George Dantzig, 1914-2005

Markus Registrada writes "George Dantzig, the inventor of the Simplex method for solving Linear Programming problems, died on May 13. He was also the now-legendary student who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems."

So sad.

[Shky (703024)]

Goodbye, dear friend.
We hardly knew ye.
And we certainly had no idea what you were talking about.

Re:So sad.

[kfg (145172)]

And we certainly had no idea what you were talking about.

Yes, that is the sad part. Not for him, mind you.

KFG

From the FWIW department...

[Spock the Baptist (455355)]

What I find interesting is that his father Tobias Dantzig. Ol' Tobias was a Russian mathematician, was a student of Henri Poincaré at the Sorbonne and the author of NUMBER: The Language of Science.

As a physics major, and grad student I bumped into a couple of three fellow students in physics that were down right scary. In all three instances they came from academic families and had *very* strong backgrounds in the subject.

One of these guys had a dad who was a professor of physics, and a mother who was a professor of mathematics. This dude graduated college Summa Cum Laude (he had a 4.0) in three years with a double major in physics and math. He was a really nice guy, quite athletic, and ---drum roll please-- dated regularly.

One seriously scary dude...

One day I said something to one of my physics profs about the dude and my prof told me about his background. My prof who was 'grand old man' of the department point out that having a background such as this fellow had put him at *great* advantage with respect to other students.

My prof was not putting the fellow down. He's point was the the fellow was without question quite gifted, but those gifts would not have been realized without his background.

Same here.

[renehollan (138013)]

While an undergrad, and later in grad school, I knew this short (I am short at 5'7", but he was shorter, about 5'2"), Vietnamese fellow, who spoke in halting English. He was scary brilliant.

I remember his Masters' Thesis defense well. At one point he made an assertion and proceeded to use it as the basis for a greater proof. He was interrupted by one of his examiners, who noted something to the effect that he hadn't mentioned that his proof was conditional on the "blah" conjecture having been proved.

He stopped, looked somewhat confused, and then a look of understanding and pride swept across his face. In his halting English he responded, "No. Wait. I prove. Last week. I have preprint of paper. Want see?" (Yes, he did, and it turned out to be correct).

As I recall, there were two more such incidents during his defense, which lasted about two hours.

Needless to say, his thesis was accepted as submitted (which is rare: most Masters' thesis are accept "with minor modification" (as in, someone found a typo, or an uncited reference)). What's ironic is that he'd effectively had enough material for three PhDs in that Masters thesis.

He went on to a doctorate, and possibly a post-doc in Mathematics.

What's really scary is that he claimed to have an older brother who was much smarter than he was.

Damn!

[by Anonymous Coward]

At least his teachers knew he wasn't cheating.

R.I.P., Dude.

Karma-whoring clarifier

[Knights who say 'INT (708612)]

"Linear programming" (as well as "mathematical programming", "convex programming", etc.) has little to do with computer programming. It's about finding the solution to problems like maximize f(x) subject to restrictions r1(x)=0 .. rn(x)=0, r1(x)>0... rn(x)>0.

Incidentally, the Simplex method -- unlike differential calculus-based methods for more general problems like the Kuhn-Tucker method -- is quite programmable on a computer, and quite efficient.

Re:Karma-whoring clarifier

[KeyboardMonkey (744594)]

Incidentally, the Simplex method -- unlike differential calculus-based methods for more general problems like the Kuhn-Tucker method -- is quite programmable on a computer, and quite efficient.

The Simplex method can be combined with Kuhn-Tucker conditions and a few small tweaks to solve quadratic problems. This is know as Quadratic Programming (QP).

Quadratic Programming is used in solving portfolio optimisation problems, a mathematical way to ensure a portfolio of risky assets are diversified.

Re:Karma-whoring clarifier

[Pseudonym (62607)]

Quadratic Programming is used in solving portfolio optimisation problems, a mathematical way to ensure a portfolio of risky assets are diversified.

It's also used in physical simulation to solve the static friction conditions that arise when many objects are in mutual contact.

Re:Karma-whoring clarifier

[PlacidPundit (881182)]

It's also used in physical simulation to solve the static friction conditions that arise when many objects are in mutual contact.

I once used it to make a perfect ham sandwich.

Re:Karma-whoring clarifier X2

[Mr.Zong (704396)]

Quadratic Programming is used in solving portfolio optimisation problems, a mathematical way to ensure a portfolio of risky assets are diversified.

Well, to backtrack a bit, we can use linear programming for making predictions "pragmatically". Think the lame old spreadsheet neural net :P

I mean, saying that linear programming has little to do with computing kind of slaps the best program ever made in its face.

