Peirce is often regarded as the earliest American scientist whose research was recognized as world class. He was an apologist for
slavery, opining that it should be condoned if it was used to allow an elite to pursue scientific enquiry.
Mathematics In number theory, he proved there is no odd
perfect number with fewer than four
prime factors. In algebra, he was notable for the study of
associative algebras. He first introduced the terms
idempotent and
nilpotent in 1870 to describe elements of these algebras, and he also introduced the
Peirce decomposition. In the philosophy of mathematics, he became known for the statement that "Mathematics is the science that draws necessary conclusions". Peirce's definition of mathematics was credited by his son,
Charles Sanders Peirce, as helping to initiate the consequence-oriented philosophy of
pragmatism. Like
George Boole, Peirce believed that mathematics could be used to study
logic. These ideas were further developed by his son Charles, who noted that logic also includes the study of faulty reasoning. In contrast, the later
logicist program of
Gottlob Frege and
Bertrand Russell attempted to base mathematics on logic.
Statistics Peirce proposed what came to be known as
Peirce's Criterion for the statistical treatment of
outliers, that is, of apparently extreme observations. His ideas were further developed by his son Charles. Peirce was an
expert witness in the
Howland will forgery trial, where he was assisted by his son Charles. Their analysis of the questioned signature showed that it resembled another particular handwriting example so closely that the chance of such a match occurring at random, i.e. by pure coincidence, was extremely small. ==National Academy of Sciences==