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The 23 Toughest Math Questions
coondoggie sends in a Network World post that begins "It sounds like a math phobic's worst nightmare or perhaps Good Will Hunting for the ages. Those wacky folks at the Defense Advanced Research Projects Agency have put out a research request it calls Mathematical Challenges, that has the mighty goal of 'dramatically revolutionizing mathematics and thereby strengthening DoD's scientific and technological capabilities.' The challenges are in fact 23 questions that, if answered, would offer a high potential for major mathematical breakthroughs, DARPA said." Some of the questions overlap with the Millennium Prize Problems of the Clay Mathematics Institute, which each carry a $1M prize.
42
Don't use MS Word.
I also have a challenge for the slashdot janitors: Link to the original source instead of an ad-laden blog.
Do you even lift?
These aren't the 'roids you're looking for.
Does anyone else here feel like we're being asking us to do someone else's math homework for them?
I prefer rogues to imbeciles because they sometimes take a rest.
How did the mathematician solve for constipation?
He worked it out with his pencil!
Do you even lift?
These aren't the 'roids you're looking for.
Bonus question: Is lending a value that is worth 125% of the house it is secured against a good idea? State your reasons why and show your working out.
Say I'm working at N.S.A. Somebody puts a code on my desk, something nobody else can break. So I take a shot at it and maybe I break it. And I'm real happy with myself, 'cause I did my job well. But maybe that code was the location of some rebel army in North Africa or the Middle East. Once they have that location, they bomb the village where the rebels were hiding and fifteen hundred people I never had a problem with get killed.
Now the politicians are sayin' "send in the Marines to secure the area" 'cause they don't give a shit. It won't be their kid over there, gettin' shot. Just like it wasn't them when their number got called, 'cause they were pullin' a tour in the National Guard. It'll be some guy from Southie takin' shrapnel in the ass. And he comes home to find that the plant he used to work at got exported to the country he just got back from. And the guy who put the shrapnel in his ass got his old job, 'cause he'll work for fifteen cents a day and no bathroom breaks. Meanwhile my buddy from Southie realizes the only reason he was over there was so we could install a government that would sell us oil at a good price. And of course the oil companies used the skirmish to scare up oil prices so they could turn a quick buck. A cute, little ancillary benefit for them but it ain't helping my buddy at two-fifty a gallon. And naturally they're takin' their sweet time bringin' the oil back and maybe even took the liberty of hiring an alcoholic skipper who likes to drink seven and sevens and play slalom with the icebergs and it ain't too long 'til he hits one, spills the oil, and kills all the sea-life in the North Atlantic. So my buddy's out of work and he can't afford to drive so he's got to walk to the job interviews which sucks 'cause the shrapnel in his ass is givin' him chronic hemorrhoids. And meanwhile he's starvin' 'cause every time he tries to get a bite to eat the only blue-plate special they're servin' is North Atlantic scrod with Quaker State.
So what'd I think? I'm holdin' out for somethin' better. I figure I'll eliminate the middle man. Why not just shoot my buddy, take his job and give it to his sworn enemy, hike up gas prices, bomb a village, club a baby seal, hit the hash pipe and join the National Guard? Christ, I could be elected President.
How we know is more important than what we know.
There is an art in finding good questions. Hilbert did it in 1900 with his 23 problems or the millenia problems in 2000. Some of the 23 problems stated are too vague. The first example: "Develop the mathematics of the brain". This covers large parts of computer science, artificial intelligence and psychology. What does "mathematically consistent" mean? A mathematical problem can be taken seriously if there is a clear goal and if there is a possibility to determine, when the problem is solved. This is not the case for many of the problems listed on this website.
..and most of the challenges have little to do with math. Meanwhile, here's something which could lead to real progress in mathematics (From the Slashdot Firehose):
An anonymous reader writes:
link
(+5, the whole point). I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains.
This also means that half my fellow mathematicians are money/power-hungry bastards who remind me that there is no benevolent god (for no such god would reward nasty characters with so much talent). I am in an environment which through peer pressure discourages those who might pursue mathematical ars gratia artis, as it were.
Plato might despair, seeing mathematics today as precisely the toy of the world of change and decay he sought to distance it from. Hardy's ode to number theory could not have been more wrong.
Fuck DARPA and fuck the NSA. And before some idiot goes all "we'd have no Internet without...", (1) says who? the Internet was designed and implemented by a host of international contributors (2) so what? the end does not justify the means. I'm in the UK, and I've had the best of my peers prodded by our equivalent agencies to leave research and go work for them, and I'm so proud of them for having refused (fuck knows with my mouth they'd never ask me). These agencies all exist, ultimately, to oppress - whether abroad or at home.
Please, do not feed the hand that bites.
Why?
"Because calculators are a pain in the ass."
They are asking the reader to create entire fields! how lazy of them.
They only want a mathematical model of the brain, a mathematical model of society as a whole, and fundamental laws of biology so they can answer 'why we are here'.
Speaking as one who trained as a cryptologic technician interpretative (Mandarin Chinese) in the US Navy, I'd say the NSA has a lot to do with the DoD. So much of the NSA's manpower consists of active-duty soldiers, sailors, marines and airmen. NSA facilities are located at army and navy bases worldwide.
Huh... I just figured out a neat, elegant solution to #17, but there's not quite enough space in this margin to fit it in...
Dude, I think I can see my house from here.
77 is better. You get 8 more.
Oooh, I remember that one. If a train leaves Chicago at 8:30 headed for Denver traveling at 45 MPH, and at 8:45 it's parent company declares bankruptcy because Congress refused to bail out the bank that owned a controlling stake in them, and it's going the wrong direction due to a glitch in one of the two data centers that handle the entire nations routing, and the train derails in Pennsylvania at 9:00 due to track damage that was never repaired from the last hurricane, killing most of the people on board, where do they bury the survivors?
I can't believe they left that off the list!
Apparently, according to Google this is a pretty dang hard question to answer:
Yep, google breaks!
For any result greater than 3 the answer is 'A suffusion of yellow'
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
Just in case anyone is late to this discussion, let's be very clear about one thing: "These are not homework problems!"*
*Thanks to George Dantzig this is now a requisite warning whenever people talk about lists of difficult problems.
EvilCON - Made Famous by
So the DoD just leaked that they already know the solution to that one. Interesting.
"I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains."
I'm also a mathematician in training, having finished an MSc. I'm about to start a PhD working on (1). I assume (2) is a reference to the study of cryptography. Studying wealth-generation techniques does not make me power-hungry or greedy, in the same way that the people working on the Manhattan project were not monsters who wanted to extinguish life.
I'm not doing this out of personal greed, I'm doing it because the mathematics involved is elegant and interesting.
Maybe you're happy working away on your abstract nonsense, but I think I'd prefer to work on something which might actually make a difference to people's lives. Just because an application has potential for abuse doesn't make it inherently evil, as you seem to suggest.
Slashdot: news for Apple. Stuff that Apple.
How about we use the correct term and call it what it is: legislation.
...and yes, I expect to get modded down just because the video is clearly pro-McCain.
Congress didn't "encourage" subprime lending. They required it. (please excuse the McCain propaganda in this video...not meant to be political but it has some very relevant facts to the question at hand)
Doesn't anyone remember "redlining" mortgages from the 80's and 90's? Here is some background info. Read the part about mortgages.
Congress reacted to this by legislating subprime lending and requiring banks to provide X% of their loans to people who probably should not have gotten them.