What are the funniest math formulas

Humor in math

Now he lies completely broken
in the hospital in plaster of paris and speaks:
& ldquor; I've often counted on fractions,
but not with such breaks! "

Finally, there are also many poems about mathematics itself and its subjects:

First mathematical accident - Ehrenfried Winkler [6]

A rectangle went with the square
on a fast motorcycle.
But neither got very far!
The speed was too high.
What neither of them thought of
there was a crash in a corner.
They rammed a wall
where she was found in an accident.
Now both were invalid:
A rhombus and a rhomboid.

The ballad of poor Epsilon Hubert Cremer [3]

The Matrix sang its slumber song
the lines and columns,
the small error link already holds
a sweet dream wound, the old one snores p
-Function,
and lonely a pale one cries
young, abandoned epsilon
at the edge of the star area.

You good father Weierstrasse,
You creator of our world there,
I only beg you for this:
Help me find a delta!
Even if it were so tiny
and almost zero at the end,
the clearest being remained dreary and empty,
if there was no delta.

But here, too, the following applies: Reading costs time that is lacking in the service of mathematics. And, let's be honest: Isn't z. For example, in the elegant proof of Banach's Fixed Point Theorem, much more poetry?

Smart sayings

The following statements by mathematicians and non-mathematicians are reproduced without comment:

A mathematician's reputation is based on the number of false proofs he has. (Abram Samoilovitch Besicovitch)

Structures are the weapons of mathematicians. (Bourbaki)

Who within a year x2 − 92y2 = 1 can solve is a mathematician. (Brahmagupta)

Anything that is just likely is likely wrong. (René Descartes)

Since mathematicians penetrated the theory of relativity, I no longer understand them myself. (Albert Einstein)

Where the laws of mathematics relate to reality they are uncertain; and where they are certain they do not relate to reality. (Albert Einstein)

I don't believe in math. (Albert Einstein)

A mathematician is a machine that converts coffee into theorems. (Paul Erdös)

Mathematics has the greatest reputation as a distraction from the sexual. (Sigmund Freud)

He's a mathematician, so he's persistent. (Johann Wolfgang von Goethe)

There is no cheerful relationship to be won with mathematicians. (Johann Wolfgang von Goethe)

Mathematicians are a kind of French: if you speak to them, they translate it into their language, and immediately it is something completely different. (Johann Wolfgang von Goethe)

But that a mathematician, out of the jumble of his formulas, comes to view nature and needs sense and understanding, independent like a healthy person, I will probably not experience. (Johann Wolfgang von Goethe)

The shortest connection between two statements about real numbers leads to complex numbers. (Jacques Salomon Hadamard)

Some people have a zero radius of view and call it their point of view. (David Hilbert)

The importance of a scientific paper can be measured by how many previous publications it makes superfluous. (David Hilbert)

Physics is far too difficult for physicists. (David Hilbert)

There is no difference between pure and applied math. The two have absolutely nothing to do with each other. (David Hilbert)

The good God created the whole numbers, everything else is human work. (Leopold Kronecker)

The so-called mathematicians by profession, based on the immaturity of the rest of the people, have acquired a credit of profundity which is very similar to that of holiness which theologians have for themselves. (Georg Christoph Lichtenberg)

Medicine makes people sick, mathematics makes them sad and theology makes them sinners. (Martin Luther)

You don't understand things in mathematics. You just get used to them. (John von Neumann)

The mathematicians, who are only mathematicians, think correctly, but only on condition that all things are explained to them by definitions and principles; otherwise they are limited and unbearable, because they only think correctly when it comes to very clear principles. (Blaise Pascal)

Math consists of proving obvious things in the least obvious way. (George Pólya)

So mathematics can be defined as the science in which we never know what we are talking about and never know whether what we are talking about is true. (Bertrand Russell)

Mathematicians have a tendency to doubt their ability to concentrate as much as other men have concerns about their sexual potency. (Stanislaw Marcin Ulam)

God exists because the arithmetic is consistent, and the devil exists because we cannot prove it. (André Weil)

Not directly related to mathematics, but quite aptly, are these quotations:

“I have noticed,” said Mr. K., “that we deter many from our teaching by giving us an answer to everything knowledge. Couldn't we, in the interests of propaganda, make a list of the questions that seem to us to be completely unsolved? "(Bertold Brecht, stories from Mr. Keuner)

He [the philosopher] believed that knowledge of every little thing, including a spinning top, for example, was sufficient for knowledge of the general. That is why he did not concern himself with the big problems, it seemed uneconomical to him. If the smallest thing was really recognized, then everything was recognized, so he only occupied himself with the spinning top. (Franz Kafka, The Spinning Top)

Anecdotes about mathematicians

Mathematicians are seen as strange people, and there are a number of anecdotes about them to prove this ([1], [5]). It is of course clear to those who know that the strange reputation of mathematicians is based precisely on such stories and has absolutely nothing to do with reality.

