Mathematically, how much more secure is fingerprint compared to textual passwords? Like is there any detailed mathematical analysis?
Fingerprints are not supposed to be used on their own for authentication. The fact that many devices are starting to do that does not mean it is a good idea. In security, you should authenticate yourself with three different factors: something you have, something you know, and something you are. You can have a smart card, or an encrypted hard disk. You can know a secret password, a pin, or a pattern. And you are a person with a fingerprint, a person with a particular typing pattern, or a person with a specific speech pattern. Often, people only use the latter two, for example a username (something you are) and a password (something you know). See these lecture notes. It explains this all very well.
A fingerprint is like a username. All a username does is allow authentication using a non-secret value so there is no issue with "error: this password is already taken". Less information is revealed when the message is "error: this username is already taken". This is the purpose of the username. But how is a fingerprint the same? A username is something easy to discover, usually it's plastered all around or simply a variation on a person's name. A fingerprint is the same. It is plastered all around. You don't need high-tech forensic equipment to pull a fingerprint off of anything. While some devices try to use slightly more advanced fingerprint scanners (e.g. using capacitance detectors to avoid being tricked by high-res photos of a fingerprint), they are still not all that good.
Finally, you asked how fingerprints compare mathematically. This cannot be answered because a fingerprint is not a mathematical value. You would have to see how the specific implementation of fingerprint reader works. How many unique points on a fingerprint does it take into account? What is the variation among different populations for these specific points? With a password, the strength is simply the equivalent of the amount of entropy present in the password. Unlike fingerprints, passwords can be made truly random.
A fingerprint is a username that you don't have to type in every time.