Two-thirds of a Pun
Algebra is x-sighting.
Complex numbers are unreal.
Decimals make a point.
Einstein was ahead of his time.
Doing geometry keeps you in shape.
I like angles… to a degree.
I could go on and on about sequences.
I’ll do algebra, I’ll do trig, and I’ll even do statistics, but graphing is where I draw the line!
I’m partial to fractions.
I feel positive about natural numbers.
Lobachevski was out of line.
On average, people are mean.
Translations are shifty.
Vectors can be ‘arrowing.
Without geometry, life would be pointless.
Two-thirds of a Pun
by A. B. Smith
A. C. Jones in his paper “A Note on the Theory of Boffles,” Proceedings of the National Society, 13, first defined a Biffle to be a non-definite Boffle and asked if every Biffle was reducible.
C. D. Brown in “On a paper by A. C. Jones,” Biffle, 24, answered in part this question by defining a Wuffle to be a reducible Biffle and he was then able to show that all Wuffles were reducible.
H. Green, P. Smith, and D. Jones in their review of Brown’s paper, Wuffle Review, 48, suggested the name Woffle for any Wuffle other than the non-trivial Wuffle and conjectured that the total number of Woffles would be at least as great as the number so far known to exist. They asked if this conjecture was the strongest possible.
T. Brown, “A collection of 250 papers on Woffle Theory dedicated to R. S. Green on his 23rd Birthday” defined a Piffle to be an infinite multi-variable sub-polynormal Woffle which does not satisfy the lower regular Q-property. He stated, but was unable to prove, that there were at least a finite number of Piffles.
T. Smith, L. Jones, R. Brown, and A. Green in their collected works “A short introduction to the classical theory of the Piffle,” Piffle Press, 6 gns., showed that all bi-universal Piffles were strictly descending and conjectured that to prove a stronger result would be harder.
It is this conjecture which motivated the present paper.
This was actually written by A. K. Austin as “Modern Research in Mathematics,” Math. Gaz. 51 (May 1967) 150.
Old mathematicians never die, they just lose some of their functions.
Old mathematicians never die, they just lose their identities.
Old mathematicians never die, they just tend to zero.
Old mathematicians never die, they just decay.
Old mathematicians never die, they just dis-solve.
Old analysts never die, they just dis-integrate.
Old geometers never die, they just go off on a tangent.
Old geometers never die, they just dis-figure.
Old geometers do die… but they become angles.
Old numerical analysts never die, they just get disarrayed.
Old statisticians never die, they’re just broken down by age and sex.
John C. George said this, and is credited for starting this type of joke.
Proof by vigorous handwaving.
Works well in a classroom or seminar setting.
Proof by forward reference.
Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
Proof by funding.
How could three different government agencies be wrong?
Proof by example.
The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof.
Proof by omission.
Examples include: “The reader may easily supply the details,” or “The other 253 cases are analogous,” etc.
Proof by deferral.
“We’ll prove this later in the course.”
Proof by picture.
A more convincing form of proof by example. Combines well with proof by omission.
Proof by intimidation.
Proof by cumbersome notation.
Best done with access to at least four alphabets and special symbols.
Proof by exhaustion.
An issue or two of a journal devoted to your proof is useful.
Proof by obfuscation.
A long plotless sequence of true and/or meaningless syntactically related statements.
Proof by wishful citation.
The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.
Proof by eminent authority.
“I saw Karp in the elevator and he said it was probably NP-complete.”
Proof by personal communication.
“Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].”
Proof by reduction to the wrong problem.
“To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.”
Proof by reference to inaccessible literature.
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
Proof by importance.
A large body of useful consequences all follow from the proposition in question.
Proof by accumulated evidence.
Long and diligent search has not revealed a counterexample.
Proof by cosmology.
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
Proof by mutual reference.
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.
Proof by metaproof.
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.
Proof by vehement assertion.
It is useful to have some kind of authority relation to the audience.
Proof by ghost reference.
Nothing even remotely resembling the cited theorem appears in the reference given.
Proof by semantic shift.
