A number of mathematical fallacies are part of mathematical humorous folklore. For example:
In mathematics, mathematical optimization (or optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives. In the simplest case, an optimization problem involves maximizing or minimizing a real function by selecting input values of the function and computing the corresponding values of the function. The solution process includes satisfying general necessary and sufficient conditions for optimality. For optimization problems, specialized notation may be used as to the function and its input(s). More generally, optimization includes finding the best available element of some function given a defined domain and may use a variety of different computational optimization techniques.
Linear and nonlinear programming have profoundly affected microeconomics, which had earlier considered only equality constraints. Many of the mathematical economists who received Nobel Prizes in Economics had conducted notable research using linear programming: Leonid Kantorovich, Leonid Hurwicz, Tjalling Koopmans, Kenneth J. Arrow, Robert Dorfman, Paul Samuelson and Robert Solow. Both Kantorovich and Koopmans acknowledged that George B. Dantzig deserved to share their Nobel Prize for linear programming. Economists who conducted research in nonlinear programming also have won the Nobel prize, notably Ragnar Frisch in addition to Kantorovich, Hurwicz, Koopmans, Arrow, and Samuelson.
Some jokes attempt a seemingly plausible, but in fact impossible, mathematical operation. For example:
Prominent mathematical economists include, but are not limited to, the following (by century of birth).
Optimality properties for an entire market system may be stated in mathematical terms, as in formulation of the two fundamental theorems of welfare economics and in the Arrow–Debreu model of general equilibrium (also discussed below). More concretely, many problems are amenable to analytical (formulaic) solution. Many others may be sufficiently complex to require numerical methods of solution, aided by software. Still others are complex but tractable enough to allow computable methods of solution, in particular computable general equilibrium models for the entire economy.
Mathematical Reviews computes a "mathematical citation quotient" (MCQ) for each journal. Like the impact factor, this is a numerical statistic that measures the frequency of citations to a journal. The MCQ is calculated by counting the total number of citations into the journal that have been indexed by Mathematical Reviews over a five-year period, and dividing this total by the total number of papers published by the journal during that five-year period.
Current Mathematical Publications was a subject index in print format that published the newest and upcoming mathematical literature, chosen and indexed by Mathematical Reviews editors. It covered the period from 1965 until 2012, when it was discontinued.
The "All Journal MCQ" is computed by considering all the journals indexed by Mathematical Reviews as a single meta-journal, which makes it possible to determine if a particular journal has a higher or lower MCQ than average. The 2018 All Journal MCQ is 0.41.
For the period 2012 – 2014, the top five journals in Mathematical Reviews by MCQ were:
Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:
A set of equivocal jokes applies mathematical reasoning to situations where it is not entirely valid. Many of these are based on a combination of well-known quotes and basic logical constructs such as syllogisms:
From the later-1930s, an array of new mathematical tools from the differential calculus and differential equations, convex sets, and graph theory were deployed to advance economic theory in a way similar to new mathematical methods earlier applied to physics. The process was later described as moving from mechanics to axiomatics.
Despite its name, mathematical induction is a method of deduction, not a form of inductive reasoning. In proof by mathematical induction, a single "base case" is proved, and an "induction rule" is proved that establishes that any arbitrary case implies the next case. Since in principle the induction rule can be applied repeatedly (starting from the proved base case), it follows that all (usually infinitely many) cases are provable. This avoids having to prove each case individually. A variant of mathematical induction is proof by infinite descent, which can be used, for example, to prove the irrationality of the square root of two.
The section's other categories of awards and their recipients are listed at ASA Section on Mathematical Sociology
Numerical analysis and symbolic computation had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as algorism which exist before the invention of electronic computer, helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needing conversely the progress of the mathematical science or applied mathematics.
Such mathematical physicists primarily expand and elucidate physical theories. Because of the required level of mathematical rigour, these researchers often deal with questions that theoretical physicists have considered to be already solved. However, they can sometimes show (but neither commonly nor easily) that the previous solution was incomplete, incorrect, or simply too naïve. Issues about attempts to infer the second law of thermodynamics from statistical mechanics are examples. Other examples concern the subtleties involved with synchronisation procedures in special and general relativity (Sagnac effect and Einstein synchronisation).
A common application of proof by mathematical induction is to prove that a property known to hold for one number holds for all natural numbers: Let
The progress of mathematical information presentation such as TeX or MathML will demand to evolution form formula manipulation language to true mathematics manipulation language (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called one purpose software which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be kept.
Robert M. Solow concluded that mathematical economics was the core "infrastructure" of contemporary economics: Economics is no longer a fit conversation piece for ladies and gentlemen. It has become a technical subject. Like any technical subject it attracts some people who are more interested in the technique than the subject. That is too bad, but it may be inevitable. In any case, do not kid yourself: the technical core of economics is indispensable infrastructure for the political economy. That is why, if you consult [a reference in contemporary economics] looking for enlightenment about the world today, you will be led to technical economics, or history, or nothing at all.