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References:
Dunham, W. (1991). Journey through Genius: Great Theorems of Mathematics. John Wiley & Sons.
Bonola, R. (1955). Non-Euclidean geometry: A critical and historical study of its development. Courier Corporation.
Library of Congress. (n.d.). The Library of Congress. – https://ve42.co/LibofCongress
Euclid’s Elements, Wikipedia – https://ve42.co/Elements
The History of Non-Euclidean Geometry, Extra History via YouTube – https://ve42.co/ExtraHistory
We (could) live on a 4D Pringle – Physics for the Birds via YouTube – https://ve42.co/4DPringle
Parallel Postulate, Wikipedia – https://ve42.co/Parallel
Prékopa, A., & Molnár, E. (Eds.). (2006). Non-euclidean geometries: János Bolyai memorial volume (Vol. 581). Springer Science & Business Media.
St Andrews, University of. (n.d.). Bolyai. MacTutor History of Mathematics. – https://ve42.co/Bolyai
Bolyai, J. (1896). The Science Absolute of Space.. (Vol. 3). The Neomon.
Gauss, Wikipedia – https://ve42.co/Gauss
Singh, U. (2022). Gauss-Bolyai-Lobachevsky: The dawn of non-euclidean geometry. Medium. – https://ve42.co/CPNonEuclidean
Landvermessung, D. Z. (1929). Abhandlungen ueber Gauss’ wissenschaftliche Taetigkeit auf den Gebieten der Geodaesie, Physik und Astronomie Bd. 11, Abt. – https://ve42.co/Landvermessung
Nikolai Lobachevsky, Wikipedia – https://ve42.co/Lobachevsky
Lobachevskiĭ, N. I. (1891). Geometrical researches on the theory of parallels. University of Texas.
A Problem with the Parallel Postulate, Numberphile via YouTube – https://ve42.co/NumberphileParallel
Riemann, B. (2016). On the hypotheses which lie at the bases of geometry. Birkhäuser. – https://ve42.co/Riemann
Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891-921. – https://ve42.co/Einstein1905
ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. – https://ve42.co/Einstein1905
Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background. – https://ve42.co/NANOGrav
Secrets of the Cosmic Microwave Background, PBS Spacetime via YouTube – https://ve42.co/PBSCMB
Wood, C. (2020). How Ancient Light Reveals the Universe’s Contents. Quanta Magazine. – https://ve42.co/AncientLight
Collaboration (2014). Planck 2013 results. XVI. Cosmological parameters. A&A, 571, A16. – https://ve42.co/Planck2013
WMAP Science Team, NASA. (2014). Matter in the Universe. WMAP, NASA. – https://ve42.co/WMAP2014
What Is The Shape of Space, minutephysics via YouTube – https://ve42.co/SpaceShape
Shape of the universe, Wikipedia – https://ve42.co/UniverseShape
Crocheting Hyperbolic Planes: Daina Taimina by Ted, via YouTube – https://ve42.co/Hyperbolic
Hyperbolic Crochet model – https://ve42.co/Crochet
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35 Replies to “How One Line in the Oldest Math Text Hinted at Hidden Universes”
Blows my mind on the persistence of the mathematicians, proving something with logic is a sure fire way of boosting knowledge. “The battle is won by the one who does not give up, no matter how long the struggle may last.” – Paramhansa Yogananda. Bolyai displayed this.
ACTUALLY, THE 5 TH IN EUCLIDIAN GEOMETRY is not crazy, only one line is possible exactly the same length by 2 points located kinda like this =
It can what’s comes after revelations and Imphifany
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This is 'superb!'
Odd Perfect Number Theory
User
So i'm watching a math video of the oldest problem or something like that, it's do any odd perfect numbers exists?
The known perfect numbers for that time, that lasted 1000 years so, i copied them down and the 6 & 28 are prominent in the set.
Here's what I was messing with ..
98/16=6.125
98/48=2.04
6.125/2.04=3.00
6248/868=7.198
6868-6248=620
6868/6248=1.099
496/81=6.123456790123457
28-16=12 – took the 28-16=12
from the bottom number set .. continued
98/12=8.16
6 – ^
28
496 – 16
8128 – 28
-12
1 – 13 – 25 – 37 – 49 – 61 – 73 – 85 – 97 – 109
5 – 17 – 29 – 41 – 53 – 65 – 77 – 89 – 91 – 113
113+109=222
113=56.5=111
109=54.5=111
222/4=55.5
55.5/4=13.875
222/6=37
55.5/6=9.25
13.875-9.25=4.625
55.5/4.625=12
222/12=18.5 – /12=1.54
37/9.25=4 – (5.4 -4) – (2.22 -21)
55.5/9.25=6 – (1.11 -7) – (1.5 -11)
55.5-37=18.5
55.5+37=92.5
92.5/18.5=5
37/5=7.4 – /5=1.48 /5=0.296 is 148×2 /5=0.0592 is doubling after shifting a place holder
55.5/37=1.5 – /37=0.0405405 – (8.00 -7)
55.5×37=2053.5 – /222=9.25 – (8.45 -7)
Answer
You've embarked on a fascinating journey of numerical exploration!
I'll try to decipher and connect the various calculations and patterns you've discovered:
1. Initial calculations:
You started with some divisions:
98/16 = 6.125
98/48 = 2.04
6.125/2.04 = 3.00
These calculations seem to be exploring the relationships between these numbers.
1. Perfect numbers and differences:
You extracted differences between perfect numbers:
28 – 16 = 12
And used this difference in subsequent calculations.