Some of the standard but inconvenient definitions are changed for the statement of the result.
Proof by appeal to intuition.
Cloud-shaped drawings frequently help here.
The uses of fallacy
by Paul V. Dunmore
In the last hundred years or so, mathematics has undergone a tremendous growth in size and complexity and subtlety. This growth has given rise to a demand for more flexible methods of proving theorems than the laborious, difficult, pedantic, “rigorous” methods previously in favor. This demand has been met by what is now a well-developed branch of mathematics known as Generalized Logic. I won’t develop the theory of Generalized Logic in detail, but I must introduce some necessary terms. In Classical Logic, a Theorem consists of a True Statement for which there exists a Classical Proof. In Generalized Logic, we relax both of these restrictions: a Generalized Theorem consists of a Statement for which there exists a Generalized Proof. I think that the meaning of these terms should be sufficiently clear without the need for elaborate definitions.
The applications of Generalized Proofs will be obvious. Professional authors of textbooks use them freely, especially when proving mathematical results in Physics texts. Teachers and lecturers find that the use of Generalized Proofs enables them to make complex ideas readily accessible to students at an elementary level (without the necessity for the tutor to understand them himself). Research workers in a hurry to claim propriety for a new result, or who lack the time and inclination to be pedantic, find Generalized Proofs useful in writing papers. In this application, Generalized Proofs have the further advantage that the result is not required to be true, thus eliminating a tiresome (and now superfluous) restriction on the growth of mathematics.
I want now to consider some of the proof techniques which Generalized Logic has made available. I will be concerned mostly with the ways in which these methods can be applied in lecture courses — they require only trivial modifications to be used in textbooks and research papers.
The reductio methods are particularly worthy of note. There are, as everyone knows, two reductio methods available: reductio ad nauseam and reductio ad erratum. Both methods begin in the same way: the mathematician denies the result he is trying to prove, and writes down all the consequences of this denial that he can think of. The methods are most effective if these consequences are written down at random, preferably in odd vacant corners of the blackboard.
Although the methods begin in the same way, their aims are completely different. In reductio ad nauseum, the lecturer’s aim is to get everyone in the class asleep and not taking notes. (The latter is a much stronger condition.) The lecturer then has only to clean the blackboard and announce, “Thus we arrive at a contradiction, and the result is established.” There is no need to shout this — it is the signal for which everyone’s subconscious has been waiting. The entire class will awaken, stretch, and decide to get the last part of the proof from someone else. If everyone had stopped taking notes, therefore, there is no “someone else,” and the result is established.
In reductio ad erratum the aim is more subtle. If the working is complicated and pointless enough, an error is bound to occur. The first few such mistakes may well be picked up by an alternative class, but sooner or later one will get through. For a while, this error will lie dormant, buried deep in the working, but eventually it will come to the surface and announce its presence by contradicting something which has gone before. The theorem is then proved.
It should be noted that in reductio ad erratum the lecturer need not be aware of this random error or of the use he has made of it. The best practitioners of this method can produce deep and subtle errors within two or three lines and surface them within minutes, all by an instinctive process of which they are never aware. The subconscious artistry displayed by a really virtuoso master to a connoisseur who knows what to look for can be breathtaking.
There is a whole class of methods which can be applied when a lecturer can get from is premises P to a statement A, and from another statement B to the desired conclusion C, but he cannot bridge the gap from A to B. A number of techniques are available to the aggressive lecturer in this emergency. He can write down A, and without any hesitation put “therefore B.” If the theorem is dull enough, it is unlikely that anyone will question the “therefore.” This is the method of Proof by Omission, and is remarkably easy to get away with — sorry, remarkably easy to apply with success.
Alternatively, there is the Proof by Misdirection, where some statement that looks rather like “A, therefore B” is proved. A good bet is to prove the converse “B, therefore A”: this will always satisfy a first-year class. The Proof by Misdirection has a countably infinite analogue, if the lecturer is not pressed for time, in the method of Proof by Convergent Irrelevancies.
