Mathematical joke

Some jokes use a mathematical term with a second non-technical meaning as the punchline of a joke. Occasionally, multiple mathematical puns appear in the same jest: This invokes four double meanings: adder (snake) vs. addition (algebraic operation); multiplication (biological reproduction) vs. multiplication (algebraic operation); log (a cut tree trunk) vs. log (logarithm); and table (set of facts) vs. table (piece of furniture). Other jokes create a double meaning from a direct calculation involving facetious variable names, such as this retold from ''Gravity's Rainbow'': The first part of this joke relies on the fact that the primitive (formed when finding the antiderivative) of the function 1/x is log(x). The second part is then based on the fact that the antiderivative is actually a class of functions, requiring the inclusion of a constant of integration, usually denoted as C—something which calculus students may forget. Thus, the indefinite integral of 1/cabin is "log(cabin) + C", or "A log cabin plus the sea", i.e., "A houseboat". ==Jokes with numeral bases==

Some jokes depend on the ambiguity of numerical bases. This joke subverts the trope of phrases that begin with "there are two types of people in the world..." and relies on an ambiguous meaning of the expression 10, which in the binary numeral system is equal to the decimal number 2. Another pun using different radices asks: The play on words lies in the similarity of the abbreviation for October/Octal and December/Decimal, and the coincidence that both equal the same number (31_8 = 25_{10}). ==Imaginary numbers==

Some jokes are based on the imaginary number , treating it as if it were a real number. A telephone intercept message of "you have dialed an imaginary number, please rotate your handset ninety degrees and try again" is a typical example. Another popular example is: "What did say to ? Get real. What did say to ? Be rational." ==Stereotypes of mathematicians==

Some jokes are based on stereotypes of mathematicians, who are often perceived as thinking in complicated, abstract terms, which can cause them to lose touch with the "real world." These comparisons liken mathematicians to physicists, engineers, or the "soft" sciences, such as an Englishman, an Irishman and a Scotsman, illustrating that other scientists undertake practical endeavors. In contrast, the mathematician proposes a theoretically valid but physically nonsensical solution. Mathematicians are also shown as averse to making hasty generalizations from a small amount of data, even if some form of generalization seems plausible: A classic joke involving stereotypes is the "Dictionary of Definitions of Terms Commonly Used in Math Lectures". Examples include "Trivial: If I have to show you how to do this, you're in the wrong class", "Similarly: At least one line of the proof of this case is the same as before," and "This proof is left as an exercise to the reader." ==Non-mathematician's math==

This category of jokes comprises those that exploit common misunderstandings of mathematics, or the expectation that most people have only a basic mathematical education, if any. The joke is that the employee fails to understand the scientist's implication of the uncertainty in the age of the fossil and uses false precision. ==Mock mathematics==

