Christian Science Monitor

Scientists—particularly these working in public institutions—should make a larger effort to communicate to society what science is and what is not; how is it accomplished; what are its primary results; and what are they helpful for. This can be the best way of demystifying science and scientists and upgrading society’s scientific literacy.

An example is the classification of finite simple teams (additionally known as the “huge theorem”), whose proof between 1955 and 2004 required 500-odd journal articles by about one hundred authors, and filling tens of hundreds of pages. A group of French mathematicians, including Jean Dieudonné and André Weil, publishing beneath the pseudonym “Nicolas Bourbaki”, attempted to exposit all of known mathematics as a coherent rigorous entire.

Then we seek for a sample, make a hypothesis, and test it in opposition to extra information (extra examples). After some iterations, when new information matches our hypothesis, we finally attempt to …

Christian Science Monitor

In order to make clear the foundations of arithmetic, the fields of mathematical logic and set theory have been developed. Mathematical logic includes the mathematical research of logic and the purposes of formal logic to different areas of mathematics; set concept is the branch of mathematics that studies units or collections of objects. The phrase “crisis of foundations” describes the search for a rigorous basis for arithmetic that occurred from roughly 1900 to 1930. Some disagreement in regards to the foundations of mathematics continues to the current day.

The Arithmetica had a significant influence on later mathematicians, corresponding to Pierre de Fermat, who arrived at his well-known Last Theorem after attempting to generalize a problem he had read within the Arithmetica (that of dividing a square into two squares). Diophantus also made vital advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation.

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