WEBVTT 00:00:00.800 --> 00:00:02.133 What I wanna do in this video 00:00:02.133 --> 00:00:04.800 is think about the origins of Algebra, 00:00:04.800 --> 00:00:07.019 the origins of Algebra. 00:00:07.019 --> 00:00:08.533 And the word 00:00:08.533 --> 00:00:10.667 especially an association with the ideas 00:00:10.667 --> 00:00:12.733 that Algebra now represents. 00:00:12.733 --> 00:00:15.689 comes from, comes from, this book 00:00:15.689 --> 00:00:18.667 or actually this is a page of the book right over there. 00:00:18.667 --> 00:00:20.800 The English translation for the title of this book is, 00:00:20.800 --> 00:00:25.662 "The Compendious book on Calculation by Completion and Balancing." 00:00:25.667 --> 00:00:28.800 And it was written by a Persian mathematician 00:00:28.800 --> 00:00:30.969 who lived in Baghdad, in, in... 00:00:30.969 --> 00:00:33.615 I believe it was in the 8th or 9th century 00:00:33.615 --> 00:00:35.800 I believe it was actually 820 A.D. 00:00:35.800 --> 00:00:37.773 when he wrote this book. 00:00:37.773 --> 00:00:38.695 A.D. 00:00:38.695 --> 00:00:41.350 And Algebra is the Arabic word 00:00:41.350 --> 00:00:43.509 that here is the actual title that he gave to it 00:00:43.509 --> 00:00:45.400 which is the Arabic title 00:00:45.400 --> 00:00:48.467 "Algebra means restoration or completion" 00:00:48.467 --> 00:00:55.084 restoration... restoration or completion... completion 00:00:55.084 --> 00:00:58.369 And he associated it in his book with a very specific operation, 00:00:58.369 --> 00:01:01.667 really taking something from one side of an equation 00:01:01.667 --> 00:01:03.501 to another side of an equation. 00:01:03.501 --> 00:01:06.586 But we can actually see it right over here. I don't know Arabic 00:01:06.586 --> 00:01:10.400 but I actually do know some languages that seem to have borrowed a little bit from Arabic 00:01:10.400 --> 00:01:12.230 or maybe went the other way around. 00:01:12.230 --> 00:01:14.941 But this says Al Kitab and 00:01:14.941 --> 00:01:18.243 I know just enough Urdu or Hindi to understand a good Indian movie. 00:01:18.243 --> 00:01:20.130 But Al Kitab 'Kitab' means "book". 00:01:20.130 --> 00:01:23.302 So this part is 'book'. 00:01:23.302 --> 00:01:27.163 Al-Muhktasar I think that means 'compendious' 00:01:27.163 --> 00:01:29.904 because I don't know the word for compendious and that seems like that. 00:01:29.904 --> 00:01:36.585 Fi Hisab, 'Hisab' means 'calculation' in Hindi or Urdu so this is calculation. 00:01:36.585 --> 00:01:38.738 Al-Gabr this is the root. 00:01:38.738 --> 00:01:41.021 This is the famous Algebra. This is where it shows up. 00:01:41.021 --> 00:01:43.533 So this is for 'completion'. 00:01:43.533 --> 00:01:46.478 You can view that as completion...completion 00:01:46.478 --> 00:01:49.715 and then Wa...Al-Muqabala 00:01:49.715 --> 00:01:52.467 that means essentially 'balancing' 00:01:52.467 --> 00:01:55.631 completion and balancing. 00:01:55.631 --> 00:01:57.133 So if we wanted to translate it 00:01:57.133 --> 00:01:58.733 and I know this is not a video on translating Arabic. 00:01:58.733 --> 00:02:01.947 but the book... the book 00:02:01.947 --> 00:02:10.624 I guess this is saying 'compendious on calculation by completion and balancing' 00:02:10.624 --> 00:02:12.564 is the rough translation over there. 00:02:12.564 --> 00:02:15.412 But that is the source of the word 'Algebra'. 00:02:15.412 --> 00:02:18.146 And this is a very very very important book. 00:02:18.146 --> 00:02:21.467 Not just because it was the first use of the word Algebra. 00:02:21.467 --> 00:02:25.000 But many people viewed this book as the first time 00:02:25.000 --> 00:02:32.000 that Algebra took on many of its modern ideas, 00:02:32.050 --> 00:02:34.533 ideas of balancing an equation, 00:02:34.533 --> 00:02:36.533 the abstract problem itself, 00:02:36.533 --> 00:02:38.995 not trying to do one-off problems here and there. 