Pure Math, Pure Joy 315
e271828 writes "The New York Times is carrying a nice little piece entitled Pure Math, Pure Joy about the beauty and applicability of pure math as carried out at the Mathematical Sciences Research Institute. There is an accompanying slideshow of pictures of mathematicians in action; I particularly loved the picture titled Waging Mental Battle with a Proof."
Ah yes... (Score:5, Funny)
Re:Ah yes... (Score:3, Funny)
Interesting, can you write down a proof for that?
What? (Score:2, Funny)
Visualizing the solution... (Score:4, Interesting)
Very cool article! I liked the statement: "Nobody knows when some abstruse bit of math will float off a blackboard at a place like this and become a..." It reminded me of the radiant primes observation [radiantprimes.com]
I imagine it will be a method similar to this that helps us discover the first billion digit prime number, not some bruteforce method. Speaking of prime numbers & slightly offtopic, on 5/31/2003 there was an eclipse (solar) over Norway from 4:43AM to 6:41AM. 5, 31, 2003, 443 & 641 are all prime...
Re:Visualizing the solution... (Score:5, Funny)
Heh heh... If you noticed that then you would've failed this too. A while back my girlfriend showed me a question from a Mensa test that clued me in to what that organization is all about:
Which is the odd one out: (a) 4 (b) 15 (c) 9 (d) 12 (e) 5 (f) 8 (g) 30 (h) 18 (i) 24 (j) 10
Well, anyone who knows a prime from a hole in the ground would choose (e), but the correct answer was (f), 8. And why? Because it is the only "symmetrical" number, as printed on the page!
Re:Visualizing the solution... (Score:2)
10 is semetrical vertically, pretty much.
Re:Visualizing the solution... (Score:2, Interesting)
Re:Visualizing the solution... (Score:5, Insightful)
What is the next in the sequence of:
1,2,4,...
My answer was . The sequence is the largest number of separate enclosed areas it is possible to make by adding a single straight line to a circle. (i.e. 1 for no lines, 2 for one line, 4 for two lines)
I hate this kind of question, because it is possible to design a sequence such that any number comes next, so any test which includes the possibility of incorrect answers is just plain wrong. Of course you should have to justify your answer, but since the IQ tests are multiple choice...
Re:Visualizing the solution... (Score:3, Funny)
Re:Visualizing the solution... (Score:2, Insightful)
0, 1, 2, ? (Score:4, Interesting)
Obviously there are many solutions. Extra points for the largest possible number (with a decent explanation)
0 > 0 = 0
1 > 1 ! = 1
2 > 2 ! ! = 2
3 > 3 ! ! ! = 6 ! ! = 720 ! approx. 2.6 E+1746
Any higher ??
Dumb question to "test" someone. (Score:5, Insightful)
How is e) (prime) less valid than the solution?
How about g) (The only number greater than 29)?
How about a) because its the "bad luck" number in Chinese culture (Too bad you missed out on that one, "white devil")?
How about j) (Because today is Sunday and I feel like its the correct answer)?
Re: Dumb question to "test" someone. (Score:2)
For example: 4 is the only one which takes that number of letters when written in English. 30 is the only who that's the number of days in a month. And so on.
(Presumably, they were talking about horizontal or rotational symmetry? Otherwise, depending on the font, '30', '10', and '18' might also qualify. In fact, in some fonts, '8' wouldn't qualify for rotational symmetry...)
(j) is correct! (Score:4, Funny)
It is clearly the only answer written in binary.
Re:Dumb question to "test" someone. (Score:2)
Mensa is right based on Ockhams razor (Score:3, Insightful)
Well, anyone who knows a prime from a hole in the ground would choose (e), but the correct answer was (f), 8. And why? Because it is the only "symmetrical" number, as printed on the page!
Well, according to Ockhams razor I would argue that Mensa is right. The concept of symmetry is much simpler than the concept of prime numbers.
Tor
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
Oh, I wouldn't argue that they were wrong; in fact I think that they set up the question this way deliberately to smack mathematically literate people who see numbers and assume that it's about number theory. They're measuring some function of intelligence minus education.
Re:Mensa is right based on Ockhams razor (Score:4, Insightful)
It's sort of like the old biased college aptitude tests and the cup/saucer question where kids from well off white families would know that cup and saucer go together, but poor minority kids had probably never encountered a saucer in their life.
