 # Unsolved Problems

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. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. such that , where is the totient function. 14. 15. 16. The Clay Mathematics Institute ( 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. In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert's problems), a number of which have now been solved, but some of which remain open. K.

Mathematical Atlas: A gateway to Mathematics Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages"). To reach the best page for your interests, use whichever of these navigation tools ("purple pages") you prefer:

Nerd Paradise : Divisibility Rules for Arbitrary Divisors It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. Physics Flash Animations We have been increasingly using Flash animations for illustrating Physics content. This page provides access to those animations which may be of general interest. The animations will appear in a separate window. The animations are sorted by category, and the file size of each animation is included in the listing. 6174 (number) 6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2.

K-MODDL > Tutorials > Reuleaux Triangle If an enormously heavy object has to be moved from one spot to another, it may not be practical to move it on wheels. Instead the object is placed on a flat platform that in turn rests on cylindrical rollers (Figure 1). As the platform is pushed forward, the rollers left behind are picked up and put down in front. An object moved this way over a flat horizontal surface does not bob up and down as it rolls along. Fibonacci in Nature The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas. We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature.

Weierstrass functions Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent.

What would happen if I drilled a tunnel through the center of th" Want to really get away from it all? The farthest you can travel from home (and still remain on Earth) is about 7,900 miles (12,700 kilometers) straight down, but you'll have to journey the long way round to get there: 12,450 miles (20,036 kilometers) over land and sea. Why not take a shortcut, straight down? You can get there in about 42 minutes -- that's short enough for a long lunch, assuming you can avoid Mole Men, prehistoric reptiles and underworld denizens en route.

Online Speed Reading tools and software Simply start by clicking on the Play button on the left. Reading is that one activity that we do every day but we don't really practice. Most people learn the basics of reading in kindergarten and never graduate to the next levels. You are probably using the same basic rudimental tools and techniques that you learned when you were 6. The average American person reads at an average speed of 180 to 240 words per minute and has done so since he was 16 years old.

What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong!

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