eldavojohn writes "A special issue of Notices of the American Mathematical Society (AMS) provides four beautiful articles illustrating formal proof by computation. PhysOrg has a simpler article on these assistant mathematical computer programs and states 'One long-term dream is to have formal proofs of all of the central theorems in mathematics.

An anonymous reader writes "Think it's impossible to see four-dimensional objects?

Accepting that numbers can do strange, new things is one of the toughest parts of math:

• There’s numbers between the numbers we count with? (Yes — decimals)
• There’s a number for nothing at all? (Sure — zero)
• The number line is two dimensional? (You bet — imaginary numbers)

Calculus is a beautiful subject, but challenges some long-held assumptions:

An anonymous reader sends in a Science News article that begins: "Human free will might seem like the squishiest of philosophical subjects, way beyond the realm of mathematical demonstration. But two highly regarded Princeton mathematicians, John Conway and Simon Kochen, claim to have proven that if humans have even the tiniest amount of free will, then atoms themselves must also behave unpredictably" Standard interpretations of quantum mechanics, of course, embrace unpredictability.

Stephan Schulz writes "Today, the CADE ATP System Competition will pit about 20 of the worlds most powerful mechanical mathematicians against each other — and for the first time they can win not only honour, but a monetary prize. The systems will reason against the clock on tasks ranging from undergraduate math problems and Cluedo-like puzzles to figuring out the possible responsibility for terrorist attacks from giant knowledge bases. If you think that is not impressive enough, they are doing it at a rate of 12 problems per hour, all day long. The competition starts at 10 a.m.

It’s an obvious fact that circles should have 360 degrees. Right?

Wrong. Most of us have no idea why there’s 360 degrees in a circle. We memorize a magic number as the “size of a circle” and set ourselves up for confusion when studying advanced math or physics, with their so called “radians”.

Pi is mysterious. Sure, you “know” it’s about 3.14159 because you read it in some book. But what if you had no textbooks, no computers, and no calculus (egads!) — just your brain and a piece of paper. Could you find pi?

I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education.

Calculus relates topics in an elegant, brain-bending manner. My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). It all fits together.

The average is a simple term with several meanings. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set.

Quick quiz: You drove to work at 30 mph, and drove back at 60 mph. What was your average speed?

Hint: It’s not 45 mph, and it doesn’t matter how far your commute is. Read on to understand the many uses of this statistical tool.