Historic maths problem 'cracked'

BBC ^ | Nov. 27, 2003 | Dr. David Whitehouse

[SteveH]

Historic maths problem 'cracked'

By Dr David Whitehouse

BBC News Online science editor

A 22-year-old student at Stockholm University, Elin Oxenhielm, may have solved part of one of mathematics' greatest unsolved problems. Called Hilbert's problem 16, it has confounded workers for over a century.

But in a few hours of inspiration she may have seen the light. Her solution is to be published in a maths journal.

Her research into so-called planar polynomial vector fields may have practical applications for computer simulations in science and economics.

Passion for maths

"I solved it before I knew its significance," Elin Oxenhielm told BBC News Online.

"It took a few months of thinking about it at first, but then the solution came remarkably quickly," she says.

Her breakthrough comes a century after the problem was posed by Prussian mathematician David Hilbert. In 1900 he gave a lecture in Paris where he laid down the 23 greatest problems for maths in the 20th century.

They were a varied selection that had confounded the greatest mathematical minds of the age.

Couched in language that only mathematicians appreciate, they included such questions as: can the continuum of numbers be regarded as a well ordered set, and can space be constructed by congruent polyhedra?

Over a century later only three of Hilbert's problems remain unconquered, numbers six, eight and 16.

Number eight is the famous Riemann hypothesis to do with prime numbers, regarded by many as the most difficult problem in maths today.

Recently problems eight and 16 on Hilbert's list have been placed on a list of the 18 biggest challenges for 21st century mathematicians.

But problem 16 may now have a partial answer.

A few hours' work

Mathematicians describe it as a question of the "topology of algebraic curves and shapes." Non-technically it deals with the way solutions to equations are arrived at.

Elin Oxenhielm's solution is of a special version of the second part of the problem, called the "boundary cycles for polynomial differential equations".

"It only took me a few hours to solve the problem once I expressed it in the correct way," she told BBC News Online.

"It is difficult to describe for non-mathematicians but the way I solved the problem may have practical applications."

It may improve the way scientists use computers to simulate such diverse phenomena as global warming and economies.

Her work is to be published in the mathematical journal Nonlinear Analysis.

Oxenhielm believes her method can be used to unlock the mystery of the entire 16th problem, and plans to write a popular book about her work.

Story from BBC NEWS:

http://news.bbc.co.uk/go/pr/fr/-/2/hi/science/nature/3243736.stm

Published: 2003/11/27 15:22:54 GMT

© BBC MMIII

[nwrep]

What does she look like?

[Lorenb420]

[jla]

fyi

[WackyKat]

I solved Hilbert 16 years ago
If I had known it was such a big deal, I would have said something about it.
Oh well. Back to work on the free energy machine.

[Texas Eagle]

Is this one of the math problems?

Three women decide to buy a gift for a friend that costs 30 dollars. Each woman chips in 10 dollars.

After the cashier rings up the sale, she informs the women that the item was on sale for 25 dollars so she gives one of the women five one-dollar bills with which to divide up between the women.

Each woman gets one dollar back meaning they have now each paid 9 dollars.

9 dollars times 3 women equals 27 dollars.

There is only 2 dollars left to divy up.

27 plus 2 equal 29. What happened to the 30th dollar?

[Michael121]

Free energy?

I made a perpetual machine..... it started and I ain't never been able to stop it..... is that worth something?

And these "rare earth batteries" just seem to last forever.... I really don't see any use for them other than a conversation piece....

[HamiltonJay]

and plans to write a popular book about her work.

Honey, sweetie, while you may have broken ground with this, you are a mathematician... and no book you ever write on this matter will ever be considered "popular" by any standard.

[jocon307]

I love the way they didn't even try to attempt to explain any of this in a way an ordinary person could understand.

Thank you BBC for not making my head hurt.

It's great to see a gal do well in math. It's very rare.

In elementary school it was the kid's best subject. We had hopes she'd stay sharp enough to go to Georgia Tech or somesuch. But she didn't even make it to honors math in high school. Well, she did take it one year only. She's still good at math, but just didn't have the real chops.

[Harmless Teddy Bear]

Honey, sweetie, while you may have broken ground with this, you are a mathematician... and no book you ever write on this matter will ever be considered "popular" by any standard.

I don't know. Who would have thought a book called "A Brief History of Time" could become so popular?

[Bogey78O]

You added up the wrong way...she had 30$ originally...gave 25 to the cashier. She then gave back 3 to each woman so she's left with the woman having paid 27$. Which is what 9 times 3 is.

After she divided sup the last 2 dollars they'll be back down to 25$ given to her. Which is right.

It's a nice semantical math problem. Sleight of hand and all. Not to different than how Democrats play with numbers.

[FreedomCalls]

Solving "part" of a math problem is not solving a math problem. I climbed the stairs today so I guess I am "part" of the way to a trip to the moon. Actually getting there is the hard part for both endeavors.

[Texas Eagle]

You added up the wrong way...she had 30$ originally...gave 25 to the cashier. She then gave back 3 to each woman so she's left with the woman having paid 27$. Which is what 9 times 3 is.

I know. That's what I said. 9 times 3 is 27. There's only 2 dollars left to distribute which makes a total of 29 dollars. What happened to the 30th dollar?

[Maelstrom]

ROFLMAO!

Each woman chips in 10 dollars.

5 dollars is handed back.

Now each woman has paid $8.333333...

$1 is given to each woman.
Now each woman has paid $9.333333... and NOT $9 each.

You should have $2 left.

[Desert88]

"What happened to the 30th dollar?"

Sales tax? ;-)

[January24th]

Perhaps, but you're closer to the moon than those that ponder what the stairs are for.

[sergeantdave]

Solving a problem and correctly applying the solution are two different matters.

(Pubbie, whether or not the student has solved the problem really doesn't matter. I support your picture 1,000%.)

[Maelstrom]

and WRONG!

LOL!

No, not you, the question itself.

[Tench_Coxe]

Being Sweden, she'll probably pose nude for the article on the breakthrough. While not understood, it will be popular.