Re:Mensa is right based on Ockhams razor (Score:2)
Re:Mensa is right based on Ockhams razor (Score:2)
That really isn't fair because the question has taken shapes which we recognize as symbols representing an abstract concept and changed their meaning into "simple shapes". It would be natural for someone to look for some unique fundamental property about one of these numbers that is not shared with the others. In this case the people writing the test should have
Re:Mensa is right based on Ockhams razor (Score:2)
Well, you would like to make the assumption that the 8 should be treated not as a symbol on the page, but as an abstraction for a numeric quantity. A reasonable assumption, perhaps,  certainly one that most would make.
But the whole point with this question type is that the answer you get depend very much on what assumptions you mak
Re:Mensa is right based on Ockhams razor (Score:4, Interesting)
The question should be unambiguous, otherwise you are testing to see if people "think like you". If you call it an intelligence test then you must be the definition of intelligence. The question should have opened by stating that these symbols should not be interpretted as representing mathematical numbers.
The Mensa/ Ockham's razor based approach is to find the solution which makes the fewest possible assumptions.
I think you are misusing Ockham's razor. Ockham said entitites should not contain any uneccesary multiplications. Theorizing that one number is unique because it is prime and the others are not does not contain any unecessary assumptions as primality is a basic feature of certain numbers that is true of them regardless of the system used to express them.
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
So you are saying because numerical symbols are simpler to explain as shapes than as a field of philosophy, that any problem involving numbers should first consider their shape since any solution involving that would be simpler to explain?
No, you haven't realized a valid use of Ockham's razor. You are simply using the validity given to it, and twisting i
Re:Mensa is right based on Ockhams razor (Score:4, Insightful)
No. I think the best way is to imagine that you have to explain both alternatives to somebody who is completely clueless, and see which is quicker and easier to explain.
Of course this method does not always work, but I think that in this case most would agree that the symmetry alternative is simpler.
"See if, you turn the paper, the 8 still looks the same. It is the same if you look at it from either direction. If you put a mirror in the middle it does not change. If you look at the other numbers, this does not happen; look!"
"See, the 5 is a prime number. That means that it can only be divided evenly by itself, and one. Division means that...[lengthy explanation]. Even division means that [lengthier explanation]. The reason that one is not included in the definition is that [....]. Now we can look at all the other numbers in turn and see that they are not prime numbers [lengthy calculations, or even lengthier explanations on how they can be indentifed quickly]. Etc. Etc."
Tor
Re:Mensa is right based on Ockhams razor (Score:2)
Danila: Isn't that odd that you have to explain to a clueless person your answers on the Mensa entrance test?
Both of these posts argue that we should take certain things for granted because of the context.
This is usually a very good strategy, but then of course the answer we get depends on our assumptions and the context. A discussion on "the right" answer becomes an excercise in deciding who has the best assump
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
If you a) Write the number in binary it is not symmetric. Mind you, it is:) OK. Scratch that. b) If you use an OCR front it is not (the top part of the glyph is skew and smaller). c) If you do not write down the number but represent it in, for instance, a binary set of charges in capacitors ina dynamic RAM device I am not sure that the concept of symmetry applies at all. d) If you write it as a Maya numeral (Which would be 1 line and 3 dot on top of it) it would only be symmetrical in one axis, but so woul
Re:Visualizing the solution... (Score:3, Interesting)
Which word of four letters can be added to the front of the following words to create other English words?
CARD BOX CODE BAG HASTE
Well, "HASTE" pretty much gives the answer away. But wait, what is a postbox, postcode or postbag? I could make a
Re:Visualizing the solution... (Score:2)
Well, anyone who knows a prime from a hole in the ground would choose (e), but the correct answer was (f), 8. And why? Because it is the only "symmetrical" number, as printed on the page!
And even worse that answer isn't right either. Even assuming that the 8 was type faced nicely, it still has vertical and horizontal reflection symmetry and rotational symmetry order 2. 10 has horizontal reflection symmetry so it is all just a crock
Re:Visualizing the solution... (Score:2)
Re:Not a mensa test question (Score:2)
Some tests are public (Score:2, Informative)
You certainly don't know what you are talking about. Some tests are public and some even free.
For instance, here [mensa.es] (Mensa Spain) [mensa.es] you have a test publicly available.
And there are some books also publicly available sold as Mensa preparatory test books.
And that's not all, they sent me home a test (which I never filled), with solutions.
So, who is the liar?
Waging mental battle with a proof (Score:4, Funny)
Re: Waging mental battle with a proof (Score:2)
Not that pure thinking isn't import to, of course. It's probably like coding: the actual coding is done at a keyboard, even if the important ideas come elsewhere.