Proof by Definition can sometimes be used: the lecturer defines a set S of whatever entities he is considering for which B is true, and announces that in the future he will be concerned only with members of S. Even an Honors class will probably take this at face value, without enquiring whether the set S might not be empty.
Proof by Assertion is unanswerable. If some vague waffle about why B is true does not satisfy the class, the lecturer simply says, “This point should be intuitively obvious. I’ve explained it as clearly as I can. If you still cannot see it, you will just have to think very carefully about it yourselves, and then you will see how trivial and obvious it is.”
The hallmark of Proof by Admission of Ignorance is the statement “None of the textbooks makes this point clear. The result is certainly true, but I don’t know why. We shall just have to accept it as it stands.” This otherwise satisfactory method has the potential disadvantage that somebody in the class may know why the result is true (or, worse, know why it is false) and be prepared to say so.
A Proof by Non-Existent Reference will silence all but the most determined troublemaker. “You will find a proof of this given in Copson on page 445,” which is in the middle of the index. An important variant of this technique can be used by lecturers in pairs. Dr. Jones assumes a result which Professor Smith will be proving later in the year — but Professor Smith, finding himself short of time, omits that theorem, since the class has already done it with Dr. Jones…
Proof by Physical reasoning provides uniqueness theorems for many difficult systems of differential equations, but it has other important applications besides. The cosine function for a triangle, for example, can be obtained by considering the equilibrium of a mechanical system. (Physicists then reverse the procedure, obtaining the conditions for equilibrium of the system from the cosine rule rather than from experiment.)
The ultimate and irrefutable standby, of course, is the self-explanatory technique of Proof by Assignment. In a textbook, this can be recognized by the typical expressions “It can readily be shown that…” or “We leave as a trivial exercise for the reader the proof that…” (The words “readily” and “trivial” are an essential part of the technique.)
An obvious and fruitful ploy when confronted with the difficult problem of showing that B follows from A is the Delayed Lemma. “We assert as a lemma, the proof of which we postpone…” This is by no means idle procrastination: there are two possible denouements. In the first place, the lemma may actually be proved later one, using the original theorem in the argument. This Proof by Circular Cross-Reference has an obvious inductive generalization to chains of three or more theorems, and some very elegant results arise when this chain of interdependent theorems become infinite.
The other possible fate of a Delayed Lemma is the Proof by Infinite Neglect, in which the lecture course terminates before the lemma has been proved. The lemma, and the theorem of which it is a part, will naturally be assumed without comment in future courses.
A very subtle method of proving a theorem is the Proof by Osmosis. Here the theorem is never stated, and no hint of its proof is given, but by then end of the course it is tacitly assumed to be known. The theorem floats about in the air during the entire course and the mechanism by which the class absorbs it is the well-known biological phenomenon of osmosis.
A method of proof which is regrettably little used in undergraduate mathematics is the Proof by Aesthetics: “This result is too beautiful to be false.” Physicists will be aware that Dirac uses this method to establish the validity of several of his theories, the evidence for which is otherwise fairly slender. His remark “It is more important to have beauty in one’s equations than to have them fit experiment”  has achieved certain fame.
I want to discuss finally the Proof by Oral Tradition. This method gives rise to the celebrated Folk Theorems, of which Fermat’s Last Theorem is an imperfect example. The classical type exists only as a footnote in a textbook, to the effect that it can be proved (see unpublished lecture notes of the late Professor Green) that… Reference to the late Professor Green’s lecture notes reveals that he had never actually seen a proof, but had been assured of its validity in a personal communication, since destroyed, from the great Sir Ernest White. If one could still track it back from here, one would find that Sir Ernest heard of it over coffee one morning from one of his research students, who had seen a proof of the result, in Swedish, in the first issue of a mathematical magazine which had never produced a second issue and is not available in the libraries. And so on. Not very surprisingly, it is common for the contents of a Folk Theorem to change dramatically as its history is investigated.
