Pierre De Fermat Quotes

Interpretations of Popular Quotes

"It is impossible to find in a straight line a point equidistant from at least three points not all in a line."

Pierre de Fermat's statement means that it is impossible to find one point on a straight line that is an equal distance (equidistant) from at least three non-collinear points (points not lying on the same straight line). This geometrical concept, often referred to as Fermat's Theorem, cannot be satisfied by any point on a straight line when the three given points are not collinear.

"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

This quote by Pierre de Fermat indicates that he had developed an exceptionally profound and groundbreaking proof for a mathematical theorem, but the limited space in his margin (margin of the book where he was writing) was insufficient to accommodate it. This statement underscores Fermat's genius as a mathematician and highlights the vastness and complexity of his findings, leaving behind an intriguing mystery that has puzzled scholars for centuries.

"If $n$ is an integer greater than 2, then the equation a^{n} + b^{n} = c^{n} has no non-trivial integer solutions when $n \geq 3$. This statement I have discovered, and I have not found it possible to express in any fewer words than these."

Pierre de Fermat is stating that there are no positive integer solutions (besides the trivial solution of a=b=c) for the equation a^n + b^n = c^n, when n is an integer greater than 2 and n >= 3. Essentially, he's claiming that this specific mathematical puzzle, known as Fermat's Last Theorem, cannot be expressed in fewer words or simpler terms.

"It is not that God plays dice with the universe; He does not play dice at all."

Pierre de Fermat's quote suggests that he believes in a deterministic universe, rather than one governed by random chance or probability. In other words, he asserts that the universe follows fixed laws and principles set by God, and there is no room for randomness or unpredictability as one might find in games of dice. Instead, the universe is an intricate system of predetermined patterns and relationships. This perspective is often associated with a belief in a designed and orderly universe rather than a chaotic or randomly-evolving one.

"Mathematicians have hitherto believed it was impossible to find two irrational numbers whose sum, difference, product and quotient are all rational, but I have found such a pair of numbers: $sqrt{2}+sqrt{3}$ and $sqrt{2}-sqrt{3}$. Indeed, the ratio of these two numbers is 1, which is a most elegant result."

This quote by Pierre De Fermat refers to his discovery of irrational numbers, specifically sqrt(2) + sqrt(3) and sqrt(2) - sqrt(3), that exhibit a unique mathematical property where their sum, difference, product, and quotient (when the second number is reciprocal) are all rational. This finding was groundbreaking because it contradicted widely-held beliefs at the time about the impossibility of such a relationship between irrational numbers. The "most elegant result" Fermat mentions here is that the ratio of these two numbers reduces to 1, which further highlights their unusual and beautiful mathematical properties.