The Aperiodical
aperiodical.com · Group blog · on HN since 2012
The Aperiodical is a group blog on recreational and popular mathematics, with news, puzzles, book reviews and commentary on proofs.
What HN saysHN links it for math news such as the aperiodic monotile and Riemann hypothesis claims; commenters also cite its book reviews and articles.
47HN people shared it
21linked it in comments
78stories submitted
742story points
10 months agolast shared
2012people per year2026
Most-shared posts
- 1Richard K. Guy (1916-2020)3 people · 14 points · first shared 2020 · 2 comments on HN
- 2Riemann Hypothesis not proved3 people · 11 points · first shared 2015 · discussion on HN
- 3A Mathematician’s Guide to Wordle3 people · 5 points · first shared 2022 · discussion on HN
- 4Now I’m calculating with constructive reals2 people · 115 points · first shared 2022 · 70 comments on HN
- 5Are you sure 51 isn’t prime? – Analysing results of the “Is this prime?” game2 people · 9 points · first shared 2016 · 3 comments on HN
- 6Atiyah Riemann Hypothesis proof: final thoughts (2018)2 people · 4 points · first shared 2018 · 1 comments on HN
- 7Aperiodical2 people · 4 points · first shared 2013 · discussion on HN
- 8An Aperiodic Monotile Exists!2 people · 1 points · first shared 2023 · discussion on HN
- 9An Alan Turing Expert Answers Your “The Imitation Game” Questions2 people · 1 points · first shared 2014 · discussion on HN
- 10The answer to the question “what is (-80538738812075974)³+80435758145817515³+2 people · 1 points · first shared 2019 · discussion on HN
- 11Classic maths books reset with LaTeX on Project Gutenberg1 people · 227 points · first shared 2012 · 28 comments on HN
- 12Alan Turing’s “Can Computers Think?” Radio Broadcasts Re-Recorded1 people · 136 points · first shared 2018 · 33 comments on HN
- 13PrimeGrid has found a new largest generalised Fermat prime1 people · 43 points · first shared 2017 · 7 comments on HN
- 14A Puzzle about a Calculator1 people · 31 points · first shared 2024 · 13 comments on HN
- 15Calculating π by Bouncing Balls in Phase Space1 people · 24 points · first shared 2015 · 1 comments on HN
What HN people wrote when they linked it
rramadass · 2024-12-15
There is also Guesstimation 2.0 by the same authors which is a sequel to Guesstimation and is just as good.
Also see Maths on the Back of an Envelope: Clever ways to (roughly) calculate anything. by Rob Eastaway - https://aperiodical.com/2019/11/review-maths-on-the-back-of-an-envelop…
Related is How to Read Numbers: A Guide to Statistics in the News (and Knowing When to Trust Them) by Tom Chivers and David Chivers - https://en.wikipedia.org/wiki/How_to_Read_Numbers
Finally, the old Soviet books by Yakov Perelman (https://mirtitles.org/?s=Yakov+Perelman) named Physics for Entertainment, Mathematics for Fun etc. also fall under the same category and are a good read.
Bonus: https://en.wikipedia.org/wiki/Back-of-the-envelope_calculation Follow other links like "Guesstimate" from the "See also" section.
dwilding · 2018-03-10
I love your explanation of how to arrive at the vector transformation function. You might enjoy reading an article I wrote a few years ago that touches on maxtrix/vector computation of linear recurrences:
http://aperiodical.com/2014/06/discovering-integer-sequences-by-dealin…
Not as detailed as your post though. Thanks for a great write up!
lupire · 2024-08-26
At timestamp 30:00 he talks about hyperlinked drill down proofs, as the format of textbooks of the future.
Leslie Lamport begged everyone to do this 7 years ago (paper and video linked from blog post [1]), based on his TLA-backed speech on a similar topic 30 years ago [2]
and I'm sure it goes back further. Proof wiki also does this, in part.
[1] https://aperiodical.com/2017/09/hlf-blogs-leslie-lamport-thinks-your-p…
[2] https://www.microsoft.com/en-us/research/publication/how-to-write-a-pr…
Aside, it's encouraging to see that someone with poor public speaking ability can still become a top mathematician and mathematical writer.
guyomes · 2024-05-31
You can fold a paper to get a torus [1]. With those foldings, the distances on the torus embedded in 3D are the same as the distances on the flat paper.
It is even theoretically possible to embed the flat paper as a torus in 3D with a C^1 surface, without polyhedral edges [2,3]. However, this surface has a fractal structure.
Finally, any torus surface embedded in 3D that is at least C^2 (with a continuous second derivative) will nessecarily stretch some distances [4].
