Web sites about mathematics should help people understand and appreciate mathematics, not confuse the crap out of them with misinformation. Unfortunately, Wolfram Mathworld does the latter.

**Example 1**. MathWorld explains here that “The numbers of palindromic numbers less than a given number are illustrated in the plot [below].”

So the left plot tells us that there are about 100 palindromes less than or equal to 20. But there are only 21 nonnegative integers less than or equal to 20, so there can’t be 100 palindromes among them. In fact, there are 11 palindromes less than or equal to 20: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 11. My guess is that the left plot illustrates the *n*-th palindromic number as a function of *n*. In any case, it’s not what MathWorld describes.

MathWorld begins its list of the “first few palindromic numbers” with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (these 10 numbers are palindromes and are all less than 10), but in the next paragraph, MathWorld states that the number of palindromic numbers less than 10 is 9. There are 9 if you don’t count zero for some strange reason, but if you don’t intend to, give a definition that excludes it (MathWorld’s definition is less than clear), and then don’t list it.

Still confused? Read the Wikipedia article.

**Example 2**. Pascal’s Triangle shouldn’t be hard to screw up, right? Wrong. Here’s MathWorld’s Pascal’s Triangle:

This triangle needs to go to the shop for an alignment. The numbers are neither lined up in columns nor staggered (the latter being the usual presentation). What are the numbers in the column containing the rightmost 4? What numbers are along the diagonal through the top? (1, 1, 1, 1, 1, 5, 6?) As shown, MathWorld’s anyway-ill-worded “each subsequent row is obtained by adding the two entries diagonally above” is meaningless.

**Example 3**. In its article on Mersenne numbers (numbers that are one less than a power of two), MathWorld attempts to explain why “[i]n order for the Mersenne number [2^{n}-1] to be prime, *n* must be prime.” MathWorld’s justification: “This is true since for composite *n* with factors *r* and *s*, *n* = *rs*. Therefore, 2^{n}–1 can be written as 2^{rs}–1, which is a binomial number and can be factored.” That’s sloppy to say the least. First, if a composite number *n* has factors *r* and *s*, it’s not necessarily the case that *n* = *rs.* Furthermore, the fact that a number can be factored doesn’t prove it’s composite. Every Mersenne number 2^{n}–1 can be factored. It’s just that when *n* is composite, there’s definitely a factorization into positive integers neither of which equals 1. Explaining it isn’t hard: In order for 2^{n}-1 to be prime, *n* must be prime. For if not, *n* = *rs* where *r* and *s* are integers greater than 1 and less than *n*; then 2^{n}–1 = 2^{rs}–1 has a factor between 1 and 2^{n}–1, namely 2^{r}–1.

**Example 4**. MathWorld describes prime numbers as “numbers that cannot be factored.” Prime numbers, like all integers, however, *can* be factored, and elsewhere, MathWorld gives the factorization of several prime numbers, such as 7: 7 = 7×1.

**Example 5**. Any of MathWorld’s articles on statistics.

In the article on the Central Limit Theorem, what is lowercase *n*? What is *f?* The “limiting cumulative distribution function” of *X*_{norm} is limiting in the sense of what approaching what? (It’s not clear to me that MathWorld’s statement of the theorem is even correct, but it’s clearly unclear.)

The article “explaining” the *p-value* has perhaps the worst definition of *p*-value I’ve ever seen when not grading exams. MathWorld says it’s “[t]he probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z __>__ z_{observed})” (wrong). Wikipedia says “In statistical hypothesis testing, the *p*-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true” (right).

October 2nd, 2010 at 11:29 pm

Bullshit. Being spied in a hetero sex act spread on the internet would be also be horrific — and would cause too many shy young people terrible damage, even leading to suicide. Stop stating that being gay gives you a monopoly on being terribly hurt.

October 4th, 2010 at 9:24 am

Kathleen Parker begins “The suicide of an 18-year-old Rutgers student following an unimaginable invasion of his privacy has launched an overdue examination of casual… disregard for other’s personal space.” Subsequently Ms. Parker claims ”there are several dimensions to the story, complicated by the fact that the victim was gay.”

I take issue with the columnist’s contention that Tyler Clementi’s homosexuality was merely a complication– that the real issue is one of invasions of personal space. “How did we get here?” she asks, “How could anyone think that another’s most private, intimate moment was fair game?” While she leads her readers through the evolution of the word “friend” from noun to verb, and the ostracizing of smokers, groping for her own answer, I feel compelled to provide the obvious one: homophobia. She appeals to the good old days, when “respecting others’ privacy was a matter of manners” oblivious to the fact that the privacy of homosexual acts was legally recognized only in 2003 with the case Texas v. Lawrence. Before that, the video would have been evidence of a criminal act and made that Tyler Clementi vulnerable to prosecution (and presumably within the bounds of good manners of law enforcers, at least) Ms. Parker’s strained attempts to ignore the obvious answer actually provide her readers with a subtle yet effective endorsement of homophobia; dismissing it as a complication that can be ignored or minimized even when that requires rewriting history. Her essay exposes a certain lack of scruples on her part, and as she instructs: “When others are victimized by another ‘s lack of scruples, be outraged.”