The Spread Sheet (I default to Excel, but insert you fav modern flavor)

Excel is probably the most powerful, robust, versatile, used for everything and the kitchen sink, program ever created. It's a freaking Swiss army knife, and it's because of Linear Programming.

We may not directly use it (ever), but Linear Programming has shaped modern computing as we know it.

Further clarifier

[jd (1658)]

Simplex is also known as Operational Research, as early versions were used during military conflicts as a way to produce the optimum use of planes/ships/men in a combat zone, allowing for time spent away from the front-line.

The military value of Simplex was simple. Resources cost money. Lots of money. You also, generally, don't have that many of them. You desperately need to get them to as many missions as possible in the shortest time (allowing for flight times to and from zones, refuelling, etc), allowing for repairs and replacements.

You've also got to find the optimum distribution of fuel, weapons, bases, etc. as the further these places are from where they need to be, the greater the risks (travel is dangerous) and the greater the delays.

Simplex is not "ideal" for a problem of this complexity, but it does a hell of a lot better than guesswork and pencil & paper solutions on the back of an envelope, which is what the British War Office was often reduced to in World War II. They had RADAR, which helped for defence, but offense was substantially more problematic.

Re:Karma-whoring clarifier

[rsilva (128737)]

I heard this from Dantzing himself in a pleneray at the International Synmposium on Mathematical Programming at Lausanne in 1997:

In that old days, where computers were new toys, the term programmin had the conotation of "planning". If I remember well, Dantzing said that one of the first uses of the Simplex was to help the Air Force to plan its operations during the war.

As for the non-implementability of gradient based methods in computers. They are as implementable as ODE solvers. This is the domain of floating point numbers, there is no exact implementations of methods. However, there are many good solvers out there solving thousands of real world problems every day. Since I come from academia, I can said some good solvers emerging from universities: the Galahad library [rl.ac.uk], whose web page also provides a list [rl.ac.uk] of other good solver like Minos, Knitro, Snopt, Loqo. There is also TANGO [ime.usp.br] which was written and is mantained by some good friends of mine, and the Open Source (CPL) IPOPT [coin-or.org].

Things don't stop there. There also many methods non non-smooth problems that employ generalization of the classical concept of gradient and Hessians, like bundle methods from Lemarechal and company, or generalized Newton methos (from Qi and company) and much more.

Optimization is a very rich field from both practical and theoretical aspects. That's why work with it.

For those of you who don't know anything about LP

[Dancin_Santa (265275)]

Here's a FAQ: http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-p rogramming-faq.html [anl.gov]

What is most interesting about LP is not that it is just a method of finding the solution to a problem, but that it extends in range over many diverse fields from (obviously) computer programming to fields such as economics and even business planning.

RIP

[Ignorant Aardvark (632408)]

It's always sad when a great scientific mind dies. And I recall, just recently, someone was joking about using the simplex method to find the best seat in a theater to see Star Wars.

Re:RIP

[physicsphairy (720718)]

And I recall, just recently, someone was joking about using the simplex method to find the best seat in a theater to see Star Wars.

Well, now we have a motive for the murder, at least.

Re:RIP

[fbform (723771)]

someone was joking about using the simplex method to find the best seat in a theater to see Star Wars.

You and the person who made that comment are both confusing the simplex method in linear programming with the Nelder-Mead downhill simplex method in non-linear programming. Yes, I am an optimization geek.

I hope Paul Erdos is right.

[FlyByPC (841016)]

If so, George has certainly earned a look at The Book. [c2.com] (The one containing all possible mathematical theorems...)

Re:I hope Paul Erdos is right.

[Quixote (154172)]

The one containing all possible mathematical theorems...

Sorry, that's incorrect. Erdos's "The Book" is supposed to contain only the most elegant proofs. Once in a while a mathematician will come up with a proof that is very elegant; such a proof is referred to as being "from The Book". Of course, there's no such "Book" in real life; one gets to see it only in the afterlife, and that too if one's been good... ;-)

Re:I hope Paul Erdos is right.

[mcg1969 (237263)]

Actually I figure that mathematicians in Hell probably get to see it as well, so they can be tormented by the knowledge of just how inelegant their proofs were.

LP's

[log2.0 (674840)]

I am actually doing part of my PhD on Linear Programming and the Simplex method. This guy was very smart to come up with what he did!

The real world application that the simplex method has is HUGE. I think he has made everyones life a little bit better although most people wouldnt realise it.

Re:LP's

[HermanAB (661181)]

LP is commonly used in the design of electronic circuits and filters - so it affected the development of just about anything with a battery or a power cord.

Re:LP's

[log2.0 (674840)]

There are way too many applications to list here. Ill give you an example though. Say you are a company that produces Chairs and Tables. You sell chairs for $10 and tables for $20. It costs you 5 units of wood to make a chair and 8 units of wood to make a table. It costs you 2 units of labour to make a chair and 3 units of labour to make a table.