00:02:39.000 --> 00:02:42.800 But Al-Khwārizmī was not the first person. 00:02:42.800 --> 00:02:44.800 And just to get an idea of where all this is happening, 00:02:44.800 --> 00:02:46.800 so he was hanging out in Baghdad. 00:02:46.800 --> 00:02:49.200 So this is, and this part of the world shows up 00:02:49.200 --> 00:02:50.667 a lot in the history of algebra. 00:02:50.667 --> 00:02:53.133 But he was hanging out right there in around the 8th or 9th century. 00:02:53.133 --> 00:02:56.160 So let me draw a little timeline here, 00:02:56.160 --> 00:02:58.000 just so we can appreciate everything. 00:02:58.000 --> 00:03:01.431 So that is... timeline. 00:03:01.431 --> 00:03:05.133 And then whether or not you are religious, 00:03:05.133 --> 00:03:09.159 most of our modern dates are dependent on the birth of Jesus. 00:03:09.159 --> 00:03:11.796 So I will put, so that is right there. 00:03:11.796 --> 00:03:13.704 Maybe we'll put a cross over there 00:03:13.704 --> 00:03:15.462 to signify that, when we wanna be non-religious, 00:03:15.462 --> 00:03:18.473 we say 'common era' 'before the common era'; 00:03:18.473 --> 00:03:19.766 when we wanna be religious, 00:03:19.766 --> 00:03:20.566 we say A.D. 00:03:20.566 --> 00:03:22.164 which means 'the year of our lord'. 00:03:22.164 --> 00:03:25.333 Anno...I don't know the latin...'Anno Domini', I believe 00:03:25.333 --> 00:03:26.434 'the year of our lord' 00:03:26.434 --> 00:03:28.950 And then when we want to ... in the religious context, 00:03:28.950 --> 00:03:30.482 instead of saying 'before common era', 00:03:30.482 --> 00:03:32.433 we say 'Before Christ', B.C. 00:03:32.433 --> 00:03:36.133 But either way, either way, so this is 1000 00:03:36.133 --> 00:03:37.533 in the common era. 00:03:37.533 --> 00:03:39.667 This is 2000 in the common era. 00:03:39.667 --> 00:03:41.652 And obviously we are sitting at least 00:03:41.652 --> 00:03:44.831 when I'm making this video, I'm sitting right about there. 00:03:44.831 --> 00:03:48.733 And then... this is 1000 before the common era. 00:03:48.733 --> 00:03:52.296 And this is 2000 before the common era. 00:03:52.296 --> 00:03:55.000 So the first traces, and I'm skipping out in 00:03:55.000 --> 00:03:56.234 and really it's just what we can find. 00:03:56.234 --> 00:03:57.369 I'm sure if we were able to dig more. 00:03:57.369 --> 00:03:58.835 We might be able to find other evidence 00:03:58.835 --> 00:04:01.121 of different civilizations and different people, 00:04:01.121 --> 00:04:04.569 stumbling on many of the ideas in Algebra. 00:04:04.569 --> 00:04:06.311 But our first records of people 00:04:06.311 --> 00:04:09.533 really exploring the ideas that are hit upon in Algebra 00:04:09.533 --> 00:04:12.200 come from ancient Babylon, 00:04:12.200 --> 00:04:14.906 around 2000 years before the common era, 00:04:14.906 --> 00:04:21.565 before Christ. So right around, right around there 00:04:21.565 --> 00:04:23.023 where there were stone tablets 00:04:23.023 --> 00:04:24.867 where it looks like people were exploring 00:04:24.867 --> 00:04:26.253 some of the fundamental ideas of Algebra. 00:04:26.253 --> 00:04:27.669 They weren't using the same symbols. 00:04:27.669 --> 00:04:31.133 They weren't using the same ways of representing the numbers. 00:04:31.133 --> 00:04:33.200 But it was Algrebra they were working on 00:04:33.200 --> 00:04:35.800 and that was once again in this part of the world. 00:04:35.800 --> 00:04:38.733 Babylon was right about... right about there. 00:04:38.733 --> 00:04:42.400 And Babylon has kind of kept the tradition of Sumeria. 00:04:42.400 --> 00:04:45.400 This whole region was called Mesopotamia 00:04:45.400 --> 00:04:47.186 -- Greek for 'between two rivers' -- 00:04:47.186 --> 00:04:49.733 But that's the first traces of people that we know of 00:04:49.733 --> 00:04:51.744 that were people who were starting to do 00:04:51.744 --> 00:04:54.720 what we would call real real Algebra. 