Has the Riemann hypothesis been proven?

Well, I guess we’ll find out on Monday.

One of the most important unsolved problems in mathematics may have been solved, retired mathematician Michael Atiyah is set to claim on Monday. In a talk at the Heidelberg Laureate Forum in Germany, Atiyah will present what he refers to as a “simple proof” of the Riemann hypothesis, a problem which has eluded mathematicians for almost 160 years.

Actually, it is highly unlikely that we will know on Monday, unless there is some obvious glaring error. Other people have to look at the proof, and it will take a while – when Grigori Perelman confirmed the Poincaré conjecture in 2003, it took until 2006 for it to be verified.

The Riemann hypothesis is one of the Millennium Prize Problems

The difference between percentage and percentage points

Note: This is a repost from my old blog. It appears as it originally did, except for the correction of an embarrassing math error and the addition of one note.It was originally written as part of the basic concept concept thought out by MarkCC at Good Math, Bad Math. The blog post is the single most visited blog post at my old blog, with daily visits ever since it came up.

Quite often I’ve come across situations where it’s unclear if someone knew the difference between percentage and percentage points, so I thought I’d write a post where I would try to explain the difference.

Simply put, percentage is relative, while percentage points are absolute.

For example, if we say that the number of female CEOs increase by 3%, we mean that the number increase with 3% of the current number of female CEOs.

If we say the number increases with 3 percentage points, we mean that the number of female CEOs increase with 3% of the total number of CEOs.

So if 5% of all CEOs are female (the current situation in Denmark, according to today’s newspapers [note: 2007 numbers]), a 3% increase would not be noticeable, since it increased the number of female CEOs to 5.15% of the total number of CEOs.

On the other hand, if we say that the number of female CEOs increases with 3 percentage points, it would mean that 8% of all CEOs would be female. Quite a difference.

Generally speaking, percentage points should be used to measure the difference between two percentages, since it gives a more clear view of the differences than when percentages are used.

Let me give an example of how it gives a clearer view.

Let’s say that a poll in year 1 shows that 10% of the population supports slavery (to take a, hopefully absurd example). In year 2 the poll shows a 20% decrease in the support compared to year 1. However, in year 3, the same number has gone up by 25% compared to year 2.

Many people would get the impression that the number of slavery supporters in year 3 is higher than in year 1, but that’s actually not the case.

In year one 10% supported slavery. The next year, the number fell by 20%. 20% of 10% is 2%, which means that 8% supports slavery. Then the number of supporters increased with 25%. 25% of 8% is 2%, so the total is back up to 10%.

If we have used percentage points, we could just say that in year 2, the number of supporters fell by 2 percentage points, and that the number of supporters increased by the same amount of percentage points in year 3. Thus making it much clearer that the amount of supporters was the same in year 1 and year 3.