SAT阅读素材:未解决的数学问题.

　　SAT阅读素材：未解决的数学问题!提高SAT阅读水平的一个必用的方法就是经常找一些SAT阅读素材进行练习，培养语感和阅读速度。

　　There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include

　　1. The Goldbach conjecture.

　　2. The Riemann hypothesis.

　　3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4.

　　4. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes).

　　5. Determination of whether NP-problems are actually P-problems.

　　6. The Collatz problem.

　　7. Proof that the 196-algorithm does not terminate when applied to the number 196.

　　8. Proof that 10 is a solitary number.

　　9. Finding a formula for the probability that two elements chosen at random generate the symmetric group .

　　10. Solving the happy end problem for arbitrary .

　　11. Finding an Euler brick whose space diagonal is also an integer.

　　12. Proving which numbers can be represented as a sum of three or four (positive or negative) cubic numbers.

　　13. Lehmer&aposs Mahler measure problem and Lehmer&aposs totient problem on the existence of composite numbers such that , where is the totient function.

　　14. Determining if the Euler-Mascheroni constant is irrational.

　　15. Deriving an analytic form for the square site percolation threshold.

　　16. Determining if any odd perfect numbers exist.

　　The Clay Mathematics Institute (www.aoji.cn of Cambridge, Massachusetts (CMI) has named seven "Millennium Prize Problems," selected by focusing on important classic questions in mathematics that have resisted solution over the years. A $7 million prize fund has been established for the solution to these problems, with $1 million allocated to each. The problems consist of the Riemann hypothesis, Poincaré conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.

　　In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert&aposs problems), a number of which have now been solved, but some of which remain open. In 1912, Landau proposed four simply stated problems, now known as Landau&aposs problems, which continue to dy attack even today. One hundred years after Hilbert, Smale (2000) proposed a list of 18 outstanding problems.

　　K. S. Brown, D. Eppstein, S. Finch, and C. Kimberling maintain webpages of unsolved problems in mathematics. Classic texts on unsolved problems in various areas of mathematics are Croft et al. (1991), in geometry, and Guy (2004), in number theory.

　　每一篇SAT阅读素材均有其主要观点或中心主题。典型的围绕文章主要观点的问题大多是：在这篇文章中作者的主要目的是什么?这篇文章主要涉及什么问题?这篇文章主要建议是什么?这篇文章总体上想要回答什么问题等。读完每一篇SAT阅读素材，我们都要针对SAT素材想想这几个问题。