Now say you have a certain amount of wood and labour to "spend", how much of each product should you produce to max yield, min waste, min cost, max profit...All different objectives give different answers.

This is a simple example that can be solved without simplex but if you were to scale it up to 1000 products with 3000 resources to be split, it can still be solved with the simplex algorithm.

I have written my own simplex solver and they are tricky but the basic algorithm is elegant.

Of course, the example I gave above is only one and there are many applications in the area of Operations Research (thats not my field btw).

Re:LP's

[log2.0 (674840)]

hehe, I was thinking about applying the LP solving technique to these types of games but they made it difficult...For example, in warcraft 3, there are different types of armour and "attacks". So you have to choose which type of armoured and attack units to make. I am very certain that Blizzard looked at the linear space and made sure that the constraints in the system all had the same n-dimensional slope.

A few years ago, I looked into it for night elves and that was the case for a few units.

Either way, if the game did have some inbalance, you *could* find it if you could be bothered :)

Not really...

[Kjella (173770)]

...if you had a unique goal function and linear equations perhaps. First of all, you are playing against an opponent, so the optimal strategy will depend on his strategy. If they have done this well, there should be a "scissors-paper-rock" balance with no dominant strategy. Secondly, the strength of a battle group is not linear (that is why you have a certain mix of heavy fortifications, long-range artillery, light troopers etc etc). It's not like you can describe it as A*x1+B*x2+C*x3.... = strength, because any one troop type alone would probably be wiped out quickly (unless you have a dominant type, which would make the game rather silly).

Kjella

Unsolvable geek problems.

[by Anonymous Coward]

"He was also the now-legendary student who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems."

How to get a date?

Re:Unsolvable geek problems.

[HoneyBunchesOfGoats (619017)]

Well, he was married, so he must have solved that problem. Unfortunately he did not elect to share the proof publicly. :)

Re:Unsolvable geek problems.

[halleluja (715870)]

How to get a date?

Just ask.

I've been enlightened!

[Bifurcati (699683)]

Now this is why I read Slashdot - where else can you get such a diverse range of people, and pick up wonderful little tidbits like the true story behind that wonderful legend about solving unsolved problems? Sure, it's available on Snopes for you to find if you know what you're looking for, but asking the right question is often a lot harder than the answer, as best illustrated bythe Hitch Hiker's guide: Meaning of life=42, Question=???. (Hey, perhaps if they'd put that up on the board, he might have been able to solve that as well!)

Re:I've been enlightened!

[papaia (652949)]

"...where else can you get such a diverse range of people, and pick up wonderful little tidbits like the true story behind that wonderful legend about solving unsolved problems?..."

As long as Rush Limbaugh hasn't succeeded in brain-washing all the Americans, some of them may still have a chance to find such tidbits here [npr.org]

Re:I've been enlightened!

[rokzy (687636)]

reminds me of someone's sig - "Microsoft is not the answer, Microsoft is the question. the answer is no."

not wanting this to be an OS flamefest though, just take the above as a joke or leave it alone.

the part about handing in unsolvable homework is great, though probably slightly embellished.

Re:I've been enlightened!

[WaterBreath (812358)]

the part about handing in unsolvable homework is great, though probably slightly embellished.

Indeed. According to Snopes, they weren't unsolvable problems. They were just unproven theorems. He didn't know this, and just thought the assignment was to prove them. And so he did. =)

So what

[keziahw (869748)]

"examples of what were suspected to be unsolvable problems" No big deal, I do unsolvable homework problems all the time.

Genius, ha

[by Anonymous Coward]

"who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems."

If he was so smart, why did he make the mistake of thinking it was homework?

Re:Genius, ha

[unixbum (720776)]

It's a well known fact that intelligence is inversely proportional to common sence.

Re:Genius, ha

[Taladar (717494)]

That would mean there are a lot of insanely intelligent people out there. I guess I am not the only one who doubts that...

Yep. He's really gone

[by Anonymous Coward]

Since neither link indicated that Mr. Dantzig had actually died, here is a link to the San Jose Mercury News article [mercurynews.com] on him.

The connection between LP and digital computers

[chris huntley (810577)]

Linear programming was among the first "real" applications of digital computers. I saw Dantzig give a talk about it at an INFORMS conference back in the 1980s.

It seems that in a visit to Von Neumann in 1947 he described LP and the simplex method a bit. (See http://www.pupress.princeton.edu/chapters/i7802.ht ml [princeton.edu].) It seems that Von Neumann understood everything pretty much immediately, and even derived the dual solution to LP in the first sitting.

I suppose we all know what Von Neumann did next ...

A new way of teaching?

