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#computablenumbers#transcendentalnumbers#chaitin'sconstant

All the Numbers - Numberphile

Numberphile

4.7M subscribers • 28 videos on Hallway

YouTube
  • Recommended by 6 people: 6 on Hacker News.
  • A classic. People kept recommending it from 2019 to 2025.
  • Presented by Matt Parker, mathematician and author

Beginner. No background in the topic needed.

1.8M views7 years ago6 recommendations

Computer scienceComputation and complexityMath for programmers

Matt Parker explains the hierarchy of numbers, from algebraic and transcendental to computable and normal numbers, showing how few we can actually describe.

Matt Parker talks about numbers - as he often does. His book "Humble Pi" is at: bit.ly/Humble_Pi More links & stuff in full description below ↓↓↓ The book on Amazon: amzn.to/2NKposg Numberphile podcast is on your podcast player. Or the website is: numberphile.com/podcast And it's on YouTube too: bit.ly/Numberphile_Pod_Playlist The Knight's Tour T-Shirt is in our Teespring store: teespring.com/stores/numberphile A bit of extra footage from this interview: youtu.be/LsBQhfkw5ag More videos with Matt: bit.ly/Matt_Videos Transcendental Numbers with Simpon Pampena: youtu.be/seUU2bZtfgM The Mile of Pi: youtu.be/0r3cEKZiLmg Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. simonsfoundation.org/outreach/science-sandbox/ And support from Math For America - mathforamerica.org/ NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Videos by Brady Haran. Editing of this video by Pete McPartlan. Patreon: patreon.com/numberphile Numberphile T-Shirts: teespring.com/stores/numberphile Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Yes we went for the sometimes English spelling constructable... Constructible is more common and probably better!

Why it's here

6 people recommend this

What people say. Recommended as an excellent, intuitive visualization of the different categories of numbers and how little we know about most of them.

ccvannormanon Hacker News • Recommends

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: link to this video

StrangeDoctoron Hacker News • Recommends

On “Calculating a record-breaking 31.4T digits of Pi with GCP”

That's actually most numbers, but we don't know any yet. link to this video numberphile (math YouTube series) describing some related concepts here.

mjleeon Hacker News • Recommends

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: link to this video

KboPAacDA3on Hacker News • Recommends

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. link to this video

deepspaceon Hacker News • Recommends

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: link to this video

gcanyonon Hacker News • Recommends

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." link to this video

gcanyonon Hacker News • Recommends

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." link to this video

jerfon Hacker News • Mentions

On “Calculus Is Deeply Irrational”

It's worse than you make it sound, though: link to 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.

Beldinon Hacker News • Mentions

On “An intutive counterexample to the axiom of choice”

See also this Numberphile video on numbers, including algebraic, computable, transcendental, and talking about numbers beyond those. link to this video

Arnavionon Hacker News • Mentions

On “Memorizing the first 100 perfect squares (2022)”

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: link to this video

globular-toaston Hacker News • Mentions

On “The number line freaks me out (2016)”

I wonder if this was the inspiration for this numberphile video? link to this video The video does go further than the article.

ccvannormanon Hacker News • Mentions

On “What can be computed? A practical guide to the theory of computation (2018) [pdf]”

corollary: Numberphile (with Matt Parker of Stand Up Maths) - "All the Numbers". Most are incomputable, of course :) 0 link to this video