0:00:00.800,0:00:02.133 What I wanna do in this video 0:00:02.133,0:00:04.800 is think about the origins of Algebra, 0:00:04.800,0:00:07.019 the origins of Algebra. 0:00:07.019,0:00:08.533 And the word 0:00:08.533,0:00:10.667 especially an association with the ideas 0:00:10.667,0:00:12.733 that Algebra now represents. 0:00:12.733,0:00:15.689 comes from, comes from, this book 0:00:15.689,0:00:18.667 or actually this is a page of the book right over there. 0:00:18.667,0:00:20.800 The English translation for the title of this book is, 0:00:20.800,0:00:25.662 "The Compendious book on Calculation by Completion and Balancing." 0:00:25.667,0:00:28.800 And it was written by a Persian mathematician 0:00:28.800,0:00:30.969 who lived in Baghdad, in, in... 0:00:30.969,0:00:33.615 I believe it was in the 8th or 9th century 0:00:33.615,0:00:35.800 I believe it was actually 820 A.D. 0:00:35.800,0:00:37.773 when he wrote this book. 0:00:37.773,0:00:38.695 A.D. 0:00:38.695,0:00:41.350 And Algebra is the Arabic word 0:00:41.350,0:00:43.509 that here is the actual title that he gave to it 0:00:43.509,0:00:45.400 which is the Arabic title 0:00:45.400,0:00:48.467 "Algebra means restoration or completion" 0:00:48.467,0:00:55.084 restoration... restoration or completion... completion 0:00:55.084,0:00:58.369 And he associated it in his book with a very specific operation, 0:00:58.369,0:01:01.667 really taking something from one side of an equation 0:01:01.667,0:01:03.501 to another side of an equation. 0:01:03.501,0:01:06.586 But we can actually see it right over here. I don't know Arabic 0:01:06.586,0:01:10.400 but I actually do know some languages that seem to have borrowed a little bit from Arabic 0:01:10.400,0:01:12.230 or maybe went the other way around. 0:01:12.230,0:01:14.941 But this says Al Kitab and 0:01:14.941,0:01:18.243 I know just enough Urdu or Hindi to understand a good Indian movie. 0:01:18.243,0:01:20.130 But Al Kitab 'Kitab' means "book". 0:01:20.130,0:01:23.302 So this part is 'book'. 0:01:23.302,0:01:27.163 Al-Muhktasar I think that means 'compendious' 0:01:27.163,0:01:29.904 because I don't know the word for compendious and that seems like that. 0:01:29.904,0:01:36.585 Fi Hisab, 'Hisab' means 'calculation' in Hindi or Urdu so this is calculation. 0:01:36.585,0:01:38.738 Al-Gabr this is the root. 0:01:38.738,0:01:41.021 This is the famous Algebra. This is where it shows up. 0:01:41.021,0:01:43.533 So this is for 'completion'. 0:01:43.533,0:01:46.478 You can view that as completion...completion 0:01:46.478,0:01:49.715 and then Wa...Al-Muqabala 0:01:49.715,0:01:52.467 that means essentially 'balancing' 0:01:52.467,0:01:55.631 completion and balancing. 0:01:55.631,0:01:57.133 So if we wanted to translate it 0:01:57.133,0:01:58.733 and I know this is not a video on translating Arabic. 0:01:58.733,0:02:01.947 but the book... the book 0:02:01.947,0:02:10.624 I guess this is saying 'compendious on calculation by completion and balancing' 0:02:10.624,0:02:12.564 is the rough translation over there. 0:02:12.564,0:02:15.412 But that is the source of the word 'Algebra'. 0:02:15.412,0:02:18.146 And this is a very very very important book. 0:02:18.146,0:02:21.467 Not just because it was the first use of the word Algebra. 0:02:21.467,0:02:25.000 But many people viewed this book as the first time 0:02:25.000,0:02:32.000 that Algebra took on many of its modern ideas, 0:02:32.050,0:02:34.533 ideas of balancing an equation, 0:02:34.533,0:02:36.533 the abstract problem itself, 0:02:36.533,0:02:38.995 not trying to do one-off problems here and there. 