Mathematician’s Answer

The Mathematician’s Answer is a meta-joke about how mathematicians usually behave in jokes. From tvtropes:

If you ask someone a question, and he gives you an entirely accurate answer that is of no practical use whatsoever, he has just given you a Mathematician’s Answer.

It goes further on to say: “A common form of giving a Mathematician’s Answer is to fully evaluate the logic of the question and give a logically correct answer. Such a response may prove confusing for someone who interpreted what they said colloquially.”

Perhaps the most famous example is the hot-air balloon joke, where a man in a hot-air balloon asks someone where he is, to which the response is, “You’re in a hot-air balloon!” The rider concludes that the responder must be a mathematician, because the answer given was absolutely correct but utterly useless.

The tvtropes site contains a bunch of examples of Mathematician’s Answer in dialog. But this kind of joke also sometimes pokes fun at actions as well as words. My favorite is the hotel joke (this version from the Cherkaev “Math Jokes” collection):

An engineer, a physicist and a mathematician are staying in a hotel.

The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed.

Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed.

Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, “Ah, a solution exists!” and then goes back to bed.

In line with the engineer/physicist/mathematician trio, another great one is the Scottish sheep joke:

A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.

“Aha,” says the engineer, “I see that Scottish sheep are black.”

“Hmm,” says the physicist, “You mean that some Scottish sheep are black.”

“No,” says the mathematician, “All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!”

And then, we have the infamous examples where it was the students ironically who used the Mathematician’s Answer on their math teachers:



Now, aside from the meta-joke status of the Mathematician’s Answer, is there any truth to it? Do math-minded people really say, “You’re in a hot air balloon,” in real life?

From all the math classes I’ve taken at college, I have never witnessed a professor respond unwittingly with a Mathematician’s Answer. Every time it was used, it was clear that it was meant as a joke. Sure, some live up to mathematician archetype, but they’re all normal people, not John Nashes.

In high school, my favorite form of humor was the pun. Starting junior or senior year of college, however, I had somehow transitioned to the Mathematician’s Answer as my go-to response when I can’t think of anything to say. It is extremely easy to use, as almost every situation can lead to this kind of joke. It’s really fun to use and really versatile.

It doesn’t even need to be used in response to a question. Just yesterday, someone remarked that it was March 1st already. Immediately, I added, “Oh yeah, that’s exactly one month away from April 1st.” The same person later asked how far 10 yards was, and, like a true mathematician, I answered by saying it was like 5 yards but double that.

Our campus Internet has one network called “RedRover” and another called “RedRover-Secure.” Someone asked what the difference between these was, and I quickly responded, “Well, they’re the same, except one of them is secure.”

I think it interests me because I’m generally fond of logical and tautological humor. The only downside of the Mathematician’s Answer is that it doesn’t really work in anything that is related to mathematics. The language of math is designed to minimize ambiguity, and even when situations do arise where there are two interpretations, it’s much harder to distinguish between a literal and a figurative meaning. One of the few mathematical ambiguities I know if is if someone writes

1 \leq x, y \leq 10,

do we choose x and y such that x is at least 1 and y is at most 10, or is it that both x and y are between 1 and 10? On the other hand, Mathematician’s Answer works really well in areas as far removed from mathematics as possible. Anyway, here is one last example:

An engineer, a physicist and a mathematician find themselves in an anecdote, indeed an anecdote quite similar to many that you have no doubt already heard. After some observations and rough calculations the engineer realizes the situation and starts laughing. A few minutes later the physicist understands too and chuckles to himself happily as he now has enough experimental evidence to publish a paper.

This leaves the mathematician somewhat perplexed, as he had observed right away that he was the subject of an anecdote, and deduced quite rapidly the presence of humor from similar anecdotes, but considers this anecdote to be too trivial a corollary to be significant, let alone funny.

