Euclid — "The prime numbers are more than any assigned multitude of prime numbers."
The prime numbers are more than any assigned multitude of prime numbers.
Get This Quote & Author's Image Illustrated On:
Click any product to generate a realistic preview. Up to 3 at a time.
* Initial load can take up to 90 seconds — revising the preview in another color is nearly instant.
Kitchen
Apparel
Other
More from Euclid
"To draw a straight line at right angles to a given straight line from a given point on it."
"The extremities of a surface are lines."
"If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be e…"
"Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its thr…"
"There are infinitely many prime numbers."
Details
From 'Elements', Book IX, Proposition 20 (Proof of the infinitude of prime numbers)
Date: c. 300 BCE
ShockingVerification
Unverifiable
Found in 1 providers: grok
1 source checked
Understanding this quote
What it means
No matter how large a collection of prime numbers you gather, there will always be more primes beyond it. Primes never run out — the list is infinite. This captures a profound truth about number structure: infinity isn't just large, it's unbounded in a precise, provable sense that defies any finite attempt to contain or complete the set.
Relevance to Euclid
Euclid proved this theorem rigorously in Elements Book IX, Proposition 20, using an elegant contradiction argument. It reveals Euclid not merely as a geometer but as a number theorist who demanded logical proof over intuition. His commitment to deductive reasoning from axioms made this insight permanent — a model of mathematical thinking that defined rigorous proof for two millennia.
The era
Around 300 BCE in Alexandria, Greek mathematicians were systematizing knowledge through logic rather than observation alone. Prime numbers fascinated ancient Greek thinkers exploring divisibility and mathematical structure. Euclid's proof emerged when Alexandria's Library made it a hub of intellectual synthesis. Establishing infinity through proof — not measurement — was revolutionary in a world that generally reasoned from concrete, physical quantities.
AI-generated insights based on extensive research and information for context. Factual errors? Email [email protected].