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Although unlikely, maybe there exists a solution where all black pieces are protected?

Tom Rokicki fascinatingly explains the story behind calculating the maximum number of moves needed to solve Rubik's cube. Video: https://youtu.be/0FAYWovO2Cc

In a Numberphile video [0], Alex Bellos also uses a triangle for 5.

[0]: https://www.youtube.com/watch?v=9p55Qgt7Ciw

ab = 37; a+b = 18; 1/a + 1/b = b/ab + a/ab = (a+b)/ab = 18/37

Donald's novel "Surreal Numbers" was written during one week of a long stay in Norway [0]. So, maybe there he got his admiration for traditional Sami clothing.

[0]: https://youtu.be/jB0aeePskBg

A "wright of passage", a "craftsperson of passage", someone who facilitates or creates transitions -- like a metaphorical bridge-builder

In French, the bear is killed. In Spanish, he is chased. In Dutch, he is shot. The Spanish look adventurous, and the French straight-forward.

A fellow mathematical sculptor is Carlo Séquin [0]. Also Jos Leys' mathematical imagination is an explorative wonderland [1].

[0]: https://people.eecs.berkeley.edu/~sequin/ [1]: https://www.josleys.com

People are misunderstanding the meaning of an off-by-one error. Suppose the plan states that hold A and hold B need to be 11 holes apart. In the true spirit of the off-by-one error, this can be interpreted in 3 ways:

- either as 11 empty holes between the holds; - as 11 holes, start counting 1 just above hold A; - or as 11 holes, start counting with hold A as number 1.

Another real-life example, is a plumber who tells the construction worker that the distance between the holes for hot and cold water needs to be 15 cm. This was meant to be measured center to center, but the constructor worker interpreted it as the distance from the right side of the first hole to the left side of the second. The result can still be admired in our house, 10 years later.

Discussion: https://news.ycombinator.com/item?id=40981272 There are 6 comments; the last one is clearly the most interesting: a link to a discussion by Terence Tao https://mathstodon.xyz/@tao/112557249982780815

Terence Tao also provides links to a presentation by James Maynard and Larry Guth: https://www.ias.edu/video/new-bounds-large-values-dirichlet-... and https://www.ias.edu/video/new-bounds-large-values-dirichlet-...

A preprint: https://arxiv.org/abs/2311.18295

See the discussion at https://news.ycombinator.com/item?id=41036526

The sentence game would be more interesting, if you'd add in 2-letter words. be - go - he - hi - ho - is - oh - Oz - so

He loses his high ego, he sizzles, he begs. He seizes his bible.

The real curve has the fraction inverted:

y ≤ x / (x+t)

This equation only fits the first part of the curve, i.e. x ≤ 1-t. Here t is a time parameter, ranging from 0 at the start to 1 when everything is fully sorted.

The other videos created by the same author are equally impressive, beginning with straightforward explanations and gradually advancing to complex topics such as gamma and digamma functions [0]. These videos fully grasp the capabilities of Grant Sanderson's Manim library to enhance their visual appeal and educational value [1].

[0]: https://www.youtube.com/watch?v=v_HeaeUUOnc [1]: https://github.com/ManimCommunity/manim

You may want to familiarize yourself with the parable of the broken window.

[0]: https://en.wikipedia.org/wiki/Parable_of_the_broken_window

Donald Knuth seems to be quite fond of Scandinavia. He did a sabbatical in Norway, where he also wrote a children's book: "Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness." Knuth's ancestors moved during the 19th century from Germany to the US. His father's family lived close to the Danish border [1].

[0]: https://www.youtube.com/watch?v=jB0aeePskBg&list=PLVV0r6CmEs... [1]: https://www.youtube.com/watch?v=VnoFvUnL6xU&list=PLVV0r6CmEs...

The same paradox is also featured prominently as part of a Mathologer video [0] and an article in Scientific American [1].

[0]: https://youtu.be/oEN0o9ZGmOM?t=523s

[1]: https://www.scientificamerican.com/article/the-sat-problem-t...

The coin around coin problem has its own wikipedia page, although some people want to delete it:

https://en.wikipedia.org/wiki/Coin_rotation_paradox

> 39. Re graphics: A picture is worth 10K words - but only those to describe the picture. Hardly any sets of 10K words can be adequately described with pictures.

How does this need to be rewritten in the sight of Dall-E, Midjourney and friends?

LLMs are especially fit for teaching students to formulate good questions. As LLMs have an endless patience, bad and boring questions anymore won't exist anymore.

French might have evolved as a latinized version of the Basque language.

See also this previous discussion:

https://news.ycombinator.com/item?id=16542395

Well, in some countries, instead of clapping two hands, people clap on tables or armchairs.

Wouldn't being innocently jailed for 9 days because of a wrong face recognition count as another example?

[0]: https://www.wired.com/story/face-recognition-software-led-to... [1]: https://www.theguardian.com/us-news/2023/apr/27/california-p...

Also interesting is the 1999 animated short film (20 min), "The Old Man and the Sea" (based on Hemingway's novel). Subtle fingertips moved around oil paint on glass.

  [0]: https://en.wikipedia.org/wiki/The_Old_Man_and_the_Sea_(1999_film)
  [1]: https://youtu.be/W5ih1IRIRxI

Well, this is just a first version, enabling to quickly prove they are the first. The coming days, the internets will be filled with many more webpages than can be possibly read. In the old days, you had to wait many months before something went from found to officially published.

Even if the lawyer would have carefully checked and corrected ChatGPT's answers, isn't he going against his professional duty by submitting private information to a website that doesn't ensure confidentiality?

It's called Lèse-majesté (in English, that is). It is still actively persecuted in Spain [0], forcing Belgium to reinterpret its current laws in order not to extradite a rap singer.

[0]: https://en.wikipedia.org/wiki/L%C3%A8se-majest%C3%A9#Spain

Claude Shannon also had early ideas about machine learning. AT&T has a 1950s video of the maestro himself demonstrating a maze solver with physical output. A true genius. In those days, geeks were dressed in suit.

0: https://techchannel.att.com/play-video.cfm/2010/3/16/In-Thei...

A really strong point is how Grant manages to explain the basic concepts, that most viewers already know in some way, in such a way that it doesn't sound like repeated general knowledge. Every time he adds in lesser known facts. A concept gets defined, but in that definition starts a roller coaster of related facts. Sometimes a little history gets mixed in, and almost magically an entertaining story is created.