A form of mathematical humor arises from using mathematical tools (both abstract symbols and physical objects, such as calculators) in unconventional ways that transcend their intended scope. These constructions are generally devoid of any substantial mathematical content, besides some basic arithmetic. Mock mathematical reasoning A set of jokes applies mathematical reasoning to situations where it is not entirely valid. Many are based on a combination of well-known quotes and basic logical constructs such as syllogisms: Another set of jokes relates to the absence of mathematical reasoning, or misinterpretation of conventional notation: \left( \lim_{x\to 8^+} \frac{1}{x-8} = \infty \right) \Rightarrow \left( \lim_{x\to 3^+} \frac{1}{x-3} = \omega \right) That is, the limit as x goes to 8 from above is a sideways 8 or the infinity sign, in the same way that the limit as x goes to three from above is a sideways 3 or the Greek letter omega (conventionally used to notate the smallest infinite ordinal number). An anomalous cancellation is a kind of arithmetic procedural error that gives a numerically correct answer: • \frac{64}{16} = \frac{\cancel 64}{\,\,1\cancel 6} = \frac{4}{1} = 4 • \sqrt[6]{64} = \sqrt[\cancel 6]{\cancel{6}4} = \sqrt{4} = 2 • \frac{\mathrm d}{\mathrm d x}\frac{1}{x} = \frac{\cancel\mathrm d}{\cancel\mathrm d x}\frac 1x = \frac{}{x}\frac 1x = -\frac 1{x^2} Mathematical fallacies . Several mathematical fallacies are part of mathematical humorous folklore. For example: \begin{align} b &= a \\ ab &= a^2 \\ ab - b^2 &= a^2 - b^2 \\ b(a - b) &= (a + b)(a - b) \\ b &= a + b \\ b &= b + b \\ b &= 2b \\ 1 &= 2 \end{align} This appears to prove that , but uses division by zero to produce the result. Some jokes attempt a seemingly plausible, but in fact impossible, mathematical operation. For example: Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? To reverse the digits of a number's decimal expansion, we have to start at the last digit and work backwards. However, that is not possible if the expansion never ends, which is true in the case of \pi and e. Humorous numbers Many numbers have been given humorous names, either as pure numbers or as units of measurement. Some examples: Sagan has been defined as "billions and billions", a metric of the number of stars in the observable universe. ''Jenny's constant'' has been defined as J = (7^{e - 1/e} - 9) \cdot \pi^2 = 867.5309\ldots. , from the pop song "867-5309/Jenny", which concerns the telephone number 867-5309. The number 42 appears prominently in the Douglas Adams trilogy ''The Hitchhiker's Guide to the Galaxy'', where it is portrayed as "the answer to the ultimate question of life, the universe, and everything". This number appears as a fixed value in the TIFF image file format and its derivatives (including, for example, the ISO standard TIFF/EP), where the content of bytes 2–3 is defined as 42: "An arbitrary but carefully chosen number that further identifies the file as a TIFF file". The number 69 is commonly used in reference to a group of sex positions in which two people align to perform oral sex, thus becoming mutually inverted like the numerals 6 and 9. Because of this association, "69" has become an internet meme and is known as "the sex number" in some communities. The number 420 is cannabis culture slang for cannabis consumption, especially smoking around the time 4:20 p.m., and also refers to cannabis-oriented celebrations that take place annually on April 20, which is "4/20" in U.S. date form. In the context of numerical humor, one classic example is the joke, "Why was six afraid of seven? Because seven eight (ate) nine!" The humor in this statement originates from a linguistic play on numbers and fundamental arithmetic. Calculator spelling Calculator spelling is the formation of words and phrases by displaying a number and turning the calculator upside down. The jest may be formulated as a mathematical problem where the result, when read upside down, appears to be an identifiable phrase like "ShELL OIL" or "Esso" using seven-segment display character representations where the open-top "4" is an inverted 'h' and '5' looks like 'S'. Other letters can also be used as numbers, with 8 and 9 representing B and G, respectively. An attributed example of calculator spelling, which dates back to the 1970s, is 5318008, which, when turned over, spells "BOOBIES". Limericks A mathematical limerick is an expression that, when read aloud, matches the form of a limerick. The following numerically correct example is attributed to Leigh Mercer: \frac{12 + 144 + 20 + 3 \sqrt{4}}{7} + (5 \times 11) = 9^2+0 This is read as follows: Another example using calculus is: \int_{1}^{\sqrt[3]{3}}z^2 dz \cdot \cos\left(\frac{3\pi}{9}\right) = \log(\sqrt[3]{e}) which may be read: The limerick is true if \log is interpreted as the natural logarithm. ==Doughnut and coffee mug topology joke==

) and back An oft-repeated joke is that topologists cannot tell a coffee cup from a doughnut, since they are topologically equivalent: a sufficiently pliable doughnut could be reshaped (by a homeomorphism) to the form of a cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle. ==Category theory==

Category theory is a common source of esoteric mathematical jokes, due to its high level of abstraction. Recall that a category is a kind of mathematical structure consisting of points and arrows between these points. For any concept in category theory, the dual concept reverses the directions of all arrows. The name of the dual concept is simply the name of the original idea with the prefix "co" added in front. Thus, The joke is that when the dual is taken twice, the direction of the arrows remains the same, and hence the double "co" is redundant. Another joke references a quote by Alfréd Rényi: "A mathematician is a device for turning coffee into theorems." If the dual is taken, the quote becomes Not only are "coffee" and "theorems" dualized, their order is also swapped, since taking the dual reverses the direction of arrows. ==See also==