On the Naming of Terms in Several Disciplines


Recently I watched an entertaining talk by Neil deGrasse Tyson in which he poked fun at the confounding complexity of biological and chemical terms, in contrast to the elegant simplicity of terms in astrophysics. The segment starts at 14:34 of the talk and goes till about 17:00.

[15:01] What do you call spots on the Sun? [Pause] Sunspots!


Indeed, terms like sunspot, red giant, supergiant, nova, supernova, ring, moon, black hole, pulsar, dark matter, dwarf planet, spiral galaxy, singularity, solar flare—it is immediately obvious what these things describe. Even terms like neutron star or Trans-Neptunian object are clear if one is familiar with neutrons or Neptune. Let us see what term sound like in other disciplines.


What do you call the most important molecule in your body that contains all your genetic information? Deoxyribonucleic acid. What do you call the energy molecule that your body runs on? Adenosine triphosphate. What do you call the most common liquid you drink (if you aren’t a college student)? Dihydrogen monoxide.


Things like these are what Tyson was getting at, where, without even going into the ideas or concepts, a student may be already confounded by the sheer terminology.

Granted, at the core all these names make sense and are very systematically denominated. For instance, “dihydrogen monoxide” describes exactly what the constituents of the molecule are: 2 hydrogen atoms and 1 oxygen atom. And “deoxyribonucleic acid” is really just a nucleic acid (a nucleotide chain) with deoxyribose as the sugar component. Even the term “deoxyribose” is well named, as it is the sugar obtained by removal (de-) of an oxygen atom (oxy) from a ribose sugar.

In this respect, I don’t think biochemical terms are really as confounding to a scientifically literate population as Dr. Tyson makes them out to be; however, I do see his point in that they would confuse the hell out of someone who is not scientifically literate. Even then, these terms would not cause an illiterate person to gain a wrong understanding.

I claim that while biochemical terms are quite abstract, at least they are not misleading.


“This allocation of resources is Pareto efficient.”

This term might have a positive connotation, as efficiency is associated with good, and so the masses may support a policy having anything having to do with it. However, it is possible that an allocation where the top 1% controls 99% of the resources is Pareto efficient. Indeed, an allocation where one person controls 100% of the resources is Pareto efficient, as the term only concerns whether the allocation could be changed such that one could benefit without harming any one else. Given the misleading connotation, it would be disastrous if this term were ever uttered by an economist—or worse yet, a politician—in public discourse.


It is especially misleading as economics generally has very simple, intuitive terms: supply, demand, goods, depression, inflation, market, labor force, bubble, money, wage, etc. These are all good terms. But sometimes, a term is just plain misleading: for instance, the fiscal cliff.

Medicine and Psychology

The terms disease and disorder are pretty misleading. A disease does not have to be infectious, and someone with a disorder could behave just as normally, whatever that means, as a “normal” person. Even sane and insane are notoriously difficult to tell apart.

one flew over the cuckoos nest scene

And what does it mean to cure someone?


That said, most psychology terms are pretty self-explantory, albeit sometimes difficult to test accurately.


A field like astrophysics in which the terms are extremely clear. The only term I find troubling is postmodern, which seems to imply something that it is not.


This is a very technical field, where speed and velocity mean different things, and if you are describing a scenario, you must use words like force, momentum, and energy very carefully. Technicality aside though, it is very obvious what the terms are about.


Given that linguistics should have something to do with this point, you might expect linguistics to have very intuitive terms. Depending on the subfield, however, there are some very non-obvious terms. What is a morpheme?

Computer Science

Like math, it is very unintuitive at times. For instance, computer scientists have no idea what a tree is supposed to look like.



Math terms are both super-technical and very non-obvious, given that half the terms are named after a person. Even for the half that are words in English, there are some issues. In topology, for instance, you might think that open is the opposite of closed, but in reality a set can be open, closed, neither open or closed, or both open and closed (in which case it is called clopen). What about injectionsurjection, and bijection—what is a “jection”?