[John Seminal (698722)]

He was also the now-legendary student who turned in solutions for what he had taken to be a homework assignment, only to find out they had been posted as examples of what were suspected to be unsolvable problems

I can't help but think if he ever would have solved those problems had he been taught first that they were unsolvable??

Schizo Person #1- "Look, there is an elephant in the room"
Schizo Person #2- "Shhh!!! There is no elephant"
Schizo Person #1- "But..."
Schizo Person #2- "No buts, you don't want them to think you're crazy"

Soon Schizo Person #1 stopps seeing the elephant. It really does not exists to him

Re:A new way of teaching?

[Lingur (881943)]

That's an excellent question. I have always been a bit frustrated in my math classes because they never teach you to think outside the box.

It's always "Do this if that comes out but do that if this comes out".
They never, ever, want you to do anything on your own, it's always:

Teacher: Do this
Me: But what if we...
Teacher: Just do it like this, you don't know what your talking about!

Who knows... maybe my school just sucks.

Re:A new way of teaching?

[Catullus (30857)]

I'm sorry, but I have to disagree. While there are, of course, many bad teachers, there are also many who encourage creative thinking and reward originality.

"P=NP?" and many other important problems in theoretical computer science are also perfect examples of problems that could be solved by someone working on their own, without even needing much input from a university. The reason that they haven't been solved so far is that they're hard - not because teachers have been "trampling creative geniuses down into the mud".

Scientists (usually) do science because they want to discover new, exciting and creative things - not because they want to suppress independent thought.

I'm also kind of amused by your claim that you'd have achieved as much as George Dantzig if you hadn't given in to all that "social conditioning" thrust upon you.

Translation

[autojive (560399)]

Translation for today's college students. :-)

Link [gizoogle.com]

Mother

[cloudmaster (10662)]

Am I the onlyone who read this and initially thought something along the lines of "what does Glenn Danzig have to do with Pi"?

No big loss

[[e-mail] (114827)]

It's hardly a loss.

None of his solo stuff after he left the Misfits was any good.

"Muthaaa!" indeed.

I really suffered LP

[ArgieNomad (850645)]

Well folks, I'm an accountant. You can have all the fun you want about having an accountant here, but that's the way it is. In Argentina, where I come from, that was the best way to land a management position in no time, which I'm still waiting for.

All that aside, I love technology in all its forms, just in case.

Studying my 4th year, we've been teached LP, as a way to solve transport route problems, and minimum stock estimates, optimizing resources and stuff, in an assignment called "Operations Research".

I hope one of my fellow students will read this, but I really doubt an graduate from Facultad de Ciencias Economicas - Universidad Nacional de Cordoba would read /.

We always dreamed about finding the damn mf that invented the simplex method, but the net was far from being an accesible thing those days, so now that I find out about Dantzig, I'm kinda sad. There was a time when I would have cursed his family and chased him if he was within reach, but now I pay him honors, as one of many bright minds that go by unnoticed for students and developing minds all over the world.

My respect

reminds me a similar story

[Muhammar (659468)]

Kids in a second grade class in Brunswick, Germany were asked to sum all integers from 1 to 100. That should have kept them busy for a while but some 8-year old boy - son of a peasant gardener - said in bored voice: "the result is 5050 of course, 50 times 101 ". His name was Gauss.

Re:reminds me a similar story

[Katchina'404 (85738)]

Either are correct. It depends on how you split the problem... Think about it.

You're calculating the average (50,5) and multiplying it by the number of items (100). 50,5 * 100 = 5050.

The other way is to add 1 + 100 = 101, then 2 + 99 = 101, etc, up to 50 + 51, hence 50 * 101 = 5050.

Leonid Khachiyan

[mesterha (110796)]

I'm sad to say Leonid Khachiyan [rutgers.edu] also died recently. He proved that linear programming can be solved in polynomial time with the ellipsoid method. I took a class on algorithms from him many years ago at Rutgers. He was an excellent teacher, and he will be missed.

At least he was lucky.

[Spy der Mann (805235)]

What happend to me was the opposite.

A few years ago my math teacher gave us an exam with one particular problem that I couldn't solve. (Apparently a typo or misplaced sign made a rather simple problem into an unsolvable one).
So I went to the library, researched on the problem, and found out it was unsolvable. I PROVED IT mathematically, but the teacher didn't believe me.
And my grade wasn't changed! Doesn't that suck!?

Lesson to be learned: Life's not fair. SPECIALLY with underpaid teachers designing the exams. Hmph.

Re:Oh, now wait a minute...

[Simon Garlick (104721)]

It's times like these we need a moderation option of "-1, crack baby".

Re:He must be rolling in his grave!

[_KiTA_ (241027)]

Well, the mods wanted to post it, but they were waiting for one of them to mathematically prove his death, and CowboyNeil insisted they show their work.