Pure Math, Pure Joy

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."

Visualizing the solution...

[calebb]

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 brute-force method. Speaking of prime numbers & slightly off-topic, 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...

Is this really true?

[Jonathan]

But the "unreasonable effectiveness" of mathematics in explaining the world, as the physicist Eugene Wigner once put it, is a minor motivation at best for those immersed in the field. Most mathematicians say they are in it for the math itself, for the delirious quest for patterns, the thrill of the detective chase and the lure of beautiful answers.

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?

[wmspringer]

Eventually, the math turns out to be useful for something. I doubt that knowing a 100-digit prime number would have been any use whatsoever a hundred years ago, but these days I don't even need to tell you how useful they are.

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?

[Joel Bruick]

This isn't restricted to mathematicians. There are people working in every field who are motivated by things other than furthering society or understanding the world. Money, of course, is the primary one, but there are certainly others.

Re:Is this really true?

[smallpaul]

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 beauty in what they do but I wouldn't offer to pay for it if I didn't think it was likely to be useful to me or my descendants.

Re:Is this really true?

[Jonathan]

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?

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 means creating some evil world-destroying weapon in the process. That always struck me as a rather offensive stereotype.

One of life's simple pleasures

[mofochickamo]

Reading this article reminded me off all the math courses I have taken from primay school through university. I can remember feeling frustrated while dueling with especially hard problems, but the satisfaction of solving them quickly made me forget the pain.

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 ;)

Coffee into theorems

[ortholattice]

Blockquoth the article:

A mathematician, the Hungarian lover of numbers Paul Erdos once said, is a device for converting coffee into theorems.

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.

Like all of Erdos's friends, Graham was concerned about his drug-taking. In 1979, Graham bet Erdos $500 that he couldn't stop taking amphetamines for a month. Erdos accepted the challenge, and went cold turkey for thirty days. After Graham paid up--and wrote the $500 off as a business expense--Erdos said, "You've showed me I'm not an addict. But I didn't get any work done. I'd get up in the morning and stare at a blank piece of paper. I'd have no ideas, just like an ordinary person. You've set mathematics back a month." He promptly resumed taking pills, and mathematics was the better for it. - Paul Hoffman,

The Man Who Loved Only Numbers

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]?

How about RSA.

[YahoKa]

RSA turned out to be a combination of different parts of number theory that turned out to change our world. Who would have thought that this [wolfram.com] and this [wolfram.com] would turn into something this amazing. Don't let anyone dismiss pure math...

Re:Visualizing the solution...

[Anonymous Coward]

So when there are two correct answers, one involving some sort of mastery of basic math, and a subtle answer involving typography, Mensa chooses the latter? That seems very wrong to me.

Re:Is this really true?

[samhalliday]

thats bollocks, artists are a million times more arrogant about their work than mathematicians. mathematicians are just dying for people to want to look at what they do... i'd give an arm and a leg to be able to properly explain to people what it is that i do, but i cant without them first understanding basic differential geometry and group theory. its like expecting an american person to understand a japanese poem without ever learning japanese. its a different language and character set.

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:Visualizing the solution...

[Wavicle]

As someone who used to find it fun to grab Mensa intelligence tests and search for "alternate correct answers" or "arguably ambiguous questions" I can assure you this sort of thing happens all the time... Take a question from their website sample test for example:

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 guess as to what they are, but I've never heard ANY of them used before. As it turns out, all three of those terms are exactly what they sound like, but are generally used in the U.K. or Australia. For example "postcode" did not enter Webster's American Dictionary until 1967. I filed this one under "biased towards other nationality or experience with foreign lingo".

It's hard to create an unbiased test intelligence, I agree. But I do expect those who write the tests to be smarter than the average genius and actively looking for slip ups like words that are colloquialisms of smaller areas or lists that contain one symmetric and one prime number and asking which is unique.

Re:Waging mental battle with a proof

[Anonymous Coward]

Or maybe conveying the concept of thought requires a medium which requires the audience to think, i.e. a book, as opposed to film, where the audience can sit and choose whether to be force-fed an image (which will convey less than the printed word) or ignore the screen (which will also convey less than the printed word).

0, 1, 2, ?

[heikkile]

One of my favourites: 0, 1, 2, ?

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 ??

Re:Mensa is right based on Ockhams razor

[Wavicle]

But the whole point with this question type is that the answer you get depend very much on what assumptions you make.

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:Pure Math

[BrainInAJar]

Does this mean the totem pole ends with philosopy? w00t. My major rules. In your face, science guys. :)

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

Re:Is this really true?

[rastos1]

Funny nobody brought this [wired.com] up yet:

After discovering the basic principle of electromagnetic induction in 1831, Michael Faraday was asked by a skeptical politician what good might come of electricity. "Sir, I do not know what it is good for," Faraday replied. "But of one thing I am quite certain - someday you will tax it."