00:04:54.720 --> 00:04:56.200 And then you fast forward 00:04:56.200 --> 00:04:58.992 and I am sure even our historians don't know 00:04:58.992 --> 00:05:03.800 all the different instances of people using Algebra. 00:05:03.800 --> 00:05:08.267 But kind of the major contributions to Algebra 00:05:08.267 --> 00:05:11.533 we saw it here in Babylon 2000 years ago. 00:05:11.533 --> 00:05:14.171 And then if we fast forward to about 200-300 A.D., 00:05:14.171 --> 00:05:15.582 so right over there, 00:05:15.582 --> 00:05:18.169 you have a Greek gentleman who lived in Alexanderia. 00:05:18.169 --> 00:05:22.000 So this is Greece right over here, but he lived in Alexandria 00:05:22.000 --> 00:05:25.041 which at the time was part of the Roman Empire. 00:05:25.041 --> 00:05:28.000 So Alexandria is right over here. 00:05:28.000 --> 00:05:29.432 And he was a gentleman by the name of 00:05:29.432 --> 00:05:32.041 Diophantus or Diaphantus 00:05:32.041 --> 00:05:33.467 or I don't know how to pronounce it. 00:05:33.467 --> 00:05:36.867 Dio... Diophantus. 00:05:36.867 --> 00:05:40.244 and he is sometimes credited with being the father of Algebra. 00:05:40.244 --> 00:05:44.508 And it's debatable whether it's Diophantus or whether it's Al-Khwārizmī', 00:05:44.508 --> 00:05:48.531 Al-Khwārizmī' who kinda started using these these terms of balancing equations 00:05:48.533 --> 00:05:50.667 and talking about math in a pure way 00:05:50.667 --> 00:05:53.548 while Diophantus was more focused on particular problems. 00:05:53.548 --> 00:05:57.032 And both of them were kind of beat to the punch by the Babylonians 00:05:57.032 --> 00:05:59.061 although they all did contribute in their own way. 00:05:59.061 --> 00:06:01.361 It's not like they were just copying what the Babylonians did. 00:06:01.361 --> 00:06:03.733 They had their own unique contributions 00:06:03.733 --> 00:06:06.328 to what we now consider 'Algebra'. 00:06:06.328 --> 00:06:08.733 But many, especially western historians, 00:06:08.733 --> 00:06:11.282 associate Diophantus as the father of Algebra. 00:06:11.282 --> 00:06:13.816 And now Al-Khwārizmī' is sometimes 00:06:13.816 --> 00:06:16.212 what other people would argue as the father of Algebra. 00:06:16.212 --> 00:06:18.352 So he made significant contributions. 00:06:18.352 --> 00:06:20.347 So if you go to about 600 A.D. 00:06:20.347 --> 00:06:22.221 So if you go to about 600 A.D. 00:06:22.221 --> 00:06:26.067 another famous mathematician in the history of Algebra 00:06:26.067 --> 00:06:29.800 was Brahma Gupta in India 00:06:29.800 --> 00:06:32.667 Brahma Gupta... in India. 00:06:32.667 --> 00:06:34.692 So... obviously and actually I don't know 00:06:34.692 --> 00:06:36.431 where in India he lived. I should look that up. 00:06:36.431 --> 00:06:39.161 But it's roughly... roughly in that part of the world 00:06:39.161 --> 00:06:42.733 And he also made a significant contributions. 00:06:42.733 --> 00:06:45.768 And then of course you have Al-Khwārizmī' 00:06:45.768 --> 00:06:48.667 who shows up right about there. 00:06:48.667 --> 00:06:52.513 Al-Khwārizmī' and he's the gentleman 00:06:52.513 --> 00:06:56.329 that definitely we credit with the name Algebra, 00:06:56.329 --> 00:06:57.862 comes from Arabic for 'Restoration' 00:06:57.862 --> 00:07:01.841 and some people also consider him to be, if not the father of Algebra, 00:07:01.841 --> 00:07:04.118 although some say he is the father, 00:07:04.118 --> 00:07:05.892 he is one of the fathers of Algebra, 00:07:05.892 --> 00:07:09.278 because he really started to think about Algebra in the abstract sense, 00:07:09.278 --> 00:07:11.025 devoid of some specific problems, 00:07:11.025 --> 00:07:12.492 and a lot of the ways 00:07:12.492 --> 00:07:16.800 that a modern mathematician would start to think about the field.