0:02:39.000,0:02:42.800 But Al-Khwārizmī was not the first person. 0:02:42.800,0:02:44.800 And just to get an idea of where all this is happening, 0:02:44.800,0:02:46.800 so he was hanging out in Baghdad. 0:02:46.800,0:02:49.200 So this is, and this part of the world shows up 0:02:49.200,0:02:50.667 a lot in the history of algebra. 0:02:50.667,0:02:53.133 But he was hanging out right there in around the 8th or 9th century. 0:02:53.133,0:02:56.160 So let me draw a little timeline here, 0:02:56.160,0:02:58.000 just so we can appreciate everything. 0:02:58.000,0:03:01.431 So that is... timeline. 0:03:01.431,0:03:05.133 And then whether or not you are religious, 0:03:05.133,0:03:09.159 most of our modern dates are dependent on the birth of Jesus. 0:03:09.159,0:03:11.796 So I will put, so that is right there. 0:03:11.796,0:03:13.704 Maybe we'll put a cross over there 0:03:13.704,0:03:15.462 to signify that, when we wanna be non-religious, 0:03:15.462,0:03:18.473 we say 'common era' 'before the common era'; 0:03:18.473,0:03:19.766 when we wanna be religious, 0:03:19.766,0:03:20.566 we say A.D. 0:03:20.566,0:03:22.164 which means 'the year of our lord'. 0:03:22.164,0:03:25.333 Anno...I don't know the latin...'Anno Domini', I believe 0:03:25.333,0:03:26.434 'the year of our lord' 0:03:26.434,0:03:28.950 And then when we want to ... in the religious context, 0:03:28.950,0:03:30.482 instead of saying 'before common era', 0:03:30.482,0:03:32.433 we say 'Before Christ', B.C. 0:03:32.433,0:03:36.133 But either way, either way, so this is 1000 0:03:36.133,0:03:37.533 in the common era. 0:03:37.533,0:03:39.667 This is 2000 in the common era. 0:03:39.667,0:03:41.652 And obviously we are sitting at least 0:03:41.652,0:03:44.831 when I'm making this video, I'm sitting right about there. 0:03:44.831,0:03:48.733 And then... this is 1000 before the common era. 0:03:48.733,0:03:52.296 And this is 2000 before the common era. 0:03:52.296,0:03:55.000 So the first traces, and I'm skipping out in 0:03:55.000,0:03:56.234 and really it's just what we can find. 0:03:56.234,0:03:57.369 I'm sure if we were able to dig more. 0:03:57.369,0:03:58.835 We might be able to find other evidence 0:03:58.835,0:04:01.121 of different civilizations and different people, 0:04:01.121,0:04:04.569 stumbling on many of the ideas in Algebra. 0:04:04.569,0:04:06.311 But our first records of people 0:04:06.311,0:04:09.533 really exploring the ideas that are hit upon in Algebra 0:04:09.533,0:04:12.200 come from ancient Babylon, 0:04:12.200,0:04:14.906 around 2000 years before the common era, 0:04:14.906,0:04:21.565 before Christ. So right around, right around there 0:04:21.565,0:04:23.023 where there were stone tablets 0:04:23.023,0:04:24.867 where it looks like people were exploring 0:04:24.867,0:04:26.253 some of the fundamental ideas of Algebra. 0:04:26.253,0:04:27.669 They weren't using the same symbols. 0:04:27.669,0:04:31.133 They weren't using the same ways of representing the numbers. 0:04:31.133,0:04:33.200 But it was Algrebra they were working on 0:04:33.200,0:04:35.800 and that was once again in this part of the world. 0:04:35.800,0:04:38.733 Babylon was right about... right about there. 0:04:38.733,0:04:42.400 And Babylon has kind of kept the tradition of Sumeria. 0:04:42.400,0:04:45.400 This whole region was called Mesopotamia 0:04:45.400,0:04:47.186 -- Greek for 'between two rivers' -- 0:04:47.186,0:04:49.733 But that's the first traces of people that we know of 0:04:49.733,0:04:51.744 that were people who were starting to do 0:04:51.744,0:04:54.720 what we would call real real Algebra. 