[1]: https://www.imaginary.org/hands-on/diplotori-flat-polyhedral-tori
[2]: https://aperiodical.com/2012/05/torus/
[3]: https://www.pnas.org/doi/full/10.1073/pnas.1118478109
[4]: https://math.stackexchange.com/questions/2291382/c2-isometric-embeddin…
saint_abroad · 2023-06-23
2 months later we have the "Spectre" - an aperiodic monotile (without reflections): https://aperiodical.com/2023/05/now-thats-what-i-call-an-aperiodic-mon…
Edit - a visual explanation of this journey: https://www.youtube.com/watch?v=IfVwelta1fE
tromp · 2023-03-23
Yes, this article goes more into the attire aspects:
https://aperiodical.com/2023/03/an-aperiodic-monotile-exists/
robinhouston · 2023-01-14
If anyone's interested in more context on that particular equation, here's an article I wrote for The Aperiodical at the time: https://aperiodical.com/2019/09/42-is-the-answer-to-the-question-what-…
hackandthink · 2022-11-29
This is a nice article:
https://aperiodical.com/2022/03/now-im-calculating-with-constructive-r…
O__________O · 2022-07-24
To be fair, hexagons alone are unable to form a sphere like surface:
https://m.youtube.com/watch?v=btPqKAGyajM
And of course the odd response from the UK government to the above petition was to basically say having a realistic football signs would increase the odds of accidents, lol:
https://aperiodical.com/2017/10/standupmaths-petition-has-had-a-respon…
greenyoda · 2022-02-11
Some HN discussion of that video a few days ago: https://news.ycombinator.com/item?id=30232413
Also, this interesting article was posted to HN the other day:
A Mathematician’s Guide to Wordle
https://aperiodical.com/2022/02/a-mathematicians-guide-to-wordle
kwhitefoot · 2021-08-13
RIP Richard K. Guy
https://aperiodical.com/2020/03/richard-k-guy-1916-2020/
JNRowe · 2021-02-23
Perhaps it was the example you were thinking of, but Christopher Danielson really brings home the extreme ambiguity of terms using vehicles and children.
I keep coming back to that every time I'm trying to have one of these conversations with people, especially when the question is deeper than whether a salad is a vehicle(as if that were possible).
https://talkingmathwithkids.com/blog/vehicle-chat-invitation/
or discussed in audio form
https://aperiodical.com/2020/08/mathematical-objects-a-vehicle-with-ch…
ColinWright · 2019-01-21
I wrote about this nearly four years ago:
https://aperiodical.com/2015/03/%cf%80-phase-space-and-bouncing-billia…
It doesn't have nifty visualisations, but the (mythical) interested reader might find this a useful complement to the video and explanation provided there.
Edit: Thought so - I did submit my write-up at the time:
https://news.ycombinator.com/item?id=9202913
ideaoverload · 2018-09-25
Sketch in writing: https://aperiodical.com/wp-content/uploads/2018/09/2018-The_Riemann_Hy…
ZeroGravitas · 2017-10-25
An image to illustrate the issue:
http://aperiodical.com/wp-content/uploads/2017/10/footballs-600x274.pn…
damnyou · 2017-06-02
Maybe they tested both and found one more aesthetically pleasing?
Maybe Game of Life simply doesn't produce patterns as interesting as Rule 30? With GoL you can only show one generation.
Maybe they were going for the randomness that rule 30 provides (you can build a PRNG from it) but Game of Life doesn't?
http://aperiodical.com/2017/05/right-answer-for-the-wrong-reason-cellu…
They're professionals like you. Give them some credit.
stcredzero · 2016-12-09
We can increase that by one to the fourth power!
http://aperiodical.com/2013/05/the-maths-of-star-trek-the-original-ser…
panzi · 2014-12-21
Here is James Grime's (Enigma and Alan Turing expert/fanboy) comments on The Imitation Game:
https://www.youtube.com/watch?v=kCSp1RZLhkg
http://aperiodical.com/2014/11/an-alan-turing-expert-answers-your-the-…
colinbeveridge · 2013-04-14
There's a nice demonstration of a zero-knowledge protocol here: http://aperiodical.com/2012/03/using-a-zero-knowledge-protocol-to-prov…
ot · 2013-02-05
Some context: the Invariant Subspace Problem is an important open problem in functional analysis [1]. There is a MathOverflow thread discussing its significance [2].
For those not familiar with functional analysis, it is basically a generalization of basic linear algebra fact that, in complex finite-dimensional vector spaces, every matrix (or to be more precise, every linear operator) has at least one eigenvector.
Cowen and Gallardo announced [3] that they proved the theorem in December, but apparently the proof is wrong, so the problem is still open.
[1] http://en.wikipedia.org/wiki/Invariant_subspace_problem
[2] http://mathoverflow.net/questions/48908/is-the-invariant-subspace-prob…
[3] http://aperiodical.com/2013/01/the-invariant-subspace-problem-solved-f…