The term rational numbers for fractions makes sense as fractions are ratios, but who came up with real, imaginary, or complex? It becomes worse in abstract algebra, where you have things like groups, rings, and fields. At least the word object is what you think it means: just anything. And measure theory makes a lot of sense. A measure is pretty much what you think it means, and almost means almost what you think it means.

I think math is the only subject where two renowned experts can have a discussion, each not having a clue what the other is talking about. In this respect, I think mathematics beats biochemistry in confusion of terminology.

Orwell, Chomsky, and the Power of Twisting Language

Choosing the right word is very important, but I’ve recently found it to be far more important than I previously thought. Influences: George Orwell, Noam Chomsky.

An Experiment

Consider the 1974 Loftus and Palmer experiment [1][2][3]. Participants were shown identical short videos of car crashes, and were then asked one of the questions:

  1. About how fast were the cars going when they smashed into each other?
  2. About how fast were the cars going when they collided into each other?
  3. About how fast were the cars going when they bumped into each other?
  4. About how fast were the cars going when they hit each other?
  5. About how fast were the cars going when they contacted each other?

The only difference is the wording. Yet it was able to produce a statistically significant result:

People will believe what they hear.

Framing the Question: Politics and Religion

There are many issues today in America that suffer similar biases from wording.

Take immigration for example. Most people would probably be against illegal aliens, but would probably be more sympathetic towards undocumented workers. With this phrasing, the same person might support giving rights to undocumented workers, yet might vote the opposite way when the media or a political party calls them illegal aliens. Even though they are referring to the same people, one term focuses to the illegality, while the other focuses on their work. Of course when you call them illegal aliens, you’re going to have a biased discussion.

Abortion falls to the same bias. It is the termination of pregnancy, yet those who are opposed label it as bad as killing babies.

Or if you are not a Muslim, you are a non-Muslim; however, Islamist extremists label you as an infidel.

And don’t think Christianity gets off the hook here. A non-Christian is similarly labeled by extremists as a blasphemer (or infidel or heretic as well). And since one can’t be both Muslim and Christian at the same time, every person on Earth is an infidel or a blasphemer. That’s just the logical truth.

Framing the Question: Science and Religion

The power of twisting language is nowhere more important than in the evolution vs creationism “debate.” The reason I put the word “debate” in quotes is that it’s really not a debate where both sides use logic, reason, and facts. Yet, as long as the creationists manage to convince people there is still “debate” by labeling the whole thing as a “debate,” then they are winning their “debate.”

So far, every debate I’ve seen between evolution and creationism, and between logic and religion in general, is more of a lecture to a stubborn adolescent who still believes in fairy tales. The power of language is so strong that in labeling the conflict as a “debate” in the first place, the creationists are creating the false presumption that there even is a debate.

They use completely wrong and misleading words to describe the theory of evolution. Even calling it a theory or hypothesis in the first place is misleading, because the word theory in everyday speech strongly focuses on the possibility of being uncertain or wrong (if I said “My theory about why the grades were lower on this test…”), whereas the word theory in science implies strong logical mechanisms and the possibility to confirm or deny through evidence (such as the theory of gravity).

To adapt this “debate” to everyday speech, we should really call it the fact of evolution. One is of course allowed to call it a theory, but only seriously if one actually understands it scientifically. Most of those who claim “it’s just a theory” don’t actually understand it at all.

A debate would imply both sides are using reason. That is hardly the case. It is really more of a clearing of misunderstandings than the use of any higher cognitive skills.

The following words are extremely well misunderstood: random, chance, selection, adapt, and purpose. Consider the following dialog, which more or less actually happened (I am putting quotes around the word “Evolutionist” as it is really just a label that shouldn’t have to exist, just as you don’t have to call people who believe the world is round “Round-Earthers”):

Creationist: It’s hard to believe that the eye happened by accident.

“Evolutionist”: Evolution doesn’t say it happened by accident.

