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All the Numbers - Numberphile

Numberphile Explainers intro
Open on YouTube First HN thread

6 HN users recommended this explainer in 6 different months between 2019 and 2025.

2007–2026
1 strong recommendation 6 recommendations 5 citations HackerTube score 6.5

HN recommends it as an accessible explanation of number categories and why almost all numbers are unknowable.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

Pull quote: “here's a video that explains from the basics what kinds of numbers exist” (HN, 2019)

Also tagged: types of numbers, transcendental numbers, normal numbers, computability, chaitin's constant, matt parker

What Hacker News said

12 labeled comments from the HN archive; up to 20 are kept per video, favoring different commenters. Each one links back to the original thread.

Strongly recommends ccvannorman August 2019 under Is e Normal?
Covers known numbers and the quest to define normal numbers
It's fascinating how little we know about everyday numbers like pi and e, it's widely assumed that they are normal but there is no proof for this (and it's extremely difficult to do so). In fact we believe the fast majority of numbers are transcendental and normal but we only actually know of a single normal number, and it is a manufactured number. Numberphile has an excellent video on the numbers we know about and the quest to find / define normal numbers: [this video]
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Recommends mjlee March 2019 under Famous Transcendental Numbers
Explains from basics what kinds of numbers exist
It feels like every time there's a mathematics post on the front page I post a video by Matt Parker. This time, here's a video that explains from the basics what kinds of numbers exist: [this video]
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Recommends KboPAacDA3 January 2020 under Chaitin's Constant
Explains relationships between number categories including Chaitin's Constant
Numberphile has a video explaining the relationship between the number categories, and includes a brief discussion of where Chaitin's Constant belongs. [this video]
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Recommends deepspace August 2020 under How real are real numbers? (2004)
Visualizes that we know essentially 0% of numbers
I found Matt Parker's video to be a good way to visualize the fact that we 'know' essentailly 0% of numbers: [this video]
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Recommends gcanyon October 2025 under The Unknotting Number Is Not Additive
Lays out classes of numbers; normal numbers vastly dominate
You might appreciate this video where Matt Parker lays out the various classes of numbers and concludes by describing the normal numbers as being the overwhelmingly vast proportion of numbers and laments "we mathematicians think we know what's what, but so far we have found none of the numbers." [this video]
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Citations, criticism and jokes

Cites it jerf August 2019 under Calculus Is Deeply Irrational
Shows we can name barely any of the numbers
It's worse than you make it sound, though: [this video] In short, it isn't just that we have more computables than non-computables; there are categories of numbers like "normal" that nominally contain "all the numbers" but we can barely even name a handful.
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Cites it Arnavion September 2024 under Memorizing the first 100 perfect squares (2022)
Relevant to normal numbers and proving pi normal
Such numbers are called "normal numbers". Pi likely is one based on all the digits we've computed for it, but we don't have any way to prove a given number like pi is normal or not. Relevant Numberphile video: [this video]
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