Are you sure you weren't talking to an econometrician.
I was recently talking to a well-known professor about what kind of math is used in theory research. He said, "The entire field of economics is coordinated around real analysis, but I have no idea why - I've never used it in research at all. What you actually need to know is proof-based linear algebra and probability theory (not necessarily measure-theoretic, although that doesn't hurt)."
No question here, just figured this information might be of value to someone.
Game theorists use topological concepts very frequently. People doing work in networks draw on results from combinatorics, and graph theory. Just get any volume of JET (or old ECTA articles when they used to be more welcoming of micro theory papers) and you'll see the kind of math that is 'required' for someone doing theory, so this statement could potentially mislead students.
That being said, being math heavy only applies to people who intend to pursue theory. The majority of the profession doing applied and empirical work will rarely encounter any 'fancy' math.
Mathy people often refer to grad-level analysis as "real analysis" as well - there's a lot of inconsistency in terms. To be clear, a first course in undergrad analysis is absolutely necessary for understanding first year grad econ theory. You'll either need to take it as a course in undergrad or study it in math camp and by yourself during your first year. The former option makes more sense.
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