Creationist: Then it has to have a purpose.

What’s going on here is not a debate at all, but an abuse of language. The eye does not have any intrinsic purpose, but it is also not an accident. Creationists often create this false dichotomy of purpose vs accident. And when they show it is preposterous for life to have developed by accident, they think they have shown it must have been done on purpose.

Randomness does not imply either purpose or accident. Why is a cheetah fast? Because in a larger pool of animals in an ecosystem, if it were slower, it wouldn’t be able to catch its prey, and it would die off, and that would have happened millions of years ago, so we wouldn’t see it today. That’s the simple logic. No accident or purpose is implied.

So many other words—good, evil, salvation, sin, faith, and I’m sure I’m missing a ton more—are all heavily loaded, ill-defined, ambiguous concepts that are twisted around by religion to suit its needs depending on the situation. This is Orwellian Doublespeak at its strongest.

Words and the Future

It is imperative that the American public understand how loaded words are affecting its choices and decisions. The election process should be dependent on the rational discussion of real issues, not by a massive popularity contest shrouded by mutual insults and loaded words oversimplifying the situation and vilifying the other party. News should be news, not political indoctrination. Language should be the way we voice our concerns to the government, not the way political parties usher us like pawns to certain death.

In addition to math and science education, which should most certainly be improved, we really do need to keep our English and history classes in able hands. But, in English classes, instead of teaching only books written long in the past, they should occasionally make students read current news articles and critically think about them. Then maybe people will realize that English is not all pointless. And once this happens, the government will be afraid, and it will be forced to listen to the educated American people, as history perhaps once intended.

How Do You Define Obvious?

Mathematical Obviousness

Mathematicians often say things like “It is obvious that…” or “It can be easily shown that…” when the desired result is relatively easy. But to a normal person, what they are saying is not obvious at all. Other fields often have similar situations. An economist might consider a particular problem trivial, yet even a bright student might not understand it at all.

Consider the following:

1 + 1 = 2

That was obvious, right? Then what about this:

\frac{1}{2} = \frac{3}{6}

You probably thought that was obvious as well. Even though the two numbers are written differently, they are the same number.

Okay, one more statement. The question is, as always: obvious or not obvious?

0.999... = 1

There are three types of people on this issue:

  1. Those who think it is true and find it obvious.
  2. Those who think it is true and find it not obvious.
  3. Those who think it is false.

My opinion, which belongs to that of the first group, is no doubt influenced by the fact that I am studying math. For me, this is the same as saying 1 + 1 = 2 or saying 1/2 = 3/6. The two expressions on the left and right sides of the equals sign are written differently, but as the math shows, they exactly equal. Yet many people cannot accept this truth, and are bent on believing 0.999… is not equal to 1.

True Story

Last year I took Math 6120, or graduate Complex Analysis. One day Professor John Hubbard was proving Jensen’s Theorem. I do not remember where in the proof it happened, but at some point, there was a small detail that Hubbard could not immediately prove.

As it turns out, the book he was using left out this particular part of the proof. When Hubbard prepared his notes, he assumed that any small detail the author left out would be “obvious,” and that he would be able to derive it quickly during the lecture.

So he writes the statement on the board and asks, “Why is this obvious?” Nobody in the room has any idea.

It took a while to figure out why that little “obvious” statement was true. And even then, Hubbard had to re-explain, as there were grad students who still did not understand it. Then we found that our justification for why it was “obvious” did not work in general, but luckily did work for this specific problem. When it was all over, this “obvious” result took about 15 minutes of our time.

