Advice for learning the original works of previous mathematicians

Question

I recently become interested in understanding the exact works of previous mathematicians, such as Peano, Frege, Russell, Hilbert, etc. Just to be clear, I'm not interested in a shallow history of past mathematics (like for example "that person came up with that"), but rather in really reading their books page by page and understand the context/motivation of what they were doing. How is that possible to do? I find that going directly to their books by myself without any guidance/commentaries is not efficient. I also don't seem to find any university courses that take the books of previous mathematicians and explain it to students. So any suggestions on that would be appreciated.

Answer 1

First, there is probably no "efficient" way to do this. You have to either slog through it, seeking the insights that the original author had or utilize other insights that you have from the study of other, possibly later things.

Don't forget that the original author was placed in time. That means that they had certain general and explicit knowledge of the field, including shared insights about what was true and what might be true. It is hard to place yourself in that context if you have studied later works that have expanded on those insights. Math builds on math as insights build on insights.

Second, to become a good mathematician, this isn't really necessary. I don't need to go through and redevelop the insights of, say, Hilbert to understand what he did. I can, studying what he left behind, follow the trail of breadcrumbs and move on from there. Such study might be fun to undertake, but mathematics has moved forward from the greats of the past.

You don need to gain insight into things, but that can be done many ways. And few, if any, of those things are "efficient". It takes hard work and a deep dive. In another field, note that it took Einstein about ten years to develop the insight that let him publish the Special Relativity paper and he had access to the great ideas of the day as he did so. He also discussed his ideas with others. It wasn't enough to re-plow the past furrows, but to build on them and deviate where necessary. Not very efficient.