[EdwardCoffin]

> Well, I guess that's debatable.

What part of it is debatable? The article clearly states that it is just a notational improvement: there was really no flaw in calculus, it was more a wart in notation. This change would not result in different answers unless the original calculations were done incorrectly.

I'd regard the current notation more like an irregular verb, or something that is spelled differently from how it is pronounced: it's inconvenient to deal with, but everyone adept at calculus knew about it and how to deal with it. This article is just describing a notational improvement that would make it easier to get right.

[johnnyb_61820]

The fact that there was a well-known kludge to get around the problems inherent in the notation doesn't make the notation right. As the paper pointed out, the new notation didn't drop magically from the sky, it is literally the application of the quotient rule to the derivative. The reason that no one noticed this notation before, is that they didn't think to apply the quotient rule to the quotient dy/dx.

If I had a problem, and my solution involved forgetting to apply the quotient rule to a prominent quotient, it would still be wrong, even if I also came out with a set of kludges that allowed me to get right answers in the most common cases.

[yters]

It seems similar to Roman numerals vs Arabic numerals. We could stick with Roman numerals, but mathematics would be pretty much at a standstill if we had to use such an unwieldy system.

A major improvement in notation is not insignificant.