# Dr. Robert Kaplan: "Mathematics: Learning to Speak our Lost Native Language" | Talks at Google

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Yeah. Please sorry, races. But I think our problem is that we yeah we've, been going across. Yeah, well. I didn't. I didn't, realize so, I was just estimating, that that might be the problem because. I like to ask to me. Well. I like your estimate above a hundred a while ago by, the way after, you. Asked, a long time ago, is. This gonna be geometry. This might be. Arithmetic. Instead, of geometry, I don't know ah sure. And then Petra I don't. Think this really counts though so, oh. So. Far. That is backward. Of something that I think dia did. Now. Zigzagging. Stop. You'll you'll never get into the lift. Great. Yes. I've. Got a funny. Question to ask before Petra, and Leia. How. Big is this board. Namely, how many squares. 5-squared. True, what. Is 5 squared it's, 25. It's. 25. What. Kind of a number is 25, possibly. It's. A square number and some odd number it's an odd number squared. It's. An odd number. Can. I go back to Nathan's. 2x2. Board, 2x2. Is what. What's. 2 times 2 this is very difficult I know but more. Or less for I mean you estimate so it's the kind of four and on, two by two boards, a board. With four. Squares. Can. We start from here will it work can. We start from here here. Here. Dear. And. The reason the 2 by 2 works, is that there's, no square in the middle of, their, two corner pieces 4. Wow. So. A 3x3. Would. Or wouldn't. 3x3. There's. That little square. 3. By 3 is trouble 5. By 5 is trouble. What's. 729. By 729. Trouble, or easy. Oh. You. Start from the first square no oh you're, from the second squared. Oh, actually. No yeah right. Starting. From the second. Square. On. An odd number. Board. Is. Trouble. Why. Petra. There, probably is a way to do it but. It's. Hard to find that's. Great if there's probably a way to do it but it's hard to find after you're saying there's just no way to find it no matter how you try five. Whole minutes oh, say. It ah sure so I'm, just gonna okay. Good so, if you start from here. You. Can't really do. Anything about it because there's. There's. Always gonna be this extra. Corner. And if you try to eliminate that corner. Middle. Pieces is not gonna work see so. Here right won't work right because. You. Have to once, you get to like when, do to the point where it's, either a. Corner. Or the center. You're. Always gonna get there you, have to you have to only go to one that's, terrific. It's gonna leave the center. Out. Or, just, one. Of the corners is, a 6x6 board gonna work or not it, will because, it's, and a 7x7. Right. You, dear, that's terrific, it's. Getting. Even number by an even, number then, it's going to work because. Like. The. Reason. There's. No middle there's no middle square, so whatever you do it won't cross that one odd square. That. One what square I square, that. One odd square. On a 25, square. Board 555. How. Many odd number squares are there and how many even number squares.

We Said right, on voice, not ever right yeah, and. Then Ellen said, if. Only there were a nice. Way of doing it a beautiful way of doing it they. Said yeah hopefully, a big. Fat, chance. And I just. Something you, know different, way of counting, it, voice. Over there, you. Could do ten bonds. That's. What what are ten bonds talk. About new terminology. So. You know one plus 9 is 10 + and + 3 plus 8 is 10 no you idiot says, this guy to, fuss 8 is 10 so, we got 10 bonds yeah we've gotten several well. Four. Or five 10. Bonds then we've run out of 10 bonds, so, is that we could make 20, bonds, you. Know 1 + 19's, and no we've already used the one in the 10 vote ah it's, hopeless, and, they're. Getting they're getting a physically, quite restless and we're sweating, and then. A little, guy of the back of the room who hadn't said a word after, that point said I know this, is wrong but which is always the preface, to the inside he. Said I know this is wrong, but. 1 plus, 20. Is 21, and so, is 2 plus 19, and I saw a sheer, luck, he, said no another. Voice I said no it's not sure Lots they're all 20 ones, what. Do you mean they're all 20 ones they're. All all, of them are 20 ones, Oh what, so, it says all those numbers, all those 20 numbers are 21, no. Says the voice over here all those thingies. Are. 21. What. Do you mean thingies the the figis. Someone. Says pairs oh, all. The pairs are 21. So. I said well how, many pairs are there someone. Says there are 10. 210. High-fives. All around the room can. We do another I see yeah what's this Ellen said what's the Sun from 1 to 100 it's. 5050. Give. Us another we. Did this for whole hell at, the end they said what. Do you call this we. Said math. Start. With. Something which is. Below. Beneath, the, audience's, dignity, and then. Hit them with the mystery. Which. Turns, out to be accessible. And. They. Are slaves to math for life. You.

2019-01-15 18:23

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The pairing solution at the end was allegedly worked out by another smart school kid - Gauss who didn't want to get bored when his teacher asked the class to sum the numbers from 1 to 100. Which maybe proves that once kids start having fun by exploring the shape of a problem, they are already half way to being mathematicians. Perhaps Pythagoras started having fun with the same problem when he was a kid by representing the numbers with rows of stones and arranging them into a triangle.

Ends with great words: "Start with something which is beneath the audience's dignity, and then hit them with the mystery which turns out to be accessible and they are slaves to math for life".

i am gonna ask my dad to dress like him or i won't love him anymore

It looks decades old video, as they r using chalks n blackboard n mic . It looks like been recorded in 90's. Very good though

It is not decades old - it was recorded in 2018.

Very great teacher . I wish I'd one when I was in my childhood. We want more such videos, on learning maths a fun way ...

I guess the answer is 10,368 for 5x5 matrix . Cause, we have 4 squares with two paths(4 corners) X 12 squares with 3 paths X rest 9 squares with 4 paths = 4 x 2 x 12 x 3 x 9 x 4 = 10,368. You can check this is a right proof using proof by induction approach. in the simple term just take 2 x 2 matrix. Now, all squares have 2 paths so 4 x 2 = 8. it is correct for 2X2 matrix then we will assume that it will also work for the above solution...

I am guessing the problem has its roots and meaning in the Koenisgberg Bridge Problem that Euler solved eventually, but can't seem to realise how starting on the 2nd square maps to Euler's theory.

Smart kids. Wish I got involved with something like this when I was younger

That's how a mathematician ought to look like!

A ten dimensional cube has 1024 corners right? A square, a 2d cube, has 4 or 2^2 corners. A 3d cube has 8 or 2^3 corners, so it follows that a 10d cube has 1024, or 2^10 corners.

Grandpa

one of the best comments on maths learning appears here 47:21

It's over 9000!

625 ways i think by watching until 28 minute

+आदित्य Aditya मेहेंदळे Mehendale I watched till the end now. How much do you think is the answer

So you missed the "has to be an even number" part?

I feel privileged to have watched and learned from such a great teacher. Thanks Google

Privilege!!!

1st commenter and viewer.

Mahendra kumar congrats

You should have brought regular children.

6250 ways of doing

Fantastic

this is really beautiful. Mr. Kaplan is so humble, empathetic, brilliant and amazing teacher

good job

He used cardinals instead of ordinals when pointing at each square. Why do MATHEMATITIANS make this mistake? 0_o And digits are not numbers. Maaaaan!!!!

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@आदित्य Aditya मेहेंदळे Mehendale I watched till the end now. How much do you think is the answer

Who are these kids.Brilliant

Yes, nice problem, simple resolution.....