Tree-house Numbers - Numberphile

11:45 "At least I tried" brady zooms in on the parker square that just feels mean...

I like when "soon on Numberphile" means "now on Numberphile but you have to click on a link in the description."

e^(π√163) is a Parker integer.

"The integers are a field" ah yes, a Parker field

When is Matt gonna write a book called "Things to make and do with terrible Python code"?

that zoom on the end was hilarious

e^π(√-1) gives -1.0000000000000, which is arguably closer to an integer than e^(π√163)

8:29 The true journey of mathematics is the stunning joy of discovering something only to realize someone did it before...

"The integers are a field"... Such a Parker thing to say

The Caboose numbers fizzled out: I wasn't impressed. The treehouse numbers give near integers: I wasn't impressed. Matt finds a connection between the two: I WAS SUPER IMPRESSED. Matt reveals he didn't find that connection: I wasn't impressed. Matt gives a little talk on the connection: I was impressed again.

Brady seems to have forgotten that he's already made a video about these numbers 12 years ago, it was titled '163 and Ramanujan Constant'.

Recommendation to the new viewer: They say at the start of the video that you don't need to see the first video, and that is true, but the conclusion of this video is deeply pleasing if you watch the other video first.

Maths God to Euler and Ramanujan: "Why is it always the two of you if something mathemagically strange happens?"

"At least you tried." Zooms in on the Parker Square. savage.

I think that Matt might have misspoken at 10:20. The integers do not constitute a field as they aren't closed under taking multiplicative inverses (dividing two integers generally does not result in an integer). Matt was probably thinking of the rationals or the reals

"The integers are a field." - Matt Parker, 2024

“Just off the top of my head” … camera points to the top of Matt’s head

Wait, this wasn't found by Ramanujan! Wolfram Mathworld says: Although Ramanujan (1913-1914) gave few rather spectacular examples of almost integers (such e^(pisqrt(58))), he did not actually mention the particular near-identity given above. In fact, Hermite (1859) observed this property of 163 long before Ramanujan's work. The name "Ramanujan's constant" was coined by Simon Plouffe and derives from an April Fool's joke played by Martin Gardner (Apr. 1975) on the readers of Scientific American. In his column, Gardner claimed that e^(pisqrt(163)) was exactly an integer, and that Ramanujan had conjectured this in his 1914 paper. Gardner admitted his hoax a few months later (Gardner, July 1975).

"Suspiciously close to an integer" is my new favorite maths term of all-time 😂 I mean, just the pure, firm rigor of the concept 😂😂

This epiphany happened for me in discovering a recurrence relation for multiplicities of eigenvalues in the stochastic matrices generated by the move-to-front rule for the linear search problem. I still remember the moment and it was over 30 years ago. Mathematics is the best.