are the references real? how do you think it got access to those papers? were they somehow already in the training data, or a result of web searches, Google scholar, etc?

None of them include a web URL but in text some are super specific ("[3, Sections 2.1 and 3.1]" and "[8, p. 367]").

The references go back to 1954 (Chronologically sorted: 1954, 1973, 1975, 1976, 1978, 1979, 1981, 1985, 1987 and 1994.)

Since reference 10 is included as "personal correspondence" maybe the reference itself was copied from one of Tutte's other papers? Or how did it get that reference?

If it were a human (going off of memory as it has been a while), they would probably be using mathscinet and their university library to obtain copies of these papers online. Many old papers are digitized and available by these means. I’m sure the AI companies have it all easily accessible and/or the entirety of mathscinet is in the training data. The “personal correspondence” is possibly lifting from another paper or journal but yeah that is a bit odd that they wouldn’t source where they lifted that from directly.

I can’t say if the citations are accurate because I didn’t check.

Yes, reference 10 jumped out at me as well. I thought personal correspondence references typically include one of the authors of the paper.