# How One Line in the Oldest Math Text Hinted at Hidden Universes

Veritasium2023-10-21

veritasium#science#physics

6M views|9 months ago

ðŸ’« Short Summary

The video explores the journey of mathematicians in understanding the fifth postulate of Euclidean geometry, which eventually led to the discovery of hyperbolic geometry and its application in modern physics. Around 300 BC, Euclid attempted to summarize all known mathematics in his 13-book series 'The Elements', using simple basic things as true postulates to build up math using logic. The fifth postulate in Euclid's work, which deals with parallel lines, seemed like a mistake and made mathematicians skeptical. Mathemat

âœ¨ Highlights

ðŸ“Š Transcript

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The video explores the journey of mathematicians in understanding the fifth postulate of Euclidean geometry, which eventually led to the discovery of hyperbolic geometry and its application in modern physics.

00:00Around 300 BC, Euclid attempted to summarize all known mathematics in his 13-book series 'The Elements', using simple basic things as true postulates to build up math using logic.

The fifth postulate in Euclid's work, which deals with parallel lines, seemed like a mistake and made mathematicians skeptical.

Mathematicians spent over 2,000 years trying to prove the fifth postulate, but it was Janos Bolyai who realized that the postulate can't be proven from the other four and could be independent.

Bolyai imagined a world where there could be more than one parallel line through a point, which led to the discovery of non-Euclidean geometries.

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Janos Bolyai, a 20-year-old mathematician, discovered a new geometry and later received recognition from Carl Friedrich Gauss for his work, which coincided with Gauss's own meditations.

10:27Bolyai joined the army in his 20s and was skilled in playing the violin and dueling.

He published his findings on a new geometry as an appendix to his father's textbook, and Gauss praised it, acknowledging the similarity to his own discoveries.

Gauss had also previously described a curious geometry with paradoxical and absurd theorems.

Bolyai's work was focused on tackling ancient math mysteries and he was regarded as a genius by Gauss.

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Riemann proposed a geometry where the curvature could differ from place to place, leading to the idea of a multi-dimensional curved geometry, which was further developed by Beltrami.

19:11Riemann suggested a geometry with variable curvature, not limited to two-dimensional planes, but extendable to three or more dimensions.

Beltrami proved that hyperbolic and spherical geometries were as consistent as Euclid's flat geometry.

Einstein's special theory of relativity is based on the concept of curved spacetime, where objects follow the shortest path through the curved geometry.

Observations in astronomy have supported the predictions of curved spacetime, and the universe is believed to be flat based on the measurement of the cosmic microwave background.

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The video discusses how the study of a single sentence from Euclid's 'The Elements' for over 2,000 years led to the discovery of paradoxical and seemingly absurd geometries, which are now fundamental to our understanding of the universe.

29:22The video highlights the importance of building knowledge and problem-solving skills, and recommends the course 'Measurement' on Brilliant for sharpening spatial reasoning skills and understanding geometry.

Bolyai's discovery of a new world where more than one parallel line could exist through a point led to the realization of curved geometries.

Einstein's theory of general relativity is based on the concept of curved spacetime, which has been supported by astronomical observations.

The shape of the entire universe and its curvature can be determined by measuring the angles of triangles, and the universe is believed to be flat based on current estimations.

ðŸ’« FAQs about This YouTube Video

### 1. What was the ancient mathematical problem that Bolyai and others worked on solving?

Bolyai and others worked on solving the ancient mathematical problem related to the parallel postulate in Euclidean geometry, which eventually led to the discovery of non-Euclidean geometries.

### 2. How did Bolyai imagine a world with more than one parallel line through a point?

Bolyai imagined a world where there could be more than one parallel line through a point by considering a curved surface, which deviates from the traditional flat Euclidean geometry.

### 3. What did the observation of the same Supernova in four different places indicate?

The observation of the same Supernova in four different places indicated that the light from the Supernova had multiple paths to reach Earth, suggesting the presence of curved SpaceTime.

### 4. How was the shape and curvature of the universe determined?

The shape and curvature of the universe were determined by measuring the angles of triangles, and the universe was found to be flat based on the observation of the Cosmic Microwave Background (CMB) and the power Spectrum.

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