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.

Comments

I have a challenge for the DoD:

[larry bagina]

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.

Benefits the NSA

[CRCulver]

The portion of the DoD most interested in maths achievements is the NSA, which employs more mathematicians than any other institution in the world (see e.g. Bamford's Body of Secrets ). So when the authors of this list talk about increasing the abilities of the DoD, they really mean increasing violation of privacy and harrasment of anyone thinking too freely.

Re:Benefits the NSA

[Anonymous Coward]

(+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.

Here's a toughy

[Anonymous Coward]

You are a banker who has US$700b in bad loans mostly provided to people who had a history of bad debt and whom have defaulted on their repayments. The Government is offering you somebody elses money to cover your poor judgement and prop up your terrible lending practices. Answer the following questions (1 point each):

1. Is US$700b enough?
2. What will be the total value wiped of the global stock markets by your ineptitude?
3. How big will your bonus be this year

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.

Re:Here's a toughy

[hackus]

Well, you should probably get the facts straight.

First of all, this has nothing to do with 700B and a banker.

This also had nothing to do with lending people with bad debt.

I mean, the sub prime mortgages total about 61 billion total, of debt, for everyone who has a home in the USA.

The issue here, is that Commercial Banks, and Investment banks where combined together under the Federal Reserve (NOT a government institution, but a private entity) in the 90's to increase credit.

So, you had ludicrous deals in the 90's and later with leveraged buyouts of companies, propped up by investment bank CEO's through leverage of like 300 to 1, which is ridiculous.

This rampant abuse of credit by the Investment bank CEO's to fund these mergers and consolidations of billions of dollars of net worth, with almost no money down except the promise of higher stock values, was greedy and criminal.

I wish you people would stop swallowing what the press tells you, and do your own research online into these problems.

I mean, it is simple Math. Home mortgages cannot possibly bring the economy down to a 700B bailout. There simply isn't that many homes mortgaged.

This entire debacle was orchestrated by the Federal Reserve, condoned by Congress and greedily executed by the CEO's of these investment banks who funded these huge mergers that have happened over the past 10-15 years.

They used your savings, they used your 401K plans, they used your future earnings as credit.

Personally I do not care what happens. Either way, if we bail out the Investment CEO's, they get to walk away from all of this and we get to pay.

If we do not pay, the investment CEO's lose everything.

Either way, the USA is bankrupt.

So if we are going to go down, I would like to take the CEO's of these investment banks with me.

Put them in the bread line right next too me.

-Hackus

Re:Here's a toughy

[Sj0]

5. Will the economy go belly-up because the rate of increase of federal debt will cause the economy to become entirely dedicated to debt maintenance, requiring generations to pay high taxes and recieve few services to get the debt to managable levels?

Answer: Yes.

Don't worry, it's only 4 trillion dollars of new debt during Bush's presidency, more than the entire inflation adjusted federal debt after WWII!

Since you mentioned Good Will Hunting

[QuantumG]

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.

the art of posing problems

[e**(i pi)-1]

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.

Re:the art of posing problems

[Yvanhoe]

A mathematically consistent formulation would have prevented me from submitting "cat /dev/null" as a proposition, with the annotation that this is a program simulating the output of a dead brain.

These are not mathematical problems (well, not all of them). Some are physics, most are algorithmic and a few are really mathematical questions. But things like "the brain" is not a mathematical object and thus has no place in the formulation of a mathematical question.

DARPA Ethics

[Ralish]

While solutions to any of these mathematical conundrums would be grand, I'm not sure I'd want to do so in the name of DARPA, or even have any association of my discoveries with DARPA.

At the end of the day, DARPA specialises in technology that is designed to benefit the military, and as a result, is frequently designed for either either killing people, or making it easier to do so. Yes, there's the whole "defence" argument; that the technology will be used for saving lives. But this is a half-truth, the lives being saved are almost always select (only lives belonging to a certain state(s) (the US and potentially its allies in this case)), and often at the cost of other lives.

This can of course degenerate into a whole ethics and morality debate on the value of human life, but ideally, I'd rather such findings published through an academic institute, e.g. a university, that doesn't have any ties to military technology, but rather, a persuasion to applying scientific breakthroughs in the advancement of the common good for humanity as a whole.

I know there have been advancements that DARPA has made that have benefited humanity as a whole, such as the Internet, but keep in mind this was not the primary intent. The Internet turned out to have enormous potential outside the military, but it was military benefits that were the primary focus of the project, and they no doubt got them; the military portion of the Internet split from the public domain and is now a highly classified network, possibly with numerous innovations that are not available to the public.

Re:DARPA Ethics

[greyhueofdoubt]

>>This can of course degenerate into a whole ethics and morality debate on the value of human life

You call a debate on the value of human life a degeneration?

Slashdot truly has become more cynical than I had imagined.

-b

They're not asking for much.

[jdc180]

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'.

No solve NP complete?

[Sobrique]

I'm quite disappointed that they didn't include the general solution to an NP complete problem in their list.

I'd like to be the top travelling salesman in the world, damnit!

Re:No solve NP complete?

[CodeBuster]

Everyone knows or at least strongly suspects that P not equal NP, it's just that nobody has been able to prove that yet. It is exceedingly unlikely that DoD or even NSA (which would certainly be interested in a proof and practical demonstration of P = NP) has proven the conjecture and even less likely that they have proven it in the affirmative ( P = NP). Decades of research by some of the best minds in theoretical computer science have barely scratched the surface of this problem (mostly closing off leads that were once thought to be promising and further reinforcing the reputation of the difficulty of the proof). The solution to this problem and a practical demonstration would be worth billions, possibly even trillions, of dollars and name placement among the great mathematicians of history. If someone had a proof it would be very unlikely that they could keep it secret for very long with those sorts of incentives for being the first to announce the discovery.

Requisite Warning

[Comatose51]

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.

After looking at the problems...

[LoyalOpposition]

Strange. I don't see the one about the train leaving Chicago at 6:00...

-Loyal

Re:Bobby Heenan Said It Best...

[PitaBred]

It matters because of rounding. It's a typical computer science mathematics problem, because it's quite common to calculate a bunch of percentages that don't add up to 100%, and they'll still be accurate. Well, mostly.

Just because you're too stupid to understand it doesn't mean you have to use foul language to put an exclamation point on your ignorance.

Re:They missed one

[Prien715]

In cash, because they sue the track operators and get a huge class action lawsuit settled out of court for a bajillion dollars.