List of Banned Words Constitutes a “Fail”

Apparently, the Lake Superior State University takes pride in its 2011 List of Banished Words, which “refudiates” the top 2010 Shakespearean gems like “viral,” “epic,” and “fail.” Here at Cornell, and doubtless many other places, we share a different opinion on the addition of new words to the English language. Such words are the backbone of current Internet culture. Perhaps the pure linguists at LSSU who condemn such modern innovations should “man up” and face the real world as it is; of course, that suggestion “I’m just sayin’.” My own take is that we, “the American people,” should ignore these superficial laws, and adhere instead to our founding fathers’ vision of life, liberty, and the pursuit of “living life to the fullest.”

Not only these, but other core American values such as freedom are contradicted by foolishly restricting the way we use words. Why should we be not allowed to use words in new ways? English, after all, is well known to be a language that grows over time. Why is Shakespeare allowed to add dozens of words to the dictionary, but the entire constituency of the Internet, consisting of millions of highly literate users, not even allowed to add a few definitions to words that are pre-existing? Below are the words in the banlist, and the reasons why each one is perfectly valid in its modern definition:


Meaning in modern culture: adj., the state of having reached a massive Internet audience.

Example: The “2011 List of Banished Words” went viral as it was facebooked 13K times.

Why pure linguists hate it: The new usage corrupts the original definition of the word, which is of or relating to a virus. Something that is viral, according to them, should have to do with biological viruses.

Why it’s perfectly acceptable: An analogy is often the best way to explain an idea. When a virus spreads, the number of people affected goes up. The same happens when certain stories are shared on the Internet. Viral seems to be the most accurate word to describe such a phenomenon.


Meaning in modern culture: adj., very awesome; very amazing

Example: At first I didn’t understand anything about language; then I had that aha moment, and it was like, epic!

Why pure linguists hate it: Epic has become so overused that the standards for something considered epic have been degraded to virtually nothing.

Why it’s perfectly acceptable: What do they want instead? A hierarchy of epicness? Besides, from the way the Internet has used it, “epic” now has a broadened definition. Today, it refers not only to things that are majestic in scope, but also things that are funny, clever, flawless, and generally anything that is well thought-out and well made. There seems to be nothing epic at all about banning words. Well, except…


Meaning in modern culture: adj. or noun, pretty much anything that doesn’t work as planned, or a plan that is extremely flawed.

Example: A: “Did you hear about that politician who said ‘refudiate’ instead of ‘repudiate’?” B: “Yeah, that was an epic fail!”

Why pure linguists hate it: Fail is supposed to be a verb: not a noun, not an adjective.

Why it’s perfectly acceptable: To refuse to use a word is to fail oneself; to force others to refuse it is a fail for mankind. It has become so common a word that it is difficult to see what would happen if it were banned.


Meaning in modern culture: noun, the component of a product that makes it shine.

Example: His latest novel once again has well-developed characters and a meaningful plot, but the wow factor that made it go viral was that the book invented 17 new words, all of which had become commonplace just one year after its publication.

Why pure linguists hate it: Overused; cliché.

Why it’s perfectly acceptable: Again, if it’s used by so many people, there’s gotta be something appealing about it. It’s because wow factor is the most precise and forcible way to describe what it describes. If you substitute it with other phrases such as “what stands out” or “the distinguishing aspect,” you run into other clichés or end up with a wordier phrase.


Meaning in modern culture: noun, the moment when you understand some fact that was previously unclear.

Example: For some reason I had thought for the longest time that Shakespeare was a French epic author; when I finally realized he was English, I had an aha moment in which my linguistics homework made a lot more sense.

Why pure linguists hate it: There’s no real reason people hate it, other than that it isn’t defined in the dictionary.

Why it’s perfectly acceptable: On the original site, someone said: “All this means is a point at which you understand something or something becomes clearer. Why can’t you just say that?” We can, why can’t we just say aha moment?


I have actually never heard this term used before, so I can’t really comment on it. From my research, it seems to just be a portmanteau of background and history. It is still two words though.

7. BFF

Meaning in modern culture: nounBest Friend Forever.

Example: Would you like to meet my new BFF? She has an epic back story.