Re:Waging mental battle with a proof (Score:3, Insightful)
I thought this photo essay did an admirable job of conveying what thinking for a living is like, yet how does one make this approachable to the general population? I had a conversation with a film director once sitting in an airport (forget his name), but he was asking me what it was like to be a scientist a
Is this really true? (Score:4, Interesting)
I sure hope this isn't really true. If mathematicans aren't really interested in helping understand the world, why should society fund them? I certainly know that a major motivation for my career in science is that understanding the world through science will help people, cure diseases, etc.
Re:Is this really true? (Score:5, Insightful)
However, seeing as how every science consists largely of mathematical models, the ends justify the means, so to speak.
In other words, while a mathematician isnt looking for a way to make a longer lasting lightbulb, his or her ideas eventually work their way into science and engineering applications, even if it takes decades to happen.
Re:Is this really true? (Score:5, Insightful)
Re:Is this really true? (Score:2, Insightful)
Thus mathematicians aren't scientists.
What about Dr. Evil? (Score:5, Funny)
Re:What about Dr. Evil? (Score:2)
Re:What about Dr. Evil? (Score:4, Funny)
Re:Is this really true? (Score:3, Interesting)
So what if the mathematicians work primarily because they enjoy math? So what if the practical applications that come of it are just a side effect? We still get those benifits; does it really matter that those benifits weren't the primary purpose of doing the work?
Re:Is this really true? (Score:3, Interesting)
Well, I guess I'm somewhat annoyed by the way Hollywood likes to present scientists  as people similar to the way the article described mathematicans  that is people that just like puzzles, not worrying about the consequences, even if it m
Re:It's not that obvious (Score:3, Funny)
Nothing. Absolutely nothing. Promise never to use them??
(installing a network sniffer right now)
Re:It's not that obvious (Score:3, Funny)
Searching 1976 to present...
Results of Search in 1976 to present db for:
"prime number": 1238 patents. [uspto.gov]
Re:It's not that obvious (Score:4, Funny)
"prime number": 1238 patents. [uspto.gov]
Ah! So prime numbers are useful for getting patents.

Re:It's not that obvious (Score:2)
Damn, if only it was 1237 patents, and I guess it would be too much to hope that there would only be one dupe.
Re:It's not that obvious (Score:5, Insightful)
Anyway, I'm almost thinking you're trolling because the rest of your post demonstrates some sort of keenness for oversimplification. Maybe you're just not out of secondary school yet, but for your information, trig, calculus and the rest are useful for a lot more stuff than what you mention. All the different areas of maths often intermingle in any physical subject.
For the interesting tidbit of information, there has yet to be a mathematical discovery which has not found practical applications. Even group theory, which at first was thought to have nothing to do with physics or any engineering sciences, was found to be very applicable to some extremely interesting problems of fundamental physics (describing the symmetries of fundamental particles).
Daniel
Re:Is this really true? (Score:3, Interesting)
Re:Is this really true? (Score:5, Insightful)
Re:Is this really true? (Score:2)
That sounds like one of those cheezy bumper sitckers about how different professions have sex.

Re:Is this really true? (Score:3, Insightful)
If mathematicans aren't really interested in helping understand the world, why should society fund them?
Because they're able to create beauty, like artists and writers and musicians do. Not all human activity should be measured with money, even if money is needed to make it happen
Re:Is this really true? (Score:3, Interesting)
Because they're able to create beauty, like artists and writers and musicians do.
This is a poor analogy. Artists, writers and musicians put their art works in places that the general public can find them. Society would never pay to create "beauty" that is impenetrable to almost anyone who does not spend full time in the field. Even "modern art" is shown in museums that millions of people go to every years. The better argument in defense of mathematics is its utility. I'm glad that mathematicians find be
Re:Is this really true? (Score:2)
You're welcome not to pay for it of course. I didn't intend an analogy, I honestly think there are some things worth doing for the hell of it, not because they are useful.
PS Excuse me if this sounds a bit stroppy, but you really should avoid the scare quotes. Nasty.
Re:Is this really true? (Score:4, Interesting)
artists are the most backstabbing bastards on the planet when it comes to enjoying each others work, and if you dont know who is "so cool" to be into this week, they will reject your conversation at a blink of an eye. try talking to a real artist about di vinci or the turner prize (or basically anyone/thing who we as the public are subjected to), and get nothing but "you are sooo not cool" looks form them. then try talking to a mathematician about euclid and try to pry yourself out of the conversation! artists disassociate themselves from society by choice, mathematicians are rejected and want back.
btw, check out arxiv.org; every math/physics release in the last 10 years has been put there free for anyone to look at; last gallery i went to, i had to pay £5 at the door.
