# Open Problems

([Inspired by](http://web.archive.org/web/20090110010052/http://apperceptual.wordpress.com/2007/12/18/open-problems/).)

Einstein's [four fundamental papers](http://en.wikipedia.org/wiki/Annus_Mirabilis_papers) of 1905 were [inspired](http://www.newyorker.com/archive/2005/02/28/050228crat_atlarge?printable=true) by the statement of three open problems in science by Henri Poincaré:

> Having earlier failed to get his doctorate in physics, \[Einstein\] had temporarily given up on the idea of an academic career, telling a friend that "the whole comedy has become boring." \[But he\] had recently read a book by Henri Poincaré, a French mathematician of enormous reputation, which identified three fundamental unsolved problems in science. The first concerned the 'photoelectric effect': how did ultraviolet light knock electrons off the surface of a piece of metal? The second concerned 'Brownian motion': why did pollen particles suspended in water move about in a random zigzag pattern? The third concerned the 'luminiferous ether' that was supposed to fill all of space and serve as the medium through which light waves moved, the way sound waves move through air, or ocean waves through water: why had experiments failed to detect the earth’s motion through this ether? Each of these problems had the potential to reveal what Einstein held to be the underlying simplicity of nature. Working alone, apart from the scientific community, the unknown junior clerk rapidly managed to dispatch all three. His solutions were presented in four papers, written in the months of March, April, May, and June of 1905.

A few years earlier, David Hilbert had published [23 open problems](http://en.wikipedia.org/wiki/Hilbert%27s_problems) in mathematics, about half of which were solved during the 20th century.

More recently, Timothy Gowers has used his blog to [promote](http://en.wikipedia.org/wiki/Timothy_Gowers#Polymath_Project) open problems in mathematics that might be solved collaboratively, online. After just seven weeks, the first problem was "[probably solved](http://gowers.wordpress.com/2009/03/10/problem-solved-probably/)," resulting in [some](http://arxiv.org/abs/1009.3956) [published](http://arxiv.org/abs/1002.0374) [papers](http://arxiv.org/abs/0910.3926) under the pseudonym 'D.H.J. Polymath.'

The Clay Mathematics Institute offers a [$1 million prize](http://en.wikipedia.org/wiki/Millennium_Prize_Problems) for the solution to any of 7 particularly difficult problems in mathematics. One of these problems has now been solved.

In 2006, researchers defined [14 open problems in artificial life](http://mitpress.mit.edu/journals/ARTL/Bedau.pdf), and their paper continues to [guide research](http://scholar.google.com/scholar?cites=9774043633427277067&as_sdt=2005&sciodt=0,5&hl=en) in that field.

And of course [there](http://dimacs.rutgers.edu/~hochberg/undopen/) [are](http://garden.irmacs.sfu.ca/) [many](http://en.wikipedia.org/wiki/List_of_unsolved_problems) [more](http://maven.smith.edu/~orourke/TOPP/) [open](http://compgeom.cs.uiuc.edu/~jeffe/open/) [problems](http://web.archive.org/web/20090110010052/http://apperceptual.wordpress.com/2007/12/18/open-problems/). [Many](http://www.combinatorics.net/problems/) [more](http://www.openproblems.net/).

One problem with [Friendly AI research](http://en.wikipedia.org/wiki/Friendly_artificial_intelligence) is that even those who _could_ work on the project often don't have a clear picture of what the open problems are and how they interact with each other. There are a [few](http://intelligence.org/upload/TDT-v01o.pdf) [papers](http://intelligence.org/upload/artificial-intelligence-risk.pdf) that introduce readers to the problem space, but more work could be done to (1) define each open problem with some precision, (2) discuss how each open problem interacts with other open problems, (3) point readers to existing research on the problem, and (4) suggest directions for future research. Such an effort might even clarify the problem space for those who _think_ they understand it.

(This is, in fact, where [my metaethics sequence](http://wiki.lesswrong.com/wiki/No-Nonsense_Metaethics) is headed.)

Defining a problem is the first step toward solving it.

Defining a problem _publicly_ can bring it to the attention of intelligent minds who may be able to make progress on it.

Defining a problem publicly and offering a _reward_ for its solution can motivate intelligent minds to work on _that_ problem instead of some other problem.