I don't think you need even an undergraduate education in mathematics to get into cryptography; for many people it's the other way around. Cryptography can be a great motivator to learn the underlying math. Concepts that may have seemed too abstract to be useful suddenly become practical tools that help you build something that solves a real problem.
I love my colleagues who have come from cryptography research programs; they are awesome! But the majority of my colleagues working on cryptography in practice come from software and security engineering backgrounds. You might think that is just a dividing line between folks who design and analyze cryptography, and those who implement it, but I don't think so. I've seen folks from both backgrounds be able to work on cryptography design and implementation.
IANAC but would the lattice stuff or the other post-quantum stuff require it? "Not having a solid math education" might be a condition with an expiration date if so.
I'm saying that working on Cryptography can also be a solid math education. You can start with very basic high-school math; primes and finite fields, extend to algebra, formal logic, information theory, codes, probability, elliptic curves, isogenies, lattices. They can build on one another, but by actually building some things. It's a great way to learn.
Could you offer some tips/advice/resource for a SWE looking to get involved in applied cryptography?
It seems like a very dense subject, with different areas being of different levels of importance depending on how deeply you’re involved (eg, researching vs writing application code)
One of my favorites is to build a DRBG; download one of the NIST DRBG specifications and try to implement it and have your implementation's output match the test vectors.
You'll be building cryptography without having to design or build the underlying foundational layers. It's actually a lot harder to compose these things then it first seem. Then as you go, try to understand where every single limit in the DRBG specifications come from. Those will teach you a lot about how security factors are worked out.
Plus it's hard; and it gets you into that phase of making big dark numbers match other big dark numbers. It's a very unforgiving form of programming.
I love my colleagues who have come from cryptography research programs; they are awesome! But the majority of my colleagues working on cryptography in practice come from software and security engineering backgrounds. You might think that is just a dividing line between folks who design and analyze cryptography, and those who implement it, but I don't think so. I've seen folks from both backgrounds be able to work on cryptography design and implementation.