Re:Is this really true? (Score:2)
(sorry for sounding rude then, me is a bit bitter against artists, and since you still call the stuff in galeries "modern art", im guessing you've never came across a real artist... you dont want to!)
Re:Is this really true? (Score:2)
yes, but you must admit that with mathematicians the backstabbing is not so big a thing as it may be with artists. sure, ive heard backstabbing stories, but they are few and far between; in art, its pretty much commonplace. i agree.. we are but mortals, we get angry, we lose our rag. but what i am saying is that it is not a sound part of mathsculture to be backstabbing. those that do are shunned.
the maths lives, but mathematicians die. this is
Re:Is this really true? (Score:5, Insightful)
These are two separate things. Many people are attracted to the natural sciences, and even engineering disciplines, not because of a desire to improve the world, but because they find pleasure and abstract beauty in those fields. Yet undeniably work in those areas can lead to benefits for "society", and therefore people doing research in those areas are funded, even if their personal reasons for doing the work have nothing to do with those benefits. Likewise with mathematics, many ideas thought of as purely abstract and disconnected from practical application have turned out, later on, to be useful tools in understanding various realworld phenomena.
It is totally unscientific and ultimately counterproductive to close off areas of inquiry because at the time they are undertaken no one can know exactly what the consequences will be. And ultimately the motivations of the people involved are irrelevant; we know based on history that there could turn out to be uses for it in the future, even if neither "we" (the society making the decision to support the research), nor those doing the research, can see any at this time, and this potentiality alone should justify providing support.
To put it another way (Score:4, Insightful)
Re:Is this really true? (Score:5, Insightful)
Guess what? It gets worse.. it's not only the mathematicians, but just about anyone and everyone involved in fundamental research.
I know I am.. I do theoretical chemistry.. and although I'd love to see something useful come out of what I do, I cannot see any immediate uses for my work.
The point is: It's the foundation research, the fundamentals, that lead to the big, *big* innovations. Although it might not seem useful at the time, it may (or may not) turn out to be very very important in the future. However, by it's nature, we can't know which research is going to pay off in practical terms.
Einsteins work on stimulated emission probably didn't look very useful back in 1910 either, but it lead to the devlopment of the laser, which noone could've predicted at that time.
That's why we need to fund this stuff.
Re:Is this really true? (Score:2, Insightful)
That's why we need to fund this stuff."
Its a good point; even if you believe that mathematics needs to yield real world applications in order to be justified, it would be short cited to restrict research to topics with anticipated applications.
However, I think research in mathematics should be encouraged for more idealogical
Re:Is this really true? (Score:3, Insightful)
Asking why you should fund mathematics is asking why you should fund art. Who ever got cured by art?
I certainly know that a major motivation for my career in science is the beauty of it.
It's like the sunset outside my window, it's like Dido's new single emerging from my speakers. Today I spent studying for my thermodynamics exam and even the simple mathematics used therein is beautiful. Wednesday is my Quantum Mechanics exam and if it weren't for the beauty of the mathematics of
Re:Is this really true? (Score:2)
Re:Is this really true? (Score:3, Insightful)
i am a PhD student in maths... and obviously i will disagree with you. but i have a reason... we may not WANT to change/understand the world; but it happens!!!
surprise surprise, but the maths we create is used by physicists (about a 50>100 year time lag), which in turn is applied and picked up by engineers/chemists/biologists (another 10>50 year lag) which ends up being some new device or revolut
Re:Is this really true? (Score:2)
Well, math is important, but some engineers/chemists/biologists aren't exactly mathematically illiterate you know...
parent is a troll
No, it's just that I don't dig that whole
Re:Is this really true? (Score:2)
believe me, pure math is a whole different ball game to the kind of maths the applied world uses. i do mathematical physics, and even our way of lookign at, say, group theory and topology is COMPLETELY different to the way the purists talk about it. ive seen applied group theory and even IT is totally different to the way we look at it. there are many MANY levels of translators, and i still
Re:Is this really true? (Score:2, Informative)
You're screwin' up the causal relationships again.
Pure math isn't a thing of beauty because discoveries yielded by it may have no *immediate* practicable value; nor is it a thing of beauty because it may be sourced in something other than a desire to solve an immediate problem.
It's a thing of beauty because it has produced fascinating finds with respect to the relationships between various prime numbers and relatively prime numbers (E
Re:Is this really true? (Score:2)
Does that mean we should fire everyone working for McDonalds and start looking for people who are really interested in how hungry their next client is and what is his
Re:Is this really true? (Score:2)
Re:Is this really true? (Score:2)
Bah, opportunist...
