Jinyoung Park's Path to Math video on IAS is a really wonderful 3 minute story of how she came to study threshold behavior in random discrete structures, just like this work. Highly recommended.
https://www.ias.edu/ideas/paths-math-jinyoung-park
Since we regularly get comments on HN about people wanting to study math in some capacity and about the challenges in doing so - I thought this was a really quote from this video:
Jinyoung (after having been a secondary school Math teacher for 7 years):
"... there was a big obstacle in studying mathematics or pursuing my career in mathematics, which was me, myself. Because I just couldn't stop thinking that oh I'm too old and I started too late or I didn't learn enough amount of mathematics in college ..."
and now here she is with some world class work to her name.
"Jinyoung is a first-generation college graduate, and after seven years as a secondary school teacher in South Korea, she went on to earn a mathematics Ph.D. from Rutgers University. Jinyoung’s story demonstrates the importance of role models at all levels of one’s education and the fact that it is never too late to begin anew."
And yet people will shit on DEI efforts. Incorporating more folks into the scientific endeavor helps combat things like stagnation in science precisely because it reduces academic incest.
Well, one problem when discussing DEI is there are many implementations of it. My own own departments only considers race or gender, and really only focuses on gender. Although I know many DEI programs really do take a more holistic view of what diversity means.
I am back in graduate school at 31 after a few years working and I also wondered if I was too old to go back. It is definitely possible if you have the drive to do it. I can say it is both easier and harder than my first time around. My drive to succeed is much higher, my focus is sharper, but my overall energy and free time budgets are more limited (kids). I would recommend if one can and wants to do it.
Math is one of those fields where there seems to be a clear correlation betwixt youth and creativity. It's just the consequence of having fresh eyes looking at an ancient problem ;)
But experience is clearly necessary due to the shear vastness of the topic. I find history and philosophy of math to be just as engaging and often crucial. Understanding the origins of probability in 17th century gambling houses, for example, sheds enormous light on the subject.
To that end, I think something like "Mathematical Evolutions" might be the best place to start:
"To tell the tale of The Isometric Problem, one must begin by quoting Virgil..."
I'm not sure the peak is driven by fresh eyes. I think fluid intelligence is a big requirement and the brain peaks in that regard in your 20's. It doesn't mean you can't still make great progress later in life, but it sure does get harder in my personal experience.
The video doesn't say (maybe because the answer is 0, but important if not) how much math Park did between the basic college math for the BS Math Education degree, and starting PhD at age ~30.
Did she study advanced math in college, or as a hobby during the pre-PhD years, or did she spend 10 years studying K-12 math very thoroughly while teaching, and then start going deeper?
Jinyoung (after having been a secondary school Math teacher for 7 years):
"... there was a big obstacle in studying mathematics or pursuing my career in mathematics, which was me, myself. Because I just couldn't stop thinking that oh I'm too old and I started too late or I didn't learn enough amount of mathematics in college ..."
and now here she is with some world class work to her name.