In my experience, people with strong mathematics, EE, CE or physics backgrounds can become ok programmers in support of their work in that field if they end up learning that skillset later in life. But that's because they've already trained their minds at a younger age to think along those kinds of lines so those neural pathways are already set.
Outside of maybe those few areas (and perhaps very few related ones), I'd say it'll be a struggle. A 20 year old will most likely code faster and more prolific. And if his code stinks, he'll tear it down and rewrite it again, better and from an orthogonal direction, while you are still plugging away getting your first project just setup.
Even experienced developers find that they really have to step aside at some point and teach, or manage. It's just a profession that favors the malleability of the young mind and it seems to have a very high burnout rate past somewhere around 40 -- meaning I see maybe 1% of developers still actively in a development role after that age, they've either entirely left the profession, or moved into a supervisory/mgmt role.
Like anything, it's a language, and the young always learn that kind of thing faster, and internalize it better (grok) than their elders.
That being said, I have seen a fair number of old-timers doing network security, and other kinds of IT "behind the scenes" infrastructure kind of jobs. Their age give them some automatic authority as they blend in with the other greybeards of those professions. One guy I knew went from running a restaurant to doing network mgmt at about 55. He's become reasonable successful in those jobs. But one thing he always laments is the impatience of the faster, younger colleagues that have to deal with him -- he invariably tries to find solo positions in small companies.
Go to university if you think that's the best route for you. I'd avoid certification factories. But your best route is actually to just start writing programs. Try getting involved with a open source project.
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