❡ Jokes and Stories
1. Some aliens decend from A of Centaurus and give to mathematicians, physicists and statiscticians three rods. They say: "If each one of you paints a segment of irrational length on these rods, we will spare humanity and earth. Otherwise, prepare for your doom". Mathematicians start to calculate Dedekind cuts and arrive to an irrational number. Physicists examine the half-life of the rod, do some integrals and take e back. Staticticians say: "The probability of choosing a rational number at random is 0", so they paint a line without calculating, of length 21/35.
2. An elevator stops and the door opens: a logician is inside. I ask: "Are you going up or down?" He replies no and leaves the elevator.
3. A statistician wants to go to a conference, but the only mean of transport is a plane and he is afraid of terrorists. He sits and calculates the probability of a bomb existing in the plane and finds it is quite high. However, the probability of two bombs in the same plane is small, so he takes a bomb and goes to his flight.
4. I have prepared peas for lunch and I am ready to eat. My algebraist friend walks in and says that the ammount of peas is unnessesary, as all are homeomorphic to each other. He trows all of the them out and now on my plate remains only one. How should I watch my diet this way? Another set-theorist friend comes in, cuts the pea, rotates the pieces and reassembles a huge pea.
5. Any two lines intersect, provided the points are thick enough.
6. Humans invented the decimal system because they have 10 fingers and 32bit computers because they have 32 teeth. Don't think about 16bits, dental care was not too good back then.
7. Statistics is the branch of mathematics where if you put your head in the oven and your feet in the fridge you are ok.
8. There is a missed oportunity in calling the monster group "Gropus".
9. PhD: (abb.) Permanent head Damage.
10. A satellite is hit by a rock and sends back images with several black lines. Should we bring barba-John to fix it? Fortunately, my uncle is responsible, who ties his car door with a rope in order not to go to a workshop. They instead decide to use missing data methods.
11. If a mathematician decides to change his career to a pornstar, he becomes a Möbius stripper.
12. Give your kids a lego cube made of cubical legos and ask them to make two smaller cubes out of it. First one wins.
13. Let there be a difficult theorem. We will show by contradiction that everyone agrees this theorem is true. Assume there exists someone who doesn't think the proof is true and consider their neck. Applying the squeeze theorem will show that this person does not exist, a contradiction.
14. There exist some mathematicians who drown in generality and others who study tensors on a set with 3 elements.
15. A physicist, a biologist and a mathematician are sitting in a street café watching people entering and leaving the house on the other side of the street. First, they see two people entering the house. Time passes. After a while, they notice three people leaving the house. The physicist says: "The measurement wasn't accurate". The biologist says: "They must have reproduced". The mathematician says: "If one more person enters the house, then it will be empty".
16. A poet, a priest, and a mathematician are discussing whether it's better to have a wife or a mistress. The poet argues that it's better to have a mistress because love should be free and spontaneous. The priest argues that it's better to have a wife because love should be sanctified by God. The mathematician says, "I think it's better to have both. That way, when each of them thinks you're with the other, you can do some mathematics".
17. Three logicians walk into a bar. The bartender says, "do you each want a drink?" The first logician says "I don't know." The second says "I don't know." The third says "Yep!"
18. A group of physicists and a group of mathematicians travel to a conference by train. Physicists have bought a ticket each, while mathematicians bought only one ticket for the whole group. When the train departs, mathematicians go to the bathroom together. The conductor knocks, they crack the door open and provide a ticket. The conductor assumes that there is only one person inside and leaves. On the way back from the conference physicists buy one ticket, while mathematicians buy none. Physicists go to the bathroom together, wait for the knock and provide their ticket. Mathematicians knock, grab the ticket and run to the bathroom in the next car.
19. Your mom's so fat she's almost everywhere.
20. 100% of rings without 1 experience identity crisis.
21. A topologist walks into A-bar and says: "Sorry, I didn't realize you were closed". (Variation: A topologist walks into a bar and says: "Sorry, I didn't realize you were closed".)
22. Yellow normed complete spaces are Bananach.
23. Two random variables were talking in a bar. They thought they were being discrete but I heard their chatter continuously.
24. I am not fat, I just do not go fast enough.
25. (Modification of the poem "Μπαλάντα στους άδοξους ποιητές των αιώνων" [Ballad to the inglorious poets of the centuries] of K. Kariotakis).
Από θεούς και ανθρώπους μισημένοι,
σαν άρχοντες που εξέπεσαν πικροί,
μαραίνονται οι Cartan· τους απομένει
πλούτος η Riemann πλούσια και αργυρή.
Οι Minkowski με μετρικές αμέτρητες την τρομερή
των Γαλιλαίων εκδίκηση μεθούνε.
Μα εγώ θα γράψω μια λυπητερή
μπαλάντα στους μαθηματικούς άδοξοι που ‘ναι.
Αν έζησαν οι Saccheri δυστυχισμένοι,
και αν οι Lobatchevski εζήσανε νεκροί,
η Αθανασία τους είναι χαρισμένη.
Κανένας όμως δεν ανιστορεί
και το έρεβος εσκέπασε βαρύ
τους μαθηματικούς που ανάξια ερευνούνε.
Μα εγώ σαν προσφορά κάνω ιερή
μπαλάντα στους μαθηματικούς άδοξοι που ‘ναι.
Του κόσμου η καταφρόνια τους βαραίνει
κι αυτοί περνούνε αλύγιστοι και ωχροί,
στην τραγική απάτη τους δοσμένοι
που κάπου πέρα η Δόξα καρτερεί,
παρθένα βαθυστόχαστα ιλαρή.
