In the fall of 1977 I began studying at NCCC. Four years later I was enrolled in a Ph.D. math program at SUNY Buffalo. I chose Buffalo because of their strong theoretical math program, and this was my interest - particularly mathematical logic and real analysis.
At the time Buffalo's graduate math program was ranked 20th in the country. There were the usual suspects at the top - MIT, etc. - then the IVYs,a few more like Stanford and Carnegie Melon, then U.B. The plan in the 60's and 70's was to make U.B. the Berkeley of the east. A hiring binge brought such greats as John Myhill, Stephen Shanuel and John Isbell, among others.
In the graduate prospectus for U.B. we were told that there were no jobs in theoretical math. I didn't pay attention,not really caring in my senior year of college. Apparently what they said was true, since my friends who went on for their Ph.D. ended up not working in math. One works in finance, and another is currently trying to get some AI certifications to find work and stay employed. A third did find work in higher ed at a small college that just closed. Another did a 6 month teaching stint and then hid the fact that he had a Ph.D. in math to get a software engineering job - a job not much different than I had worked part time in my junior year of college.
I passed my first two qualifying exams with ease, having an interest in topology, which was two abstractions above calculus. It seemed to come easy. In the second class we had 8 problems to solve. I solved 7, which was the most of anyone in the class. A couple Asian students solved 3 or 4. The problem I did not solve was a box product topology problem, which was unsolved at that point. It is still unsolved, as the professor, Scott Williams, worked on it his whole career. I did prove several theorems that could have been published, however. I proved several statements that would be an immediate consequence of the box product topology problem which is how I knew the problem was unsolved, because none of the statements themselves were proven theorems.
Also in that semester I took an 800-level computer science seminar called, "Machine Inductive Inference". I did not have the prerequisites, but I had room for an extra course, so I took it. This work is foundational now for machine learning and related things.
Before the class began our secretary asked me if I could drive John Myhill to the seminar, since it was on the Ridge Lea campus and Dr. Myhill did not drive. I said yes. I also drove Po Cheng Chen to the seminar, who was a math graduate student and also did not drive.
I soon learned why Dr. Myhill wanted to attend. In the first two weeks the professor, Dr. John Case, proved quite a number of theorems that were provem by Dr. Myhill in the 50's and 60's. It was a great experience getting to know Dr. Myhill. He was British and did foundational computer science that built upon Turing, Von Neumann and other greats. Myhill also was a great.
At the end of the semester Dr. Case passed out a stack of current research papers. Our task was to provide a synopsis of our paper. I guess that way we would be reading at the forefront of research in that field. My paper was written by a Russian, where he proved 5 or 6 theorems about probablistic inductive inference machines. Three of his theorems were incorrect, so I restated the theorems correctly and provided my own proof for each. I could have published in that field very easily.
While I was wading through all this terse math I also taught Differential Equations at NCCC at night. I was a fun venture. I am still friends with a couple of my students.
