetera.
The reason why algebra used in our daily lives even if we don't want it to be is for convenience.
(Which is the same reason why this post is under "answer" instead of under "comment".)
Happy Studying!
—CT-2/002-24
• Why are there multiple fathers of algebra that people credit differently? Sure, the ancient Babylonians could have used Babylonian numerals or something, and the others their form of numbers and symbols, and each person contributed differently. But does algebra have an end? Can we one day, stop discovering more algebraic formulas. Or is algebra this infinite thing that goes on and on and on?
• Great question! I believe that math as a whole is a subject that is constantly expanding as mathematicians discover new laws, formulas, and different ways of looking at math. Algebra is just part of the constantly changing form of math, and so it changes as well over time. Eventually there may be an end to discovering new algebraic formulas, but it will probably take an incredibly long time; and when discovering algebra has come to an end, there will probably be whole new topics of math to study and learn.
• what when can we use algebra in?
• Algebra can and should be used in many math-related problems. It can be used to find exact answers, maxima, minima and Sal knows what else.
• I want to become an interpreter (foreign languages are my passion!) Would I ever need to use Algebra in my day-to-day life? If I'm translating words and phrases for someone, aren't numbers universal? Why would I have to learn Algebra if I want to go into a field that deals with spoken language?

In all my years of school, nobody has ever given me an answer besides "it's required by the state." (I'm in the United States in my Junior year of High School.)
• Math does more than just teach you a bunch of numbers and operations, it helps you do logic, problem solving, and maybe even thinking outside of the box. All these skills could come in handy to any job including interpreter. Plus, what do you mean by interpreter, are you going to work for the State Department, or what? You will have to continue on with Math in college also which is not much better than you have to do it to pass high school.
• I am a student from egypt who was studying in the national system and now I am preparing for my sat test in order to study abroad in the US. I'm not having any problems in studying english but I am really confused about mathematics I have tried to apply what I have studied in answering the tasks of khan academy but it isn't helping so much so I am confused from where to start.
• Rather than going though Math, you might be better looking at the SAT section of Khan and practice Math (and English there) which has more problems geared toward those that might show up on the SAT. Here in America, our students often take the PSAT in 9th and 10th grade which scores can be linked to Khan to work on areas of weakness, but if you have not done this, studying under the SAT section might be more benificial than doing the math classes.
• Why was algebra invented in Arabic and when am I going to use algebra in the future?
• Al-Khwarizmi did all his work in Arabic since he was basing in it the context of 9th-century Arab Abbasid culture. When he wrote his manuscript on mathematics, the world al-jabr was in the title, and the word algebra was derived from it.

Depending on what career path you choose in life, you could be using algebra every day. Careers based in business, mathematics, computer technology, science, medicine, and architecture and just some examples of jobs where algebra is crucial. Algebra is also used in more mundane activities like budgeting and managing finances or doing taxes.

Additionally, algebra creates a basis for so much more in math, and all other branches of math use algebra in some way. Learning algebra is one of the most important things you can learn.