How to pronounce “hilbert” in English

- Hilbert's Hotel is a hotel with infinitely many rooms.

Hilbert's Hotel, it violates Euclid's principle.

Hilbert space is the name we attach to the space of all possible wave functions.

Hilbert-- there's a quote here.

of Hilbert's Hotel becomes kind of clear.

when Hilbert wanted all of mathematics to be formalized.

of Hilbert space, the space of all the possible wave functions?

The Hilbert problems set forth at the beginning of the 20th century for mathematicians to work on.

where Hilbert gives his arousing speech declaring war on uncertainty.

when I teach Hilbert's Hotel in class, I always demand that the students provide, you know, the explanation of- of how to do it.

bit earlier with Hilbert's program.

and the Hilbert program.

Russell and Hilbert paragons of of of of sanity.

schizophrenic grandsons and even Hilbert had a schizophrenic son.

it's just exactly the same as Hilbert's train again, because every fraction consists of two integers: the numerator and the denominator.

How many people know what vectors in Hilbert space are?

And Noether was invited by David Hilbert and Klein to go to Gottingen to explain it.

familiar with this metaphor this is Hilbert's the Hilbert hotel.

a set is countable if it fits into Hilbert's Hotel, 'cause Hilbert's Hotel basically is the set of natural numbers in terms of the room numbers.

arrives, and Hilbert's train has infinitely many train cars...

And people like me think that quantum gravity implies that the Hilbert space is actually finite-dimensional.

I mean, Hilbert was this incredible advocate for her, but he was very unsuccessful for a very, very long time.

the greatest mathematician of the time was David Hilbert uh who for 30 years

In the audience, legendary mathematician David Hilbert was intrigued.

- Yeah, let's talk about Hilbert's Hotel.

But one can go on with Hilbert's Hotel, for example.

There's another famous quote of Hilbert in his retirement address where, he proclaims, "Wir müssen wissen, wir

That was just a thought experiment he uses to solve one of Hilbert's mathematical questions about whether all problems are

in which these quantum wave functions live are this crazy thing called a Hilbert vector space, right?

- That is until, in 1900, German mathematician David Hilbert addressed the International Congress of Mathematicians, in Paris.

It was exactly equivalent to the Bianchi identities, the half-solution Hilbert had found.

going to talk about countable sets, then I would suggest that we talk about Hilbert's Hotel, which really makes that idea perfectly clear.

- You separate the hotel into even and odd rooms, and you squeeze in the new Hilbert bus people into the odd rooms and the previous occupants

equinumerous with a set of natural numbers is just the same thing as to fit into Hilbert's Hotel.

more elements in terms of its size because it's still just a countable infinity and it fits into Hilbert's Hotel.

And, and Hilbert was famously supportive of set theory.

I guess, actually, Hilbert famously said that he thought mathematics was just a game in which you're playing with symbols.

For simple systems like an electron in nonrelativistic quantum mechanics or quantum field theory, Hilbert space is almost always infinite-dimensional.

It's just that many-worlds lets the wave function be wherever it wants to be in Hilbert space.

But basically, all of these Gaussians are vectors in Hilbert space, right?

One of the great examples was David Hilbert, who's arguably the most influential mathematician of the 20th century.

She became only the second woman in Germany to earn a PhD in mathematics, and she used this expertise to help Hilbert

With one paper, she had uncovered the source of all conservation laws, and she had solved the problem in general relativity that eluded Hilbert and Einstein.

But on the following weekend, a giant bus pulled up, Hilbert's bus. And Hilbert's bus has, of course,

And when I talk about Hilbert's Hotel,

And a kind of easy way to understand what that's saying in terms of Hilbert's Hotel is that

So there's another way to push this a bit harder, and that is when Hilbert's train

And so we have an infinity of infinities of the train passengers together with the current occupants of the hotel, and everybody on the train wants to check in to Hilbert's Hotel.

And so Hilbert said, "Well, look, we have to fix this