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It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, [44] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.
The independence of the mathematical objects is such that they are non physical and do not exist in space or time. Neither does their existence rely on thought or language. For this reason, mathematical proofs are discovered, not invented. The proof existed before its discovery, and merely became known to the one who discovered it. [13]
From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.
This is sometimes cited as history's first mathematical discovery. [60] Due to the variations among testimonies, such as the story of the ox sacrifice being accredited to Pythagoras upon discovery of the Pythagorean theorem rather than Thales, some historians (such as D. R. Dicks) question whether such anecdotes have any historical worth ...
The history of science is often seen as a linear story of progress [27] but historians have come to see the story as more complex. [28] [29] [30] Alfred Edward Taylor has characterised lean periods in the advance of scientific discovery as "periodical bankruptcies of science". [31] Science is a human activity, and scientific contributions have ...
This is a timeline of pure and applied mathematics history.It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic ...
The Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. It looks like a simple, innocuous question, but ...
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship with other human activities. Major themes that are dealt with in philosophy of mathematics include: Reality: The question is whether mathematics is a pure product of human mind or whether it has some reality by itself. Logic and ...