What is an approximation of the average number of supernovae every century in the Milky Way? Besides giving out a number and quoted source I would appreciate a short derivation of this number/formula based on our current data and knowledge of supernovae and the Milky Way. Show some traceable reasoning that proofs the source.
Aditionally, how many of these actually (on average) happening supernovae (also in neighbor galaxies) are spotted by amateur and professional astronomers?
 A: Diehl et al. (2006) used gamma ray observations to map $^{26}$Al in the galaxy. Because $^{26}$Al has a half-life long compared to the expected rate of supernova, but not so long we expect the SN rate in the galaxy to have changed dramatically over that time, it might be an indicator of the recent SN rate. Actually carrying through this calculation relies on a lot of assumptions and models being correct. Ultimately, they arrive at an answer of about 2 per century.
Another approach is to use  Hakobyan et al.'s estimates of the SN rate per $10^{10}$ solar luminosities as a function of galaxy type, and use estimates of the Milky Way luminosity and galaxy type. The Milky Way is probably a SBb (loosely would barred spiral), so the rate from Hakobyan is about 1.5 per year per $10^{10}$ solar luminosities, with large uncertainties. A very rough estimate of the Milky Way luminosity is about $2 \times 10^{10}$ solar luminosities, leading to an estimated rate of about 3 per century. The uncertainties here are huge, so this is completely consistent with Diehl's estimate approach above. (I'm actually quite surprised they are so close.)  