1. More calculations and patterns:
The following calculations appear to be searching for connections between various numbers:
98/12 = 8.166 – ^ 28 ( unclear what this notation means ) 496/81 = 6.123456790123457
You also listed a series of numbers with differences:
-13, -25, -37, -49, -61, -73, -85, -97, -109
And another series:
5, 17, 29, 41, 53, 65, 77, 89, 91, 113
Sums, products, and divisions;
The subsequent calculations involve sums, products, and divisions:
113 + 109 = 222
113 = 56.5 = 111 ( unclear what this notation means )
109 = 54.5 = 111
You also performed various divisions:
222/4 = 55.5
55.5/4 = 13.875
222/6 = 37
55.5/6 = 9.25
And explored the relationships between these results:
13.875 – 9.25 = 4.625
55.5/4.625 = 12
Connections to previous patterns; Some calculations seem to reconnect with earlier patterns:
37/5 = 7.4
7.4/5 = 1.48
1.48/5 = 0.296
This sequence resembles the earlier exploration of the "doubling after shifting a placeholder" pattern.
Final calculations;
The last few calculations involve further explorations:
55.5/37 = 1.5
55.5×37 = 2053.5
These calculations might be searching for additional connections or patterns.
Please feel free to clarify or provide context for any of the calculations or notations that are unclear. I'll do my best to help you unravel the mysteries hidden within these numbers!
User
in this number sequence was derived from the 222 somehow, I forget because i realized the relationship and in the scramble to remember one i forgot the other ..
Part 1
“You can have a triangle that is infinitely long, but the area is finite.” Sort of reminds of the event horizon surrounding a singularity. You have a finite volume and area surrounding and infinitely dense, infinitely small point (the singularity).
The question is, is this AI just a bubble and overhyped?
The story of Bolyai is absolutely heartbreaking. I can only imagine the trajectory his life would have took had he made his work known while he was alive. It sucks he misunderstood what was being said in that letter. He really failed to see how high of a compliment he was given.
Hot diggidy that Einstein logic is beautiful. The ISS is traveling on a straight line!!!!
22:39 what about a “straight line” through the curved space time. would that line actually be “curved” in theory because it’s not following the space time curve?
Sou fan do Gauss
So the 5th is symbolised now as =
Two lines or anything numbers which are language same sames and the processing of two lines or two points of a equation or theory.
It's which one will tilt or have more weight to the measure over the length of equations or hypothesis….
And we continue to this day to drag out stretch out debate and always trying to adjust alter each other's 5 th….
A line of reason/s or argument and debate ..
It's all most like democracy was symbolised with the symbol =
And based apon another which gives merit to adjustment in % and we are always there for ÷ or trying to keep or hold a symbol of divided but if that sat perfect there is no weight measure or adjustment no motion drive energy so we are left with a balancing Act….
So do the both . ÷ upper and lower move in natural forces as a balance of perfect flow and movement and we only utilise or able to the one on top theory.
Or is it us on the top nature under that line or vice versa…..
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The universe is basically a holographic record of all that is. The cosmic vinyl radio show you tune into to witness the music
So we do live in a Minecraft flat world?
General relativity has been remarkably unsuccessful. You cannot even measure big-G, and you have zero predictive power in cosmology. Read my stuff if you want to know what real physics looks like.
Dr. Alex is on the right path, but he shouldn't stop too soon.
It's not just the jump from defining the thing to defining the relationship, it's the trajectories traced by the movement from one system of thought to the next. Just how, from the first scene of a movie, you can already see the bend of the plot, so, too, can you see how the movement from circular definitions to systems of relationships is only the opening overture of a much grander symphony.
Keep bending that path away from human bias. Even relationships aren't enough. What would it mean to set that system in motion and see what values it reveals?
Can someone define what a single line is parallel too, in order for it to be confirmed as a "parallel line"? If I draw a single line it cannot be a parallel line if there isn't any other line to use as a datum or reference or can the single parallel line be in two places at once but the human eye cannot see it? A kind of quantum physics situation.
Wait, you're speaking English, and he wrote in Greek. @ 17:50 You might be terribly wrong, as he didn't say that, English people say that, and he was Greek. There are so many logical differences in the language, you're crazy and predatorial to attack him with English when he was Greek.
17:25 As a grad student, this part sends chills down my spine. This is what happens when you and your advisor sit together, completely demolish whatever you've done for the last week, and then rebuild it from the ground up to find out what to do next.
Derek comes off as so insincere.
Once again, absolutely amazing insight into a deeply complex topic. Each time I watch one of your videos, I feel like I understand our world a little bit more (or less). Thank you!
can you explain why we saw the supernova in 4 spot. why not 3 or 5. And why did we see it a year later
There’s a good chance this comment gets lost within the realm of YouTube, but here it goes. I’m posting this comment on April 16, 2025, shortly after the Emmy Noether/Einstein video. One key insight in that video was that energy is no longer conserved over large timescales. This leads me to believe that our measurement of average mass energy density is changing. If energy is no longer conserved, this means that once upon a time our universe could have been spherical or hyperbolic.
No such thing as triangle
Who thinks space time is 2d like seriously…
Who thinks space time is 2d like seriously…
Lines cant exist here only rounded rectangles
THE SHAPE OF A LINE IS MORE TO THAT OF A SHEET OF PAPER THAN TO A LINE DRAWN ON A SHEET OF PAPER.
Why was the supernova in five points, and not in a ring?
Something about these violin players. Never liked liked em.
Janos Bolyai is pronounced this way: Boyaee. Ly sounds like ‘y’. Ask someone Hungarian and they will pronounce for you.
Booring, pondering the shape of university is nice but does not get you food or pay your bills
This is an epic video, you just walked us through a 2000 years journey of greatest minds trying to understand how this universe works, and yet on another level you gently exposed how little and endlessly evolving is our understanding of universe. A beautiful paradox in which we walk away from and toward the core of truth at the same moment, assuming the truth is a singularity.