When David Hilbert heard that one of his students had given up mathematics to become a poet, he said: “I am not surprised. He had too little imagination for mathematics, but enough for poetry. "

David Hilbert was famous for his poor mental arithmetic. Once in his lecture he was faced with the problem of having to calculate 8 times 7: "Well, gentlemen, how much is 8 times 7?" "55?" Another: "57!" Then Hilbert: "But Gentlemen, the solution can only be either 55 or 57! "

Isaac Newton boasted to his friend John Wallis, "My dog ​​Diamond knows a little bit of math. Before lunch today he proved two sentences. ”To which Wallis replied“ Your dog must be brilliant! ”. "Oh no," said Newton, "the first sentence was wrong, and in the second he overlooked a pathological exception."

Bartel Leendert van der Waerden invited his colleagues to finish his visiting professorship in Göttingen. Carl Ludwig Siegel did not want to take part and wrote van der Waerden that unfortunately he could not come because he had died. Van der Waerden then sent him a condolence telegram in which he expressed his deep sympathy for this stroke of fate.

A student turned to John von Neumann: "Excuse me, Professor von Neumann, could you help me with this analysis problem?" Von Neumann: "All right, if it goes quickly - I'm very busy." Student: " I have difficulties with this integral. ”Von Neumann:“ Show me. ... Ah yes, the result is \ (\ frac {2} {5} \ pi \) “. Student: “I know that, but I don't understand how you come up with it.” Von Neumann: “All right, let me see again. … The answer is \ (\ frac {2} {5} \ pi \). " Student (annoyed): "Yes, of course, I know the answer, but I don't know how to derive it!" Von Neumann: "What do you want, I've now calculated it in two different ways!"

Norbert Wiener was approached by a student with a math question. Wiener discussed the problem and then asked which direction he had come from. The student showed them to him. “Aha,” said Wiener, “then I haven't eaten yet,” and continued on to the cafeteria.

Circle squarers, angular three-parters and others

Not for fun, but in all seriousness, even today underemployed non- or would-be mathematicians 'solve' tasks whose unsolvability has long been proven, or discover sensational connections that have so far been overlooked by established science or by the government (probably together with crashed UFOs and the like) are kept under lock and key. Curiosities of this and similar kind can be found in [4] and [7].

Jokes

The supposedly shortest math jokes "There's a joke." and & ldquor;& epsiv; < 0“="" mit="" den="" steigerungen="">& epsiv; & Lt; 0 ”and“& epsiv; → −∞ “are only briefly mentioned, as are jokes that have something to do with stray balloonists, the existence of at least one black sheep or the catching of lions in the desert.

Unfortunately, many jokes about mathematicians are based on shabby prejudices - that mathematicians are somehow strange and unfamiliar, for example, or that they are finicky, know-it-all and often conceited and arrogant [2]. This is pure nonsense - the truth is, the most common of the non-mathematicians is the one with whom something is wrong. It is also incorrect to claim that mathematicians can be attributed to the frequent use of words such as "sufficient", "necessary", "at least", "at most", "modulo", "trivial", "obviously". , "elementary" etc. can recognize. Furthermore, mathematicians have the reputation of always wanting to know everything exactly, to provide all things with strange names of their own and to formalize even the simplest connections to such an extent that no one except (at most) themselves understands what it is all about. Modulo of rare exceptions, these too are obviously untenable assumptions.

Before getting serious about the subject math joke can deal, this term must be specified. Let \ ({\ mathbb {S}} \) be the set of finite non-empty strings over the (finite) alphabet A., consisting of the Latin letters and the usual punctuation marks. So it is A. the amount of small and capital letters and punctuation marks and \ begin {eqnarray} {\ mathbb {S}}: = \ displaystyle \ underset {n = 1} {\ overset {\ infty} {\ cup}} {A} ^ {n}. \ end {eqnarray}M. be the set of all mathematicians. M. is sufficiently clearly described by what has been said so far. For mM. and \ (s \ in {\ mathbb {S}} \) mean wm (s) that

  • m in s recognizes a relation to mathematics, and
  • m when meeting with s at least provokes a serene emotional response.

