If you were starting from zero in 2026 and your only goal was to develop the deepest possible understanding of programming, computers, and mathematics, how would you approach it? Would you attend college, and if so, which major or courses would you choose? Could a carefully planned self-study path take you further? Ignore salaries, job opportunities, work-life balance, and credentials—I'm interested purely in becoming as skilled and intellectually well-rounded as possible.
4 Answers
I’d start with the mathematical and historical foundations: logic, proofs, discrete math, number theory, calculus, probability, physics basics, and the history of computation. Then I’d work through computer architecture and a hands-on course that builds a computer from simple gates. After that, I’d study data structures, algorithms, operating systems, programming languages, and compiler construction. The important part is not just consuming material—write the programs, reproduce the experiments, and explain the concepts in your own words.
I’d read deeply, but I wouldn’t rely on books alone. Follow a rigorous computer science curriculum while constantly implementing what you learn. Build a computer from basic logic gates, write an operating system component, implement a compiler or interpreter, and make increasingly complex projects without hiding behind frameworks. Studying older or less fashionable systems and languages can also reveal ideas that modern development often abstracts away.
College can provide structure, deadlines, feedback, and a broad sequence of subjects, but it won’t make you a great programmer by itself. Most of the important growth still comes from independent study and practice. A self-directed curriculum can cover nearly all of the core material, especially if it includes discrete math, algorithms, operating systems, computer architecture, programming languages, databases, networking, and theory. Aim for a balance of roughly 70–80% hands-on work and the rest theory, adjusting toward more practice as your fundamentals improve.
I’d alternate structured education with real programming work. Spend a year taking serious computer science courses, then a year building software in a different area, and repeat. The strongest engineers I’ve met tend to combine a solid academic foundation with unusual, varied experience. The point isn’t grades or collecting credentials—it’s using school to build fundamentals and using projects or work to learn how those ideas behave in practice.
That path sounds good, but the math should be more targeted than simply watching general calculus material. Proof-writing, discrete mathematics, linear algebra, probability, and theory of computation will usually pay off more directly for understanding computer science.