Μα ξέροντας πως όλοι τους ξεχνούνε,
νοσταλγικά εγώ κλαίω τη θλιβερή
μπαλάντα στους μαθηματικούς άδοξοι που ‘ναι.
Και κάποτε οι μελλούμενοι καιροί:
«Ποιος άδοξος μαθηματικός» θέλω να πούνε
«την έγραψε μιαν έτσι πενιχρή
μπαλάντα στους μαθηματικούς άδοξοι που ‘ναι;»
(Although it is difficult to translate poems, here is a rough translation).
Hated by gods and men,
like rulers who have fallen bitter,
the Cartans wither; all that remains for them
is Riemann's rich and silver wealth.
The Minkowskis, with countless metrics, are intoxicated by the terrible
revenge of the Galileans.
But I will write a sad
ballad to the mathematicians who are inglorious.
If the Saccheris lived unhappy,
and if the Lobatchevskis lived dead,
their Immortality is granted.
But no one recounts
and the umbra has covered heavily
the mathematicians who research unworthily.
But I, as an offering, make a sacred
ballad to the mathematicians who are inglorious.
The world's contempt weighs on them
and they pass by unbending and pale,
given to their tragic deception
where somewhere beyond Glory endures,
virgin profoundly cheerful.
But knowing that everyone forgets them,
nostalgically I cry the sad
ballad to the inglorious mathematicians.
And someday future times:
"Which inglorious mathematician" I want them to say
"wrote such a meager
ballad to the inglorious mathematicians?"
26. A farmer ties a goat to a pole in a square field and ask his algeraist friend how long the rope should be in order for the goat to eat (1/4)th of the field. The algebraist answers that it is impossible.
27. Mathematics is like pork: Every part is good.
28. [...]
1. The Murder Weapon
The following is by J. H. Conway:
Coxeter came to Cambridge and he gave a lecture, then he had this problem for which he gave proofs for selected examples, and he asked for a unified proof. I left the lecture room thinking. As I was walking through Cambridge, suddenly the idea hit me, but it hit me while I was in the middle of the road. When the idea hit me I stopped and a large truck ran into me and bruised me considerably, and the man considerably swore at me. So I pretended that Coxeter had calculated the difficulty of this problem so precisely that he knew that I would get the solution just in the middle of the road. In fact. I limped back after the accident to the meeting. Coxeter was still there, and I said, "You nearly killed me." Then I told him the solution. It eventually became a joint paper. Ever since, I've called that theorem "the murder weapon." One consequence of it is that in a group if \(a^2=b^3=c^5=(abc)^{-1}\), then \(c^{610}=1\).
2. The Sandwich Rejection
The following story was told to us by M. Dafermos in Crete. To be frank, it is difficult for us to believe such a story, but we share it nevertheless, because it is funny and undocumented.
There once was a mathematician in Greece after junta who wanted to continue his studies in Princeton. He filed an application, but a problem was that instead of translating "Βραβείο ηρώων Πολυτεχνίου" to "Award for the heroes of Polytechnion" in his CV, he instead opted for "Rebels award". The examination commitee was very sceptical in Princeton, thinking of denying his application because of it, despite displaying great mathematical capabilities. Dafermos found one of the mathematicians of the commitee and explained what the award really was. The mathematician said that he would transfer this to their meeting, so Dafermos waited outside eagerly. After some time the mathematician walks out and Dafermos asks what happened. He replies something of the form: "You cannot imagine what happened! I haven't eaten all morning and when I go in, they have prepared food for us. I go in, I grab some coffee and a sandwich. The coffee was ok, but the sandwich... The sandwich was the worst sandwich I have ever eaten, absolutely horrendous. I don't think you have ever eaten a sandwich like this before Mihali". Dafermos asks what happened with the application. He replies: "Oh, I don't know, I didn't say anything, the sandwich was so bad that I immediately left". In the end they rejected the application.
3. 91 is the smallest number which looks like a prime but it isn't
The following is by J. H. Conway:
Now, lots of you probably thought that 91 was prime. Well, in fact you are near the truth. 91 is actually the first number that looks prime but isn't. So, this is a rotten theorem and a discovery that I'm very proud of and I'll give you the proof of it. You see, if a number is divisible by 2, 3 or 5 it doesn't even look prime. Okay, so 91 at least evades that test. It follows if the number looks like a prime but isn't, it must be made out of sevens and elevens and thirteens and higher. Seven 7s are 49 and that looks square and we know this isn't prime. Then seven 11s is 77 and that doesn't look prime. But seven 13s is 91, end of the proof.
4. The Goose Reward
Of course in vector space you can have a (Hamel) basis and therefore represent any element as a finite combination of the basis elements (possibly uncountable basis). For doing analysis another kind of basis is preferable, that is a Schauder basis, where it is possible to write every element as an infinite series involving the basis elements (always countable "basis", by definition). $$x = {\lim_{n \to \infty}}^{||\cdot||} \sum_{k=1}^n \lambda_k e_k = \sum_{k=1}^\infty \lambda_k e_k$$ This infinity requires an added stucture to our vector space that can express convergence, that is the Banach space structure. It is not difficult to prove that every Banach space with Schauder basis is seperable, however the converse was something that gave headaches to the mathematicians of the era. Per Enflo in 1972 managed to construct a seperable Banach space without a Schauder basis, thus disproving the converse. Earlier, actually a lot earlier, in 1936, Mazur had written about a similar problem on the Scottish Book, promising a live goose reward to whoever managed to find a solution. Even after 36 years, Mazur kept his promise and awarded a live goose to Per Enflo for his achievement, in a ceremony held at Stefan Banach Center. The ceremony was broadcast thoughout Poland. A picture can be found here.
Some of them are posted in our Math Club's facebook webpage.