All the Numbers - Numberphile
Why Hacker News recommends it
HN recommends it as an accessible explanation of number categories and why almost all numbers are unknowable.
What it is
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.
Recommended by 6 HN commenters across 6 different months, 2019 to 2025.
What Hacker News said
Strong rec ccvannorman · 2019-08 · on “Is e Normal?”
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]
Recommends StrangeDoctor · 2019-03 · on “Calculating a record-breaking 31.4T digits of Pi with GCP”
That's actually most numbers, but we don't know any yet. [this video] numberphile (math YouTube series) describing some related concepts here.
Recommends mjlee · 2019-03 · on “Famous Transcendental Numbers”
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]
Recommends KboPAacDA3 · 2020-01 · on “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]
Recommends deepspace · 2020-08 · on “How real are real numbers? (2004)”
I found Matt Parker's video to be a good way to visualize the fact that we 'know' essentailly 0% of numbers: [this video]
Recommends gcanyon · 2025-02 · on “The number line freaks me out (2016)”
This video parallels the article, going further. I love the tag line, "We know none of the numbers." [this video]
Recommends gcanyon · 2025-10 · on “The Unknotting Number Is Not Additive”
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]
Cites jerf · 2019-08 · on “Calculus Is Deeply Irrational”
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.