Q:

Is there any scientific proof that 2%-3% target inflation rate is ideal?

There are a couple of central banks (RBA, Federal reserve for example) that use inflation rate as a key indicator to regulate their official cash rates. 
Those target inflation rates usually range from 2%-3%.
This is taken from federal reserve's official website:

Over time, a higher inflation rate would reduce the public's ability to make accurate longer-term economic and financial decisions. On the other hand, a lower inflation rate would be associated with an elevated probability of falling into deflation

World has changed in the past 10 years or so:

World's prevailing overnight cash rates have plunged from 3%-20% in the 20th century to 0%-3% in the past 5 years.
So is there any scientific proof that 2% inflation rate (or 2%-3% in RBA's case), is still the optimum target in today's low interest rate regime? 

A:

Science doesn't work on the basis of "proof". Proof is something that belongs only in the realms of mathematics and philosophical logic. Whereas science works on the basis of the best-available explanation that fits the available evidence.
That's as true of physics as it is of economics.
The challenge in economics is that it's much harder to do experiments to gather additional evidence, particularly in macro-economics. So decisions have to be made on the basis of quite thin evidence. Nevertheless, the principle is the same: we look for the best-available explanation that fits the available evidence.
The point of a 2-3% inflation target was that it was neither too high nor too low. And that's based on the harm we see being done during periods of deflation (such as the Great Depression) and during periods of high inflation (the oil crises in the early and late 1970s).
And because it's a target, rather than a cap or a floor, that means that it's applicable in a period of high inflation and high interest rates; and it's applicable in a period of near-zero inflation and near-zero interest rates. The evidence that supported this target pre-2007, is still the evidence that supports it now.

