Meaning: The quote "I have hardly ever known a mathematician who was capable of reasoning" is attributed to the ancient Greek philosopher Plato. This quote reflects Plato's views on the distinction between mathematics and reasoning, as well as his overall philosophy on knowledge and truth.

Plato was a philosopher who lived in ancient Athens, and he is widely considered one of the most influential thinkers in the history of Western philosophy. He was a student of Socrates and the teacher of Aristotle, and his philosophical ideas have had a profound impact on various fields, including mathematics, science, ethics, and political theory.

In this quote, Plato seems to be making a provocative statement about mathematicians and their capacity for reasoning. On the surface, the quote may appear paradoxical, as mathematics is often considered a highly logical and rational discipline that requires advanced reasoning skills. However, it is important to consider the context in which Plato made this statement and the philosophical framework that underpins his views.

Plato's philosophy was deeply concerned with the nature of knowledge and reality. He believed in the existence of an objective, eternal realm of forms or ideas, which he considered to be the true source of knowledge and truth. In contrast, the physical world that we perceive through our senses was, for Plato, a mere reflection or imitation of these higher forms.

In the context of this philosophical framework, Plato's statement about mathematicians can be interpreted as a critique of the limitations of empirical or sensory knowledge. While mathematics is a rigorous and systematic discipline that relies on logical reasoning and abstraction, Plato may have been suggesting that true reasoning and understanding require a deeper engagement with the realm of forms, rather than mere calculation and manipulation of symbols.

Plato's views on mathematics and reasoning also need to be understood in the context of the historical development of mathematical thought. In ancient Greece, mathematics was closely linked to philosophy, and the study of geometry, arithmetic, and astronomy was considered an essential part of a well-rounded education. However, Plato may have been emphasizing the distinction between the technical skills of calculation and the higher intellectual faculties of reasoning and understanding.

It is also worth noting that Plato's own dialogues, particularly the "Republic" and the "Timaeus," contain extensive discussions of mathematics and its role in understanding the nature of reality. In these works, Plato presents mathematical concepts as tools for grasping abstract truths and patterns that transcend the material world. This perspective aligns with his broader metaphysical and epistemological views, which emphasize the importance of transcending the sensory world in the pursuit of genuine knowledge.

In conclusion, Plato's quote about mathematicians and reasoning should be understood within the context of his philosophical ideas about knowledge, truth, and the nature of reality. While on the surface, the quote may seem paradoxical, a deeper exploration reveals Plato's emphasis on the distinction between technical skills in mathematics and the higher faculties of reasoning and understanding, as well as his broader philosophical framework that prioritizes engagement with the realm of forms.