We use it to run the math jokes a means \ begin {eqnarray} {\ mathbb {W}}: = \ left \ {s \ in {\ mathbb {S}} | \ # \ {m \ in M ​​| {w} _ {m} (s) \} \ ge \ frac {\ # M} {2} \ right \}. \ end {eqnarray}

Objections that this definition is somewhat “vague” can be brushed off the table by pointing out that most mathematicians use the term in a similar way mathematical proof would explain. Well-defined or not, the question immediately arises as to the power of \ ({\ mathbb {W}} \). As a countable union of finite sets \ ({\ mathbb {S}} \) and thus also the subset \ ({\ mathbb {W}} \) is at most countable. In fact, that applies

Sentence: \ ({\ mathbb {W}} \)is countably infinite.

Proof (according to David Alberts, personal communication): It remains to show that \ ({\ mathbb {W}} \) is not finite. \ ({\ mathbb {W}} \) is not empty, because the following series of characters is an element of \ ({\ mathbb {W}} \):

A statistician is a guy who says, with his head in the oven and his feet in the refrigerator, that on average he feels fine.

By swapping the partial character series “oven” and “icebox” one obtains another element of \ ({\ mathbb {W}} \). Hence # \ ({\ mathbb {W}} \) ≥ 2. Assuming \ ({\ mathbb {W}} \) were finite, for example \ ({\ mathbb {W}} = \ {{s} _1 , \ ldots, {s} _k \} \) with 2 ≥ k ∈ & Nopf;, where sjA.nj be with appropriate nj ∈ & Nopf; for 1 ≤ jk. Then make the chain s & colone; s1sk. With \ (n \ space: = \ space \ displaystyle {\ sum} _ {j = 1} ^ {k} {n} _ {j} \) is sA.n. Because of n > nj applies ssj for 1 ≤ jk, i.e. \ (s \ space \ notin \ space {\ mathbb {W}} \). On the other hand it follows for everyone mM. already out wm(s1) obviously wm(s), d. H. the following applies \ (s \ space \ in \ space {\ mathbb {W}} \): contradiction. So \ ({\ mathbb {W}} \) is not finite. Q. E. D.

If one generalizes the value \ (\ frac {1} {2} \) used in the definition of \ ({\ mathbb {W}} \), one obtains a finer structure of \ ({\ mathbb {S}} \ ). In addition be for G ∈ [0, 1] \ begin {eqnarray} {{\ mathbb {W}}} _ {g}: = \ {s \ in {\ mathbb {S}} | \ # \ {m \ in M ​​| {w} _ {m} ( s) \} \ ge g \ #M \} \ end {eqnarray} the Jokes about the smile g. Obviously \ ({{\ mathbb {W}}} _ {\ text {0}} = {\ mathbb {S}} \) and \ ({{\ mathbb {W}}} _ {\ frac {1} {2}} = {\ mathbb {W}} \), and denotes \ ({\ mathbb {P}} \ text {(} {\ mathbb {S}} \ text {)} \) the power set of \ ( {\ mathbb {S}} \), then the mapping defined by \ (\ gamma (g): = {{\ mathbb {W}}} _ {g} \) is \ begin {eqnarray} \ gamma: ([0,1], \ le) \ to ({\ mathbb {P}} ({\ mathbb {S}}), \ supset) \ end {eqnarray} isotonic, d. H. orderly. For \ (s \ space \ in \ space {\ mathbb {S}} \) means \ begin {eqnarray} \ omega (s): = \ sup \ {g \ in [0,1] | s \ in {{\ mathbb {W}}} _ {g} \} \ end {eqnarray} the Wittiness of s and \ (\ omega \ space: \ space {\ mathbb {S}} \ to \ text {[0, 1]} \) the Witty function. Defined for \ (s \ space \ in \ space {\ mathbb {S}} \) by \ begin {eqnarray} \ lambda (s): = \ min \ {n \ in {\ rm {{\ mathbb {N}}}} | s \ in {A} ^ {n} \} \ end {eqnarray} the figure \ (\ lambda \ space: \ space {\ mathbb {S}} \ to {\ rm {{\ mathbb {N}}}} \), then becomes through \ begin {eqnarray} \ varphi (s): = \ frac {\ omega (s)} {\ lambda (s)} \ end {eqnarray} the Joke efficiency function \ (\ varphi: {\ mathbb {S}} \ to \ text {[0,} \ space \ space \ text {1]} \) explained. Lovers, more vivid ‘Paragraphs would say that a joke is more effective the shorter it is and the more people laugh about it. The investigation of topological properties (with the introduction of certain topologies on \ ({{\ mathbb {W}}} _ {g} \)) of ω and ? and their restrictions on the joke sets \ ({{\ mathbb {W}}} _ {g} \) and others witt-theoretical functions is the subject of analytical joke theory. On the other hand, the algebraic joke theory with string operations on \ ({\ mathbb {S}} \), whose restrictions to certain equivalence classes in \ ({{\ mathbb {W}}} _ {g} \)< agenum="" _449und="" der="" verträglichkeit="" dieser="" klassenbildung="" mit="" den="" witztheoretischen="">

