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A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change .
Coercive logic is a concept popularised by mathematician Raymond Smullyan, by which a person who has agreed to answer a question truthfully is forced to perform an undesired action, where not doing so would mean breaking their agreement. [1] Smullyan presents the concept as a question:
Given this change in the intellectual climate, it has since then been more common to find "passive polymaths", who consume knowledge in various domains but make their reputation in one single discipline, than "proper polymaths", who—through a feat of "intellectual heroism"—manage to make serious contributions to several disciplines.
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A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems .
Mathematical Platonism is the metaphysical view that (a) there are abstract mathematical objects whose existence is independent of us, and (b) there are true mathematical sentences that provide true descriptions of such objects. The independence of the mathematical objects is such that they are non physical and do not exist in space or time.
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
The Handbook of Mathematical Logic [1] in 1977 makes a rough division of contemporary mathematical logic into four areas: . set theory; model theory; recursion theory, and; proof theory and constructive mathematics (considered as parts of a single area).