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Birthday paradox: In a random group of only 23 people, there is a better than 50/50 chance two of them have the same birthday. Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations. Boy or Girl paradox: A two-child family has at least one boy.
When the research is complete and the researcher knows the (probable) answer to the research question, writing up can begin (as distinct from writing notes, which is a process that goes on through a research project). In term papers, the answer to the question is normally given in summary in the introduction in the form of a thesis statement.
Problem statement. A problem statement is a description of an issue to be addressed, or a condition to be improved upon. It identifies the gap between the current problem and goal. The first condition of solving a problem is understanding the problem, which can be done by way of a problem statement. [1]
Pierre Duhem. As popular as the Duhem–Quine thesis may be in philosophy of science, in reality Pierre Duhem and Willard Van Orman Quine stated very different theses. Duhem believed that only in the field of physics can a single individual hypothesis not be isolated for testing. He says in no uncertain terms that experimental theory in physics ...
Church–Turing thesis. In computability theory, the Church–Turing thesis (also known as computability thesis, [1] the Turing–Church thesis, [2] the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of computable functions. It states that a function on the natural numbers can ...
The problem concerns two envelopes, each containing an unknown amount of money. The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox.
Gettier problem. The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge. Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups. The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory ) grew steadily in ...