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Hello I'm a software engineer who just wants to start research in mathematics soon. I'm interested in the foundations and hence I'm picking mathematical logic. As I have never touched undergraduate-level maths and I was doing mostly programming since my 11th grade, I accept that I have knowledge gaps. But instead of building my foundations from self-study and thinking about starting research after n years, I want to start soon.

I'm thinking of beginning with the first research papers that usually graduate students get introduced to in mathematical logic and if any material would not make any sense, I will pick up the undergraduate level book on logic and starting build my gaps to understand that part. Even I can pick textbooks from high school level if something in undergrad text won't make sense but "I just want to continue research (or research exploration) and foundations building in parallel".

Hope it will be doable. So could you tell me about first research papers in mathematical logic that I can start reading on? Thanks.

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  • $\begingroup$ Graduate students generally start by taking certain courses or reading books. As an example, you might read David Marker's Introduction to Model Theory, either as an undergrad (if offered) or early postgrad. Similarly many notes for actual postgrad courses can be found online. I would recommend checking out intro logic books, then choose a subfield of logic your interested in, e.g.: model theory, proof theory, computability, etc. Computability and Logic by Boolos might be up your alley considering a background in programming. $\endgroup$
    – solatia
    Commented Oct 10 at 9:28
  • $\begingroup$ For new fields, it might be common for graduate students to read the original papers by the founders of the field. However this is not usually the case, as there are generally plenty of books that organize the theory much better. Graduate students usually read papers once they've understood the basics of the field (by reading books and taking courses), to begin exploring newer & deeper theories where the literature may not be as organized. This is usually for learning the material required to write their own thesis $\endgroup$
    – solatia
    Commented Oct 10 at 9:33
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    $\begingroup$ Unlike some fields in computer science, writing a math paper requires a very long process of learning that would take at least 5-6 years to complete. You even would not start any research without any background. $\endgroup$
    – Hanul Jeon
    Commented Oct 10 at 19:39

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You are getting downvoted because your expectations seem too high to everyone. What you want is simply not going to work. Good research is culture, and culture requires knowledge. Yet, I do not see why not letting you discover that on your own.

I'll just throw at you some recent developments in my field I find interesting and potentially fruitful. Good luck.

Abbadini, Guffanti: Quantifier-free formulas and quantifier alternation depth in doctrines.

Arkor, McDermott: The pullback theorem for relative monads.

Paré: Multivariate functorial difference.

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