What is theoretical computer science?

Is TCS Mathematics, Science, or Something Else?

• Many argue theoretical computer science (TCS) is essentially mathematics: axioms, theorems, formal models, proofs.
• Others say TCS sits between math and science: some parts are purely formal, others study real systems (distributed systems, networking, performance) and behave more like empirical sciences or engineering.
• Debate over whether calling it “computer science” is a misleading historical artifact versus a harmless linguistic quirk.
• Some prefer a sociological definition: TCS is “whatever people who call themselves theoretical computer scientists work on,” recognizing shifting boundaries over time.

Science, Proof, and Falsifiability

• A long subthread debates whether “nothing can be proven in science,” contrasting empirical falsification with mathematical proof.
• One side leans on a Popper-style view: scientific statements can only be falsified, never verified; math is different because axioms are fixed.
• Others push back, saying science is better viewed as building predictive models, quantifying uncertainty, and offering explanations, not just falsifying hypotheses.
• There is disagreement over definitions of “hypothesis” (proposition vs explanatory model vs statistical hypothesis), and whether strict statistical formalization is the “right” technical core of the scientific method.

TCS and Real-World Computing

• Several comments support the article’s idea that TCS should explain and predict real computing, drawing analogy to theoretical physics.
• Examples: distributed systems, networking, algorithm engineering, and empirical complexity work that incorporate hardware constraints and realistic input sizes.
• Others note that some highly abstract complexity questions (e.g., P vs NP) still have deep conceptual and indirect practical value, even when not tightly coupled to current practice.

Breadth and Scope: US vs Europe and Subfields

• Some report European “theoretical CS” including HCI, operating systems, VLSI, and hardware, forcing students to learn algorithms, PL theory, and circuit design together.
• They claim narrower US programs (more math-heavy, less hardware/interaction) can hurt both intellectual depth and job prospects.
• Another view: CS as a whole already includes both formal/theoretical and empirical/engineering subfields; tension arises mostly when TCS is framed as only math.

Theory Drifting from Reality

• Von Neumann’s warning about math drifting into aesthetic, highly “baroque” directions is cited; some worry TCS could do the same if treated purely as formal systems.
• Others think arguments over labels (“math vs science”) matter little to actual research progress and are mainly about hiring and departmental politics.