0:04:54.720,0:04:56.200 And then you fast forward 0:04:56.200,0:04:58.992 and I am sure even our historians don't know 0:04:58.992,0:05:03.800 all the different instances of people using Algebra. 0:05:03.800,0:05:08.267 But kind of the major contributions to Algebra 0:05:08.267,0:05:11.533 we saw it here in Babylon 2000 years ago. 0:05:11.533,0:05:14.171 And then if we fast forward to about 200-300 A.D., 0:05:14.171,0:05:15.582 so right over there, 0:05:15.582,0:05:18.169 you have a Greek gentleman who lived in Alexanderia. 0:05:18.169,0:05:22.000 So this is Greece right over here, but he lived in Alexandria 0:05:22.000,0:05:25.041 which at the time was part of the Roman Empire. 0:05:25.041,0:05:28.000 So Alexandria is right over here. 0:05:28.000,0:05:29.432 And he was a gentleman by the name of 0:05:29.432,0:05:32.041 Diophantus or Diaphantus 0:05:32.041,0:05:33.467 or I don't know how to pronounce it. 0:05:33.467,0:05:36.867 Dio... Diophantus. 0:05:36.867,0:05:40.244 and he is sometimes credited with being the father of Algebra. 0:05:40.244,0:05:44.508 And it's debatable whether it's Diophantus or whether it's Al-Khwārizmī', 0:05:44.508,0:05:48.531 Al-Khwārizmī' who kinda started using these these terms of balancing equations 0:05:48.533,0:05:50.667 and talking about math in a pure way 0:05:50.667,0:05:53.548 while Diophantus was more focused on particular problems. 0:05:53.548,0:05:57.032 And both of them were kind of beat to the punch by the Babylonians 0:05:57.032,0:05:59.061 although they all did contribute in their own way. 0:05:59.061,0:06:01.361 It's not like they were just copying what the Babylonians did. 0:06:01.361,0:06:03.733 They had their own unique contributions 0:06:03.733,0:06:06.328 to what we now consider 'Algebra'. 0:06:06.328,0:06:08.733 But many, especially western historians, 0:06:08.733,0:06:11.282 associate Diophantus as the father of Algebra. 0:06:11.282,0:06:13.816 And now Al-Khwārizmī' is sometimes 0:06:13.816,0:06:16.212 what other people would argue as the father of Algebra. 0:06:16.212,0:06:18.352 So he made significant contributions. 0:06:18.352,0:06:20.347 So if you go to about 600 A.D. 0:06:20.347,0:06:22.221 So if you go to about 600 A.D. 0:06:22.221,0:06:26.067 another famous mathematician in the history of Algebra 0:06:26.067,0:06:29.800 was Brahma Gupta in India 0:06:29.800,0:06:32.667 Brahma Gupta... in India. 0:06:32.667,0:06:34.692 So... obviously and actually I don't know 0:06:34.692,0:06:36.431 where in India he lived. I should look that up. 0:06:36.431,0:06:39.161 But it's roughly... roughly in that part of the world 0:06:39.161,0:06:42.733 And he also made a significant contributions. 0:06:42.733,0:06:45.768 And then of course you have Al-Khwārizmī' 0:06:45.768,0:06:48.667 who shows up right about there. 0:06:48.667,0:06:52.513 Al-Khwārizmī' and he's the gentleman 0:06:52.513,0:06:56.329 that definitely we credit with the name Algebra, 0:06:56.329,0:06:57.862 comes from Arabic for 'Restoration' 0:06:57.862,0:07:01.841 and some people also consider him to be, if not the father of Algebra, 0:07:01.841,0:07:04.118 although some say he is the father, 0:07:04.118,0:07:05.892 he is one of the fathers of Algebra, 0:07:05.892,0:07:09.278 because he really started to think about Algebra in the abstract sense, 0:07:09.278,0:07:11.025 devoid of some specific problems, 0:07:11.025,0:07:12.492 and a lot of the ways 0:07:12.492,0:07:16.800 that a modern mathematician would start to think about the field.