The classification of elements from W according to purely content-related aspects is relatively simple. Mostly low ?-. but high ω- Values ​​reach character ranges from \ ({\ mathbb {W}} \), which in addition to "mathematician" also contain partial character series such as "physicist" or "engineer", as the following examples show (some of which, however, also have other permutations of these Partial character series are known):

Mathematicians and physicists take the train to a scientific conference. Every physicist has bought a ticket, but all mathematicians have only one ticket. The physicists are happy and think: “These unworldly mathematic idiots. They'll be thrown off the train at the next stop! ”The conductor comes. The mathematicians hide in the train toilet. The conductor knocks on the toilet door: “The ticket, please!” The mathematicians put their ticket under the door, the conductor clicks and walks on. The physicists are amazed: "Look at the mathematicians, these eggheads sometimes have very useful ideas.We can do that too! ”No sooner said than done, the physicists only bought one ticket on the return trip. But whoops: the mathematicians don't even have a ticket! The physicists are thievingly happy, the mathematicians just smile quietly to themselves. The conductor approaches. The mathematicians disappear into one train toilet, the physicists into the other. Shortly before the conductor arrives, a mathematician sneaks out again and knocks on the physicist's door: "The ticket, please!"

Note: never use mathematical methods without understanding them.

An engineer and a mathematician are attending a physics lecture. It's about string theory, and the lecturer rages around in rooms with eleven dimensions. The mathematician is obviously enjoying it, but the poor engineer gets dizzy and sick. Glad that the agony is over, he asks the mathematician afterwards: "Now just say you have understood this terrible thing!" The mathematician hesitates for a moment - you can see his effort to think down to engineering level. “Yes, of course,” he says finally, “you just have to visualize things.” “Visualize ??? How can you visualize eleven dimensions ??? "" Well, I first imagine an n-dimensional space and then I specialize in the case n = 11.“

The surveyor has the flu. That is why the physicist and the computer scientist are sent to the university courtyard to determine the height of a flagpole. "Theodolite" is a foreign word, and so they try desperately and in vain to climb to the top of the mast with the tape measure. A mathematician comes by by chance and feels sorry for both of them. He pulls the flagpole out of its holder, lays it on the floor, measures it, puts it back up and walks on. Physicists and computer scientists stand there speechless for minutes. Then the physicist hits his forehead: “Typical mathematician, useless for anything! We want the height of the mast, and it gives us its length!“

A mathematician, a physicist and a philosopher are standing on the roof of a burning skyscraper. The fire brigade has spread a jumping sheet. The philosopher says: "If there is a God, he will help me". He jumps and lands far from the target. The physicist takes his pocket calculator, calculates a few formulas, jumps and lands in the middle of the cloth. The mathematician scribbles on his notepad for a while, takes a run, jumps and flies away upstairs. Sign error!

A lawyer, a doctor and a mathematician talk about whether it is better to be married or to have a girlfriend. The lawyer claims a girlfriend is definitely better because most marriages break up and end in divorce and expensive litigation. The doctor sees the matter from his point of view and thinks that marriage offers security, promotes a regular way of life and is therefore healthier. The mathematician, however, when asked for his opinion, thinks: “Money? Health? I don't care about any of that. I have both a wife and a girlfriend. I tell the friend that I need time for my wife and my wife thinks I am with the friend. During that time I can do math undisturbed. "

Brief characterizations of mathematicians have higher ?-Values:

How do you recognize an extrovert mathematician? - An extrovert mathematician looks at your feet while talking to you.

An engineer believes that his equations are an approximation of reality. A physicist < agenum="" _450glaubt,="" daß="" die="" wirklichkeit="" eine="" annäherung="" an="" seine="" gleichungen="" ist.="" ein="" mathematiker="" käme="" nie="" auf="" die="" idee,="" sich="" über="" so="" etwas="" den="" kopf="" zu="">

A mathematician is a person who not only immediately understands a thought presented to him, but also immediately recognizes the reasoning error on which it is based.