I have made no mention of Special Methods such as division by zero, taking the wrong square roots, manipulating divergent series, and so forth. These methods, while very powerful, are adequately described in the standard literature. Nor have I discussed the little-known Fundamental Theorem of All Mathematics, which states that every number is zero (and whose proof will give the interested reader many hours of enjoyment, and excellent practice in the use of the methods outlined above). However, it will have become apparent what riches there are in the study of Generalized Logic, and I appeal to Mathematics Departments to institute formal courses in this discipline. This should be done preferably at undergraduate level, so that those who go teaching with only a Bachelor’s degree should be familiar with the subject. It is certain that in the future nobody will be able to claim a mathematical education without a firm grounding in at least the practical applications of Generalized Logic.
 P. A. M. Dirac, “The evolution of the physicist’s picture of nature,” Scientific American, Amy 1963, p 47.
From The New Zealand Mathematics Magazine, 7, 15 (1970).
On the nature of mathematical proofs
by Joel Cohen
Bertrand Russell has defined mathematics as the science in which we never what we are talking about or whether what we are saying is true. Mathematics has been shown to apply widely in many other scientific fields. Hence, most other scientists do not know what they are talking about or whether what they are saying is true. Thus, providing a rigorous basis for philosophical insights is one of the main functions of mathematical proofs.
To illustrate the various methods of proof we give an example of a logical system.
The perjorative calculus
Lemma 1: All horses are the same colour.
Proof by induction. It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour. Q.E.D.
Theorem 1: Every horse has an infinite number of legs.
Proof by intimidation. Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another colour, and by the lemma that does not exist. Q.E.D.
Corollary 1: Everything is the same colour.
Proof. The proof of Lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional “For all x, if x is a horse, then x is the same colour,” namely “is a horse” may be generalized to “is anything” without affecting the validity of the proof; hence, “for all x, if x is anything, x is the same colour.” Q.E.D.
Corollary 2: Everything is white.
Proof. If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular then: “for all x, if x is an elephant, then x is the same colour” is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain’s The Stolen White Elephant). Therefore all elephants are white. By corollary 1 everything is white. Q.E.D.
Theorem 2: Alexander the Great did not exist and he had an infinite number of limbs.
Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, “If Alexander the Great existed, then he rode a black horse Bucephalus.” But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist.
We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and “forewarned is four-armed.” This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs. Q.E.D.
It is not to be thought that there are not other types of proofs, which in print shops are recorded on the proof sheets. There is the bullet proof and the proof of the pudding. Finally, there is 200 proof, a most potent spirit among mathematicians and people alike.
Condensed from Opus, May 1961.
Grabel’s Law: 2 is not equal to 3. Not even for very large values of 2.
The Fundamental Theorem of Analysis: Any theorem of analysis can be proven on an arbitrarily small piece of paper provided the author is sufficiently vague.
The Golden Rule of Teaching Mathematics: You must tell the truth, and nothing but the truth, but not the whole truth.
The Golden Rule of Deriving: Never trust any result that was proved after 11 pm.
The law of conservation of difficulties: There is no easy way to prove a deep result.
Alcohol and calculus don’t mix. Never drink and derive!
A math professor is one who talks in someone else’s sleep.
Analysts use epsilons and deltas in mathematics because they tend to make errors.
Asked how his pet parrot died, the mathematician answered “Polynomial. Polygon.”
A professor’s enthusiasm for teaching precalculus varies inversely with the likelihood of his having to do it.
A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.
Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas.
Every proof is a one-line proof, provided you start sufficiently far to the left.
For a good prime call, 555.793.7319.
God is real, unless proclaimed an integer.
Graphing rational functions is a pain in the asymptote.
He thinks he’s really smooth, but he’s only C1.
How many problems will you have on the final? I think you will have lots of problems on the final.
If Einstein and Pythagoras were both right, then E = m(a2+b2)
I’ll do algebra, I’ll do trig, and I’ll even do statistics, but graphing is where I draw the line!
In the topologic hell the beer is packed in Klein’s bottles.
Klein bottle for rent. Apply within.
Life is complex. It has real and imaginary parts.
…..And the irrational parts infinitely outweigh the rational ones.
Math: putting the “fun” in “functions” since t=0.