Why pure linguists hate it: The “forever” part is never true. You can have a BFF for 10 minutes, and then have a different BFF. Which means that person never was a BFF in the first place.

Why it’s perfectly acceptable: Just kidding, I actually agree with the linguists on this one.


Meaning in modern culture: verb, to show stereotypically masculine traits.

Example: After Jim retreated from fighting the grizzly bear with his bare hands, his pals made fun of him, saying “fail,” and told him to man up.

Why pure linguists hate it: It is “bullying and sexist.” (quote from the link)

Why it’s perfectly acceptable: Again, I agree with the linguists. I assure you that the term was used in the introduction only for attention-grabbing.


Meaning in modern culture: verb, to repudiate.

Example: One soldier refudiated the order to man up during a hopeless assault, choosing instead to strategically retreat. She was the only survivor, the only one to live life to the fullest.

Why pure linguists hate it: The word is repudiate, not refudiate. Refudiate is just a slip of the tongue made by Sarah Palin.

Why it’s perfectly acceptable: When you say refudiate, everyone will understand it. The difference is so small that it’s almost like a regional accent. Plus, /p/ and /f/ aren’t TOO different as far as consonants go.


I’ve never even remotely heard of this term, but apparently it has a political back story, so I’ll skip it.


Meaning in modern culture: noun, the American people.

Example: In November 2008, the American people wanted change, not fail.

Why pure linguists hate it: Again, because it’s so overused by politicians.

Why it’s perfectly acceptable: There’s nothing wrong with the phrase. I seriously don’t understand why any person, especially an American, would be against this. The only valid complaint I could find is that the phrase “the American people” lumps all Americans into the same group, implying we all want and do the same thing. This however is a purely semantic issue. Anyone with any intelligence in any field should know that “the American people” is a generalization and not an absolute.


Meaning in modern culture: interjection, what I just said is my honest opinion, but I wish that it not be associated with me in any way. OR, what I just said had nothing to do with what we were saying before, but just pretend that it was related somehow.

Example: A: “I like things viral.” B: “What?” A: “I’m just sayin’.”

Why pure linguists hate it: When formally used, it is a redundancy: of course you just said it!

Why it’s perfectly acceptable: A lot of the time, we engage in casual conversation instead of formal conversation. (And according to sociologists, casual conversation is often more important than formal conversation. I’m just sayin’.) In informal conversation, some phrases are there just for the sake of conversation. If pure linguists want people to stop saying “I’m just sayin’,” they’ll have to get people to stop saying a lot of other things too.


Meaning in modern culture: verbs, to use Facebook/to use Google for something.

Example: I didn’t understand the article she facebooked, so I googled it. Then I had an aha moment.

Why pure linguistics hate it: They hate it in general when people use nouns as verbs. It impacts them so greatly.

Why it’s perfectly acceptable: Actually, according to the OED (Oxford English Dictionary), google is a perfectly valid verb meaning to search for information on Google. As for facebook, I’m not quite sure. I still use Facebook only as a noun, but that might soon change. There’s nothing wrong with its being used as a verb.


Meaning in modern culture: verb, to have what you consider an enjoyable and meaningful life.

Example: I first thought of becoming a lawyer, but then I decided that stealing from the American people would be immoral, and that rather, I would live life to the fullest.

Why pure linguists hate it: The phrase is overused, redundant, and senseless.

Why it’s perfectly acceptable: It’s an idiom—it doesn’t need to make literal or logical sense. And of course, “live life” is a redundancy, but it’s eloquent. The verb “live” is more powerful than the noun “life,” but if you just said “live to the fullest,” it would be utterly forgettable. To live life to the fullest is also to live the most memorable one.

So the next time you hear someone complaining against the growth of the English language, you should tell them to live life to the fullest, enjoy a few fails, and have some epic experiences. Maybe you’ll give that person an aha moment. At worst, if the person starts arguing vehemently with you, you could simply reply, “I’m just sayin’.”