It is the early 1970s, and computer science is discovering that some problems resist every clever algorithm anyone tries — not for lack of effort, but perhaps for a deep reason. Characterize the true computational difficulty of the traveling-salesman decision problem: is there a fast route visiting every city under a given budget? Place it precisely within the emerging hierarchy of complexity classes, and spell out what a fast general solution would imply — a vast web of problems long believed intractable falling at once. The stakes are foundational. Get it wrong and careers are wasted seeking an efficient algorithm that likely cannot exist, or problems merely hard are abandoned as hopeless — this classification reorganized what the whole field means by 'solvable.'
Girshick's toolkit is the modern vision stack: R-CNN (2014) and its descendants, Fast/Faster R-CNN, Mask R-CNN, and Segment Anything — learned features, region proposals, and large-scale gradient descent, evaluated empirically on benchmarks. It is a formidable methodology whose core move is to replace hand-designed pipelines with learned ones and measure what works. Nothing in that repertoire touches this problem. Neural networks can be trained to emit decent TSP heuristics (a small modern literature does this), but the 1971 question is not about good tours: it demands definitions of P and NP, a reduction from SAT through Hamiltonian cycle, and the statement of what a polynomial algorithm would collapse — pure proof, zero data. Girshick's empirical deep-learning methods, born four decades later, have no reductions and no lower bounds to offer. Floor territory.
Hopper's revolution was linguistic and organizational: the A-0 compiler (1952), FLOW-MATIC, and COBOL made programming accessible to people who were not mathematicians, on the conviction that machines should speak closer to English. Her famous nanosecond — the foot of wire she handed students — shows she thought concretely about computational cost, and a compiler writer of her era certainly met combinatorial explosions in optimization passes. But nothing in her practice touches the problem's demands. The question is not how to express a TSP program clearly — trivial in COBOL or anything else — but whether any program can run fast, and why the answer organizes a whole hierarchy of problems. Complexity classes, nondeterminism, and reductions are theory of a kind her resolutely practical career never engaged. The toolkit is simply orthogonal.
Battle #51 · 8/9/2026, 8:41:16 PM · this result is deterministic: the same two personas on this problem always resolve the same way.