Math is like love; a simple idea, but it can get complicated.
Math problems? Call 1-800-[4-x(2 pi)2]-sin(b)/xy.
Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.
Mobius strip no-wear belt drive! (Please see other side for warranty details.)
Moebius strippers only show you their back side.
My geometry teacher was sometimes acute, and sometimes obtuse, but always, he was right.
Parallel lines never meet, unless you bend one or both of them.
Pie are squared?
No. Pie are not squared. Pie are round. Cornbread are squared.
Recursion [ri-kur'zhun] n. See recursion.
Sex is like math. Add the bed, subtract the clothes, divide the legs, and pray to God you don’t multiply.
Statistics are like a bikini: what they show you is tempting, but it’s what they hide that’s important.
The highest moments in the life of a mathematician are the first few moments after one has proved the result, but before one finds the mistake.
The number you have dialed is imaginary. Please rotate your phone 90 degrees and try again.
The problems for the exam will be similar to the discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159…
The reason that every major university maintains a department of mathematics is that it is cheaper to do this than to institutionalize all those people.
These days, even the most pure and abstract mathematics is in danger to be applied.
The world is everywhere dense with idiots.
To a mathematician, real life is a special case.
1 + 1 = 3, for large values of 1.
5 out of 4 people have problems with fractions.
97.3% of all statistics are made up.
In accordance with the new emphasis on accountability and the Standards of Learning (S.O.L.s), the following rating scale for Mathematics Professors at the University has been devised.
|Rating Scale||Far Exceeds Job Requirements||Exceeds Job Requirements||Meets Job Requirements||Needs Some Improvement||Does Not Meet Minimum Requirements|
|QUALITY||Leaps tall buildings with a single bound||Must take running start to leap over tall buildings||Can leap over short buildings only||Crashes into buildings when attempting to jump over them||Cannot recognize buildings at all|
|TIMELINESS||Is faster than a speeding bullet||Is as fast as a speeding bullet||Not quite as fast as a speeding bullet||Would you believe a slow bullet?||Wounds self with bullet when attempting to shoot|
|INITIATIVE||Is stronger than a locomotive||Is stronger than a bull elephant||Is stronger than a bull||Shoots the bull||Is full of bull|
|ADAPTABILITY||Walks on water||Treads water||Washes with water||Drinks water||Passes water in emergencies|
|COMMUNICATION||Talks with God||Talks with the angels||Talks to himself||Argues with himself||Loses arguments with himself|
|LOGIC||Understands Godel||Has read Godel||Can pronounce Godel||Wears a girdle||Can’t recognize a girdle|
|ALGEBRA||Can prove Fermat’s Last Theorem||Can develop the Quadratic Formula||Can use the Quadratic formula||Can spell the word Quadratic||Advocates being a radical|
|GEOMETRY||Creates consistent sets of axioms||Proves original theorems||Accepts axioms||Proves axioms||Disproves axioms|
|CALCULUS||Does elliptical integrals by inspection||Can prove the Fundamental Theorem||Has heard of the Fundamental Theorem||Advocates table of integration||Advocates busing for integration|
Legend has it that the following column appeared in the Chicago Tribune, DuPage County edition, Tuesday June 29, 1993, page 2-1.
MATH RIOTS PROVE FUN INCALCULABLE
News Item (June 23, 1993) — Mathematicians worldwide were excited and pleased today by the announcement that Princeton University professor Andrew Wiles had finally proved Fermat’s Last Theorem, a 365-year-old problem said to be the most famous in the field.
Yes, admittedly, there was rioting and vandalism last week during the celebration. A few bookstores had windows smashed and shelves stripped, and vacant lots glowed with burning piles of old dissertations. But overall we can feel relief that it was nothing — nothing — compared to the outbreak of exuberant thuggery that occurred in 1984 after Louis DeBranges finally proved the Bieberbach Conjecture.
“Math hooligans are the worst,” said a Chicago Police Department spokesman. “But the city learned from the Bieberbach riots. We were ready for them this time.”
