If they are learning... and learning effectively and efficiently. It doesn't matter. If you think the videos take too much time... you could suggest he try a "video speed-up" plugin... watch things at like 130% or 140%.
Weight the reviews... 1 star gets .5 points, 5 star gets 1. Then balance it out. Or take those 1 star reviews with a grain of salt. I don't think you are risk adverse to reading books... I think you keep talking yourself out of it. So, next time you have a book suggestion... go get it and read it. Ignore the reviews. +1 for the Library if you have one that has the book. Easier to ignore reviews that way. :)
I've always looked at Introversion/Extroversion using the battery example. As an Introvert, we recharge our battery by being alone, and drain it in groups. An extrovert is the opposite... charge in groups, drain when alone.
Outside of "charging your battery", it's a matter of skills and preferences. You can learn to deal with groups better, and (when allowed) pick the events you want to deal with.
If those meetings are important, don't avoid them. But if they are "social gathers because someone wants you to go"... then you can think twice.
I think it all depends on what sort of programming you want to do. I do a lot of internal web development for a business. Math is rarely used beyond the basics. Algorithms and such just aren't needed. Problem solving and applying logic to an problem/project is... but the high-end maths? Nope.
So... decide what sort of work you want to do, and plan accordingly.
Welcome to the team! We all feel that way at some point. Others have given some excellent reasons why this happens... so I'll just leave you with a quote.
"If you're the smartest person in the room, you're in the wrong room." - Someone on The Internet
Check out Simple Programmer. He has a lot of articles and email list stuff about building a blog. Quality content on a regular basis is key. Be consistent, and keep writing.
Pronounced "pie tree" or "pee tree"? as in "pitri dish"?
As @arkitaip said... it doesn't say anything to me, but that isn't a bad thing. Depending on how it's pronounced, it may not be very phonetic in spelling, so if you plan on using the internet, people will need to know how to spell your company to find your website.
Fail early, fail often. Try lots of new projects outside your "skills". See what interests you, and where you want to go.
We learn by trial and error. But I think you already know that. I think what you need (to paraphrase the Wizard of Oz)... is a piece of paper that says you are a developer.
You know how you get that? You write it on your resume. That's it.
To be a developer, you call yourself one. Period.
To be a good developer, and one that people want to hire, you have to to have the experience. And it sounds like you have that. Different from mine, different from other peoples... but you have it. Look for new positions that need your skills. It's a great way to grow.
I'm with you in that I'd prefer to stay to see it into production. However, you have a commitment to your employer in that you agreed to start on Date X.
So, I see two options.
1) Explain to your new employer why you think you should delay starting. Go with what they say.
2) Explain to your current employer that the dates are already set, and that you need to leave.
Certainly. Obviously, there are some things where age is a requirement. I'm not going to become a professional footballer at 40. But most professions are not age specific.
I'm not the biggest fan, but SimpleProgrammer.com has some great tips on how to get your name known in the programming world. It's mostly centered around blogging... but it's good stuff.