Kidding
Re:Is this really true? (Score:2)
Smells like a troll, but I answer: Mathematicians produce new ways to model things. Mathematical methods and models have proven to be useful in almost all sciences. What today seems like pure "useless" math may well tomorrow find an application in some totally unexpected ways. Where would engineering be without geometry? Physics without calculus?
Even when math fails to find a solution to some "total
Re:Is this really true? (Score:2)
Re:Is this really true? (Score:2)
I have no pity for people that pursue business or marketing degrees then whine that they're not happy in corporate cubiclehell. Go back to school or STFU.
Regardless, mathematicians still have to produce results too, in the form of proofs, theorems, papers, and/or teaching. Saying that they're being "paid to sit around all day thinking" does a disservice to the fact they're doing as much "work" as the guy writing marketing proposals all day.
That's the nice thing about math (Score:2, Insightful)
Fish (Score:4, Funny)
Who knew that I had a future in advance mathematics when I was doodling in my math notebook during class? : )
They took the pic just as he was about to draw the eye...
terrible journalism (Score:3, Insightful)
Re:terrible journalism (Score:2)
Re:terrible journalism (Score:2)
But it does have a tendency to find application in all sorts of fields and become "dirty". Does it make the article wrong?
Slahsdot reproduces NYT in it's entirety. (Score:4, Insightful)
Pure Math, Pure Joy [slashdot.org]
Does Google = God? [slashdot.org]
Harry Potter and the Entertainment Industry [slashdot.org]
Re:Slahsdot reproduces NYT in it's entirety. (Score:2, Funny)
a recent experience with matrices (Score:4, Insightful)
One of life's simple pleasures (Score:4, Interesting)
This article also reminded me of a good book (story wise, not much math) that a lot of you have probably read. It's called Fermat's Enigma [amazon.com]. If you haven't read it you should. It's a really good book and an easy read. I might even make you want to read a real math book again ;)
I also love the last picture.... (Score:3, Funny)
Look how seriously the guy on the right side is watching a fish being drawn...
You can trust the NYT (Score:3, Informative)
I work in the maths department of a University, and yes.. it's very much like this. We sit around all day in small groups, staring at blackboards, "battling with proofs". Just like in that wonderful movie with the violent australian, "A Beautiful Mind".
No.
Re:You can trust the NYT (Score:5, Funny)
Re:You can trust the NYT (Score:3, Insightful)
I'm a computer scientist who does a bit of theory. By far the very best, most enjoyable and most rewarding thing I've done as a graduate student is work on proofs. Usually in small groups, often on a blackboard (although I prefer having colors so
Coffee into theorems (Score:5, Interesting)
Erdos himself was a device for converting speed into theorems. Ironically he lived to be 83 years old, prolifically creating new math until the very end.
My guess is that more mathematicians use amphetamines than is commonly acknowledged. This is how some older mathematicians try to keep their "edge".
BTW have you computed your Erdos Number [oakland.edu]?
Re:Coffee into theorems (OT) (Score:2)
And why exactly is this ironic [slashdot.org] ?
Re:Coffee into theorems (OT) (Score:2)
Irony is a state of affairs or an event that seems deliberately contrary to what one expects and is often amusing as a result.
Read your own linked article. Isn't it tiring being so stupid?
How about RSA. (Score:3, Interesting)
Are the spooks running out of mathematicians?! (Score:4, Funny)
Math is cool now? (Score:3, Funny)
misery loves company (Score:3, Informative)
My (insert close relative here) does minimal surfaces and hangs out with some of these guys. They look far too neatly dressed in the pictures. Anyway, for a good time, you might want to take a look at some of the galleries of images that these crazy minimal surfaces guys do. I remember about ten years ago, one of my (insert close relative)'s colleagues sold a few images to the Grateful Dead for their concerts.
http://www.msri.org/publications/sgp/jim/images/ [msri.org]
http://www.gang.umass.edu/ [umass.edu]
There is another site out at Minnesota but I'm too lazy to look for it today.
Pure Math (Score:3, Insightful)
Re:Pure Math (Score:4, Interesting)
Seriously though, it's a circle. Philosophy is just psych. Psych is just biology. Biology is just chemistry. Chemistry is just physics. Physics is just math. And math is just philosophy
Euclid alone has looked on beauty bare (Score:4, Insightful)
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
Edna St. Vincent Millay
Nobody takes notes like those!! (Score:3, Funny)
Funny... (Score:3, Informative)
Mathturbation (Score:3, Funny)
You've missed the entire point of the article (Score:2)