Top Ten Unsolved Problems

In the previous blog, I mentioned I would map the 151 unsolved problems to my top ten. My only criteria was that at least one unsolved problem was to be chosen from the seven (7) categories.

The following is my list (links are to the corresponding wikipedia references):

http://en.wikipedia.org/wiki/List_of_unsolved_problems

The list of unsolved problems may refer to several conjectures or open problems in various fields. The fields are listed below with the corresponding number of unsolved problems in each field (in parenthesis). It is then followed by the major unsolved problem(s) in each field (open for review).

Unsolved problems in linguistics - (13)
Unsolved problems in economics - (8)
Unsolved problems in mathematics - (55)
Unsolved problems in philosophy - (18 )
Unsolved problems in physics - (36 )
Unsolved problems in chemistry - (13)
Unsolved problems in neuroscience -( 8)

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http://en.wikipedia.org/wiki/Unsolved_problems_in%20_linguistics

(1) Origin of language is the major unsolved problem, despite centuries of interest in the topic.
-------------------------------------------------------http://en.wikipedia.org/wiki/Unsolved_problems_in_economics

(2) What caused the Industrial Revolution? This remains the most important unsolved question in all of, not only economics, but social science
--------------------------------------------------------http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics

(3) Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: Every even integer greater than 2 can be written as the sum of two primes.

(4) The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science. It is considered to be the most important problem in the field - the Clay Mathematics Institute has offered a $1 million US prize for the first correct proof. In essence, the P = NP question asks: if 'yes'-answers to a 'yes'-or-'no'-question can be verified quickly, can the answers themselves also be computed quickly? In this context, "quickly" means "in polynomial time".

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http://en.wikipedia.org/wiki/Unsolved_problems_in_philosophy

(5) Firstly, what are the criteria for intelligence? What are the necessary components for defining consciousness? Secondly, how can an outside observer test for these criteria?
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http://en.wikipedia.org/wiki/Unsolved_problems_in_physics

(6) Dark matter: What is dark matter?[1] Is it related to super symmetry? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?

(7) Quantum gravity: How can gravity and general relativity be realized as a fully consistent quantum field theory? Is string theory (M-theory) the correct approach? More pressing, how much experimental information can be extracted about physics near Planck scale?
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http://en.wikipedia.org/wiki/Unsolved_problems_in_chemistry

(8) What is the structure of water? According to Science Magazine in 2005, one of the 100 outstanding unsolved problems in science revolves around the question how water forms hydrogen bonds with its neighbors in bulk water.
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http://en.wikipedia.org/wiki/Unsolved_problems_in_neuroscience

(9) Self awareness: What is the neuronal basis of subjective experience, wakefulness, alertness, arousal and attention? What is its function? Perception: How does the brain transfer sensory information into coherent, private percepts? What are the rules by which perception is organized? What are the features/objects that constitute our perceptual experience of internal and external events? How are the senses integrated? Is face perception special (e.g. innate)? What is the relationship between subjective experience and the physical world?

(10) Development and evolution: How and why did the brain evolve (the way it did)? What are the molecular determinants of individual brain development


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In parallel to this effort of documenting my new top ten science/math problems, I encountered a web site that documented the "why the top ten of any topic is of interest": http://www.modernlifeisrubbish.co.uk/article/10-reasons-why-top-10-lists-are-so-popular ,

and also a web site on a similar list of the top 10 unsolved science problems :

http://listverse.com/science/10-great-unsolved-problems/


Note the parallel between my new list and this web list. We both used the same source, (Wikipedia), but we used different criteria on what what to be considered for the top ten.