Translator: Tomás Guarna Reviewer: Gisela Giardino You can imagine: You're in a bar, or, you know, a disco, like that, and you start talking to a girl, and after a while this comes up in the conversation: "and what do you do? " And as you think your job is interesting you say: "I'm a mathematician. " (Laughter) 33.
51 % of girls (Laughter) in that moment pretend to get an urgent call and leave. (Laughter) And 64. 69 % of girls desperately try to change the topic and leave.
(Laughter) There's a 0. 8 % made up by your cousin, your girlfriend and your mother (Laughter) that knows you work in something weird but don't remember what (Laughter) and there's a 1 % that follows the conversation. When that conversation follows, invariably in some moment, one of these two phrases shows up: A) "I was terrible at math, but it wasn't my fault, it's that the teacher was horrendous.
" (Laughter) And B) "But that math thing, what is it for? " (Laughter) I'll deal with case B. (Laughter) When someone asks you what math is for, they're not asking you about the applications of mathematical sciences.
They're asking you: "And why did I have to study that bullshit I never used again in my life? " (Laughter) That's what they're asking you really. Given this, when they ask a mathematician what math is for, us mathematicians split in two groups.
A 54. 51 % of mathematicians assumes an attacking posture, and a 44. 77 % of mathematicians assumes a defensive posture.
There's a strange 0. 8 %, among which I include myself. Who are the ones who attack?
The attacking ones are mathematicians that tell you the question makes no sense, because mathematics have their own sense by themselves, they're a beautiful edification with its own logic built by itself and that there's no use in one always looking after the possible applications. What's the use of poetry? What's the use of love?
What's the use of life itself? What kind of question is that? (Laughter) Hardy, for example, is an exponent of this attack.
And those who stand in defense tell you that even if you can't notice, dear, math is behind everything. (Laughter) They always name bridges and computers, always. If you don't know math, your bridge falls off.
(Laughter) In reality computers are all about math. Now these guys always happen to tell you that behind information security and credit cards are prime numbers. These are the answers your math teacher will give you if you ask him.
Those are the defensive ones. Okay, but, who's right then? Those who say math doesn't need to be useful at all, or those who say that it's really behind everything?
In reality both are right. But I told you I'm of that strange 0. 8 % that says something else, right?
So, go on, ask me what math is for. (Audience asks the question) Okay! A 76.
34 % of people have asked, there's a 23. 41 % that shut up, and a 0. 8 % that I don't know what those guys are doing.
Well, dear 76. 31 %, it's true that math can be useless, it's true that it's a beautiful edification, a logical one, one probably one of the greatest collective efforts the human being has ever made along history. But it's also true that there where scientists, where technicians, are looking for mathematical theories, models that allow them to advance, there they are, in the edification of math, which permeate everything.
It's true that we have to go somewhat deeper, we're going to see what's behind science. Science works by intuition, by creativity, and math dominate intuition and tame creativity. Almost everyone who hasn't heard it before is surprised by the fact that if one took a sheet of paper 0.
1 mm thick, one of those we use normally, big enough, and that I could fold 50 times, The thickness of that pile would take up the distance from the Earth to the Sun. Your intuition tells you: "Impossible. " Do the math and you'll see it's right.
That's what math is for. It true that science, all science, not only has a purpose because it makes us understand better the beautiful would we're in. And because it does, it helps us avoid the traps of this painful world we're in.
There are sciences that grasp this very application. Oncological science, for example. And there are others we look from afar, with some jealousy sometimes, but knowing we are what supports them.
All the basic sciences are the support of them, and among these is math. All that makes science be science is the rigor of math. And that rigor belongs to it because its results are eternal.
Probably you said before, or you were told sometime, that diamonds are forever, right? It depends on what one understands by forever! A theorem, that really is forever!
(Laughter) The Pythagorean theorem, that is still true even if Pythagoras is dead, I'm telling you. (Laughter) Even if the world collapsed the Pythagorean theorem would still be true. Wherever any two sides and a good hypotenuse get together (Laughter) the Pythagorean theorem works to the max.
(Applause) Well, us mathematicians devote ourselves to making theorems. Eternal truths. But it isn't always easy to know what is an eternal truth, a theorem, and what is a mere conjecture.
You need a demonstration. For example: imagine you have a big, enormous, infinite field. I want to cover it with equal pieces, without leaving any gaps.
I could use squares, right? I could use triangles. Not circles, those leave little gaps.
Which is the best piece I can use? The one that to cover the same surface has the smallest border. Pappus of Alexandria, in the year 300 said the best was to use hexagons, like bees do.
But he didn't demonstrate it! The guy said "hexagons, great, come on, hexagons, let's go with it! " He didn't demonstrate it, he stayed in a conjecture, he said "Hexagons!
" And the world, as you know, split into pappists and anti-pappists, until 1700 years later, 1700 years later, in 1999 Thomas Hales demonstrated that Pappus and the bees were right, the best was to use hexagons. And that became a theorem, the honeycomb theory, that will be true forever forever and ever, for longer than any diamond you may have. (Laughter) But what happens if we go to 3 dimensions?
If I want to fill the space, with equal pieces, without leaving any gaps, I can use cubes, right? Not spheres, those leave little gaps. (Laughter) What is the best piece I can use?
Lord Kelvin, the one of the Kelvin degrees and all said, he said that the best was to use a truncated octahedron (Laughter) that as you all know (Laughter) is this thing over here! (Applause) Come on! Who doesn't have a truncated octahedron at home?
(Laughter) Even if it's plastic. Kid, bring the truncated octahedron, we have guests. Everybody has one!
(Laughter) But Kelvin didn't demonstrate it. He stayed in a conjecture, Kelvin's conjecture. The world, as you know, split between kelvinists and anti-kelvinists (Laughter) until a hundred-and-something years later, a hundred-and-something years later, someone found a better structure.
Weaire and Phelan, Weaire and Phelan found this little thing over here, (Laughter) this structure they put the imaginative name of the Weaire-€“Phelan structure. (Laughter) It seems like a strange thing but it isn't that strange, it's also present in nature. It's very curious that this structure, because of its geometric properties, was used to build the swimming building in the Beijing Olympic Games.
There Michael Phelps won 8 gold medals, and became the best swimmer of all times. Well, of all times until someone better comes along, no? As it happens to the Weaire-€“Phelan structure, it's the best until something better shows up.
But be careful, because this one really has the opportunity, that if a hundred-and-something years pass, even if it's in 1700 years, someone demonstrates that this is the best piece possible. And then it will be a theorem, a truth forever, forever and ever. For longer than any diamond.
So, well, if you want to tell someone you'll love them forever (Laughter) you can give them a diamond, but if you want to tell them that you'll love them forever and ever, give them a theorem! (Laughter) However, you'll have to demonstrate, that your love doesn't stay a conjecture. (Applause) Thank you.