Sometimes very high ?-Values ​​reach short strings of characters. referring to mathematical objects. These strings of characters are mostly not recognized as jokes by non-mathematicians:

What is yellow, crooked, normalized and complete? - A banana room.

What is a cluster point of Poland? - Warsaw.

What is a polar bear? - A rectangular bear after a coordinate transformation.

What is nutritious and commutated? - An Abelian soup!

What is big and gray, swims in the sea and cannot be orientated? - Möbius Dick.

"The number you dialed is purely imaginary. Please turn your phone 90 degrees and try again. "

F i bb ooo nnnnn aaaaaaaa ccccccccccccc ccccccccccccccccccccc iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.

Two straight lines meet in the Euclidean plane. One of them says: "Now you spend one, next time it's my turn."

A dance ball takes place in the space of differentiable functions. On the dance floor, cosine and sine dance up and down, the polynomials form a ring around the identity, and the tangent makes the most amazing jumps. Only the exponential function stands alone all evening. Out of pity, the logarithm goes to her at some point and says: "Man, integrate yourself!" "Already tried", complains the exponential function, "But that didn't change anything!"

The exponential function goes for a walk with one of its approximation polynomials and an additive constant when suddenly the differential operator comes around the corner. The constant takes flight, the polynomial is also shocked into all its members, only the exponential function remains calm and smiles at the differential operator: "I am exand you can't do anything to me! "To which the differential operator means:" And I am \ (\ frac {d} {dy} \)! "

How many times can you subtract 7 from 83, and what is left in the end? - You can subtract 7 from 83 as often as you want, and every time there is 76 left.

First basic rule of engineering mathematics: All series converge against the first term.

"Evidence" of the following kind is popular:

Theorem: A cat has at least nine tails.

Proof: No cat has eight tails. A cat has more tails than no cat. So a cat has at least nine tails.

The negation of a false statement is not always a true statement. For example, the statement "This sentence contains six words" is incorrect, but its negation "This sentence does not contain six words" is also incorrect.

Finally, some elements of \ ({\ mathbb {W}} \) that cannot be clearly assigned to any of the previous classes:

"Do you know the joke about the stochastic?" - "Probably."

In the middle of the mathematical lecture, one of the people present raised his hand and shouted: "I have a counterexample for what you are talking about!"

"What about your friend, the mathematician?" "I left her. I call her and she tells me that she is in bed and is struggling with 3 strangers! "

American mathematicians discovered a new whole number. It's somewhere between 27 and 28. You don't yet know how it got there or what it's doing, but it seems to behave very strangely when you put it in some equations.

Two mathematicians in a bar argue about the mathematical level of education of the average citizen. The one who thinks that most people are stupid and have no idea has to go to the bathroom. In the meantime the other one calls the waitress and tells her that he will ask her something later and that she should answer "a third x to the power of three".

After patiently telling her about it several times, it seems to work to a certain extent, and as she leaves she mumbles to herself: "One-third, six-high, three, one-third, high, ..." The friend comes back, and the other says: "I'll prove to the waitress afterwards that that most people understand something about mathematics. ”When the waitress is clearing the dishes, he asks her about the antiderivative of x2. She answers casually: "A third x to the power of three." The friend is completely off his socks, his worldview collapses. And as she leaves, the waitress says over her shoulder: "Plus any constant."

There are three kinds of mathematicians: those who can count to 3 and those who cannot.

literature

[1] Ahrens, W .: Mathematicians anecdotes. Teubner Leipzig, 1940.

[2] Beutelspacher, A .: "I was always bad at math ...". Vieweg Braunschweig / Wiesbaden, 1996.

[3] Cremer, H .: Carmina Mathematica. YES. Mayer Aachen, 1972.

[4] Dudley, U .: Mathematics between madness and wit. Birkhäuser Basel, 1995.

[5] Ehlers, A .: Dear Hertz! Physicists and mathematicians in anecdotes. Birkhäuser Basel, 1994.

[6] Hornschuh, H.-D .: Humor around mathematics. Manz, 1989.

[7] Kracke, H .: Math-musical puzzle. Dümmler Bonn, 1992.

[8] Radbruch, K .: Mathematical traces in literature. Scientific Book Society Darmstadt, 1997.

[9] Wille, F .: Humor in Mathematics. Vandenhoeck & Ruprecht Göttingen, 1984.

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- Prof. Dr. Guido Walz