If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:8:23

Video transcript

the laws of nature but the mathematical thoughts of God and this is a quote by Euclid of Alexandria who was a Greek mathematician and philosopher who lived about 300 years before Christ and the reason why I include this quote is because Euclid is considered to be the father the father of geometry and it is a neat quote regardless of your views of God whether or not God exists or the nature of God it says something very fundamental about nature the laws of nature are but the mathematical thoughts of God that math underpins all of the laws of nature and the word geometry itself has Greek roots geo comes from Greek for earth metree comes from Greek for measurement you're probably used to something like the metric system and Euclid is considered to be the father of geometry not because he was the first person who studied geometry you could imagine the very first humans might have studied geometry they might have looked at two twigs on the ground that looks something like that and they might have looked at another pair of twigs that look like that and said no this is a bigger opening what is the relationship here or they might have looked at a tree they might have looked at a tree that had a branch that came off that had a branch that came off it like that and I said well there's something similar about this opening here and this opening here or they might have asked themselves what is the ratio or how does the what is the relationship between the distance around a circle and the distance across it and is that the same for all circles and is there a way for us to feel really good that that is definitely true and then once you got to the early Greeks they started to get even more more thoughtful essentially about geometric things when you talk about you know the Greek mathematicians like like Pythagoras but why who came before Euclid but why the reason why Euclid is considered to be the father of geometry and why we often talk about Euclidean geometry is around 300 BC and this right over here is a picture of Euclid painted by Raphael and no one really knows what you could look like even when he was born or when he died so this is just Rafael's impression of when you what Euclid might have looked like while he was teaching in Alexandria but what made you chlid the father of geometry is really his his writing of Euclid's elements and what the elements were were 13 volumes of essentially a 13 volume textbook and arguably the most famous text book of all time and what he did in those 13 volumes is he essentially did a rigorous thoughtful logical march through geometry and number theory and then also solid geometry so geometry in three dimensions and this right over here is the frontispiece for the english version of or the first translation of the English version of Euclid's elements and this was done in 1570 but it was obviously first written in Greek and then during much of the Middle Ages that knowledge was shepherded by the Arabs and it was translated into Arabic and then eventually in the late Middle Ages translated it back translated into Latin and then obviously eventually English and when I say that he did a rigorous March what Euclid did is he didn't just say oh I think the you know the what if you take the square of one side of a right triangle this is the length of one side of a right triangle and the length of the other side of the right triangle is going to be the same as the square of the hypotenuse all these other things and we'll go into depth about what all of these things are means he says I don't want to just feel good that it's probably true I want to prove to myself that it is true and so what he did in elements especially the six books that are concerned with planar geometry in fact he did all of them but from a geometrical point of view he started with basic assumptions so he started with basic assumptions and those basic assumptions and geometric speak are called axioms or postulates and from them he proved he deduced he deduced other statements or propositions or these are sometimes called theorems and then he says now I know if this is true and this is true this must be true and he could also prove that other things cannot be true so then he could prove that this is not going to be the true he did he didn't just say well every circle I've said has this property says I've now proven that this is true and then from there we can go and deduce other other propositions or theorems and we could use some of our original axioms to do that and what's special about that is no one had really done that before rigorously proven beyond a shadow of a doubt across a whole broad sweep of knowledge so not just one proof here or there for an entire for an entire set of knowledge that we're talking about a rigorous march through a subject so that he could build this scaffold of axioms and postulates and theorems and propositions and theorems of propositions are essentially the same thing and essentially for about two thousand years after Euclid so this is unbelievable shelf life for a textbook people didn't view you as educated if you had not read if you did not read and understand Euclid's elements and Euclid's elements the book itself was the second most printed book in the Western world after the Bible this is a math textbook it was second only to the Bible when the first printing presses came out they said okay let's print the Bible what do we print next let's print Euclid's elements and to show that this is relevant fair in into the fairly recent past although some would you know whether not you argue that about 150 hundred 60 years ago as the recent past this right here is a direct quote from Abraham Lincoln obviously one of the great American presidents I like this picture of Abraham Lincoln this is actually a photograph of Lincoln in his late 30s but he was a huge fan of Euclid's elements he would actually use it to find to in his mind he would while he was riding his horse he would read Euclid's element while he was in the White House you would read Euclid's element but this is a direct quote from Lincoln in the course of my law reading I constantly came upon the word demonstrate I thought at first that I understood its meaning but soon became satisfied that I did not I said to myself what do I do when I demonstrate more than when I reason or prove how does demonstration differ from any other proof so in Lincoln saying there's this word demonstration that kind of means something more more you know proving beyond doubt something more rigorous more than just simple you know kind of feeling good about something or reasoning through it I consulted Webster's dictionary so Webster's dictionary was around even around when Lincoln was around they told of certain proof proof beyond the possibility of doubt but I could form no idea of what sort of proof that was I thought a great many things were proved beyond the possibility of doubt without recourse to any such extraordinary process of reasoning as I understood demonstration to be I consulted all the dictionaries and books of reference I could find but with no better results you might as well have defined blue to a bot to a blind man at last I said Lincoln he's talking to himself at last I said Lincoln you can never you never can make a lawyer if you do not understand what demonstrate means and I left my situation in Springfield went home to my father's house and stayed there till I could give any proposition in the six books of Euclid at sight so the six books concerned with planar geometry I then found out what demonstrate means and went back to my law study so one of the greatest American presidents of all time felt that in order to be a great lawyer he had to understand to give any be able to prove any proposition in the sixth book of in the six books of Euclid's elements at sight and and also once he was in the lighthouse you continue to do this to make him in his mind to fine-tune his mind to become a great president and so what we're going to be doing in the geometry playlist is essentially that what we're going to study is we're going to think about how do we really tightly rigorously prove things we're essentially going to be in a slightly more modern form be studying what Euclid studied 2,300 years ago to really tightening our reasons to really tighten our reason to really tighten our reasoning of of different statements and being able to make sure that when we say something we can really prove what we're saying this is really some of the most fundamental real mathematics that you will do arithmetic was really just computation now in geometry and what we're going to be doing is really Euclidean geometry this is really about what this is really what math is about making some assumptions and then deducing other things from those assumptions