Hello Minerva!
You sound very similar to me! I am a mathematician with a background in analytic philosophy, as well as that other, often less amiable, sort…
I was an atheist for about ten years, before one day thinking about the original apostles and their martyrdom, as well as pentecost, and suddenly was given the grace of faith. This was a little over a year ago, and I finally entered the Church this Easter. I know exactly what you are going through! Reading Plantinga is the right way to go. He is of course not Catholic, but Calvinist. However, he made a huge impact on analytically-minded Christian philosophers in the last century, and continues to do so today. His classic works are great: God and Other Minds, The Nature of Necessity, etc. If you don’t already have it, I cannot recommend highly enough an anthology of articles he has written called The Analytic Theist. In that, you will find the rudiments of all the ideas that are going through your head now. After reading that I realized that I didn’t need to drop my analytic style because the mothod itself was no threat to my faith. Historically, the articles did the same for many practicing Christian philosophers who read them originally. Also, remember that positivism qua logical positivism is no longer taken seriously by analytic philosophers for very good reason. Quine was largely responsible for dismantling their verificationist theory of meaning, etc.
Aquinas, et al. are always a wonderful resource, but I would actually (for you) recommend reading Plantinga, maybe Swinburne, etc., before going straight to Aquinas. While Aquinas is, of course, thoroughly logical and brilliant, the logic is not the same kind that we are used to in modern math, or even necessarily in analytic philosophy. Also, there are some excellent books on Thomism that I think you would enjoy. First, Analytical Thomism, which is a movement in analytic philosophy which reads Thomas analytically. It’s clear that if Thomas were alive today, he would at the very least engage with analytics, and would likely be one himself. Also, Twentieth Century Thomism is very interesting. I can’t recall the authors at the moment, but you can google the books, or go to amazon.
Finally, always read JPII’s encyclicals, as well as Benedict’s encyclicals and other books. Read the Church Fathers, other spiritual writers like Mother Teresa, Saint Therese of Liseaux, etc. etc. One phenomenal thing that I have found about faith is that when you engage it, you realize that it is a kind of knowledge. After, essentially, a lifetime of atheism, I now know that God exists every bit as well as I know that my fiancee loves me, that I can count on my parents for support, that my friends will be there for me, because God is doing and has done, and indeed has always done, those things for me, even before I knew it. When I pray, I know that I was praying to Him, and I know that He heard me, and I know that He responded or will respond in the future, and that I will hear Him, and know Him more deeply. I know that He loves me and everyone more than I or anyone can even comprehend. I know this becuse I experience it every day.
Lastly, don’t let Mass creep you out. It’s the way that Christ has been worshipped since the beginning and it only appears strange to you because the secular culture in which we live is blind to the Mass and can never approach its deep mysteries and saving graces. The sacraments are a gift for us, from God. God bless you on your journey. Please keep in touch!
Jon