The Ulam spiral, or prime spiral (in other languages also called the Ulam Cloth) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a “long and very boring paper”[1] at a scientific meeting. Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65,000.[2][1][3] In March of the following year, Martin Gardner wrote about the Ulam spiral in his Mathematical Games column;[1] the Ulam spiral featured on the front cover of the issue of Scientific American in which the column appeared.

My new motto is "Math every day." I'm giving myself one year to master all the math I was supposed to have learned in high school and college: algebra, geometry, trigonometry, limits and conic sections, differential calculus, integral calculus, multivariate calculus, simple differential equations, linear algebra and eigenvectors/eigenvalues, discrete math and logic, probability and statistics. I "knew" it all at one time or another, without really understanding what the heck it was for, so I should be able to put it all together again fairly quickly, if I put my mind to it.

Math every day. You learn things a little at a time. Practice something every day for half an hour and you'll become comfortable with it in no time.

The Erdős number (Hungarian pronunciation: [ˈɛrdøːʃ]) describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.
The same principle has been proposed for other eminent people in other fields.

It gets worse when you ask students to do anything meaningful with fractions. Like: "Explain whether 4/3 or 3/4 is closer to 1, and how you know."

#5,000: Entirely arbitrary.

Right now, we've got the worst of both worlds. Science isn't really free, because the courses are expensive and the textbooks are expensive. But the public thinks that anyone is allowed to know, so it must not be important.

Ideally, you would want to arrange things the other way around.

Between childhood and adulthood, neural map of the brain rearranges to conceptualize arithmetic

I once saw a show on new learning techniques. They took a first or second grade music class and told the students they were going to play them a song and that they should come up with a way of remembering the tune. Each of the children came up with a different method mostly using crayons and construction paper. They created different ways to designate the notes and loudness and spaced things to indicate the timing, etc. Then they showed each student how the method they came up with mapped to sheet music. According to the program I was watching this was really effective in teaching children how to read sheet music