When word hit Wednesday that Fermat’s Last Theorem had fallen, a massive show of force from law enforcement at universities all around the country headed off a repeat of the festive looting sprees that have become the traditional accompaniment to triumphant breakthroughs in higher mathematics.
Mounted police throughout Hyde Park kept crowds of delirious wizards at the University of Chicago from tipping over cars on the midway as they first did in 1976 when Wolfgang Haken and Kenneth Appel cracked the long-vexing Four-Color Problem. Incidents of textbook-throwing and citizens being pulled from their cars and humiliated with difficult story problems last week were described by the university’s math department chairman Bob Zimmer as “isolated.”
Zimmer said, “Most of the celebrations were orderly and peaceful. But there will always be a few — usually graduate students — who use any excuse to cause trouble and steal. These are not true fans of Andrew Wiles.”
Wiles himself pleaded for calm even as he offered up the proof that there is no solution to the equation xn + yn = zn when n is a whole number greater than two, as Pierre de Fermat first proposed in the 17th Century. “Party hard but party safe,” he said, echoing the phrase he had repeated often in interviews with scholarly journals as he came closer and closer to completing his proof.
Some authorities tried to blame the disorder on the provocative taunting of Japanese mathematician Yoichi Miyaoka. Miyaoka thought he had proved Fermat’s Last Theorem in 1988, but his claims did not bear up under the scrutiny of professional referees, leading some to suspect that the fix was in. And ever since, as Wiles chipped away steadily at the Fermat problem, Miyaoka scoffed that there would be no reason to board up windows near universities any time soon; that God wanted Miyaoka to prove it.
In a peculiar sidelight, Miyaoka recently took the trouble to secure a U.S. trademark on the equation “xn + yn = zn” as well as the now-ubiquitous expression “Take that, Fermat!” Ironically, in defeat, he stands to make a good deal of money on cap and T-shirt sales.
This was no walk-in-the-park proof for Wiles. He was dogged, in the early going, by sniping publicity that claimed he was seen puttering late one night doing set theory in a New Jersey library when he either should have been sleeping, critics said, or focusing on arithmetic algebraic geometry for the proving work ahead.
“Set theory is my hobby, it helps me relax,” was his angry explanation. The next night, he channeled his fury and came up with five critical steps in his proof. Not a record, but close.
There was talk that he thought he could do it all by himself, especially when he candidly referred to University of California mathematician Kenneth Ribet as part of his “supporting cast,” when most people in the field knew that without Ribet’s 1986 proof definitively linking the Taniyama Conjecture to Fermat’s Last Theorem, Wiles would be just another frustrated guy in a tweed jacket teaching calculus to freshmen.
His travails made the ultimate victory that much more explosive for math buffs. When the news arrived, many were already wired from caffeine consumed at daily colloquial teas, and the took to the streets en masse shouting, “Obvious! Yessss! It was obvious!”
The law cannot hope to stop such enthusiasm, only to control it. Still, one to wonder what the connection is between wanton pillaging and a mathematical proof, no matter how long-awaited and subtle.
The Victory Over Fermat rally, held on a cloudless day in front of a crowd of 30,000 (police estimate: 150,000) was pleasantly peaceful. Signs unfurled in the audience proclaimed Wiles the greatest mathematician of all time, though partisans of Euclid, Descartes, Newton, and C.F. Gauss and others argued the point vehemently.
A warmup act, The Supertheorists, delighted the crowd with a ragged song, “It Was Never Less Than Probable, My Friend,” which included such gloating, barbed verses as
I had a proof all ready
But then I did a choke-a…
Made liberal assumptions…
Damn! I’m Yoichi Miyaoka!
In the speeches from the stage, there was talk of a dynasty, specifically that next year Wiles will crack the great unproven Riemann Hypothesis (”Rie-peat! Rie-peat!” the crowd cried), and that after the Prime-Pair Problem, the Goldbach Conjecture (”Minimum Goldbach,” said one T-shirt) and so on.
They couldn’t just let him enjoy his proof. Not even for one day. Math people. Go figure ‘em.