Amdahl's law
expressionprogramming
The speedup from parallelizing a task is capped by its serial fraction: infinite processors cannot beat 1/s.
Gene Amdahl argued it against early multiprocessor enthusiasm in 1967: if 10 percent of a job is inherently sequential, no amount of parallel hardware yields more than a tenfold speedup. The law disciplines every scaling conversation, from multicore chips to distributed pipelines, by pointing optimization at the serial bottleneck first. Gustafson later offered the optimistic reframe for growing problem sizes, but Amdahl still rules fixed workloads.
Amdahl's law states that the speedup from parallelizing a program is limited by the fraction that must run serially. If a tenth of the work cannot be parallelized, then infinite processors still only get you a tenfold speedup, and the arithmetic gets discouraging fast.
The implication that matters is that adding cores has a ceiling determined by the algorithm rather than the budget. A workload that is ninety-five percent parallel caps at twenty times, no matter how much hardware arrives, and the last few percent of serialization is usually the hardest to remove because it is coordination, locking or ordering that exists for a reason.
Gustafson's law is the standard counterargument and is worth holding alongside it. Amdahl assumes a fixed problem size, and in practice people given more computing power solve larger problems rather than the same problem faster, and larger problems often have a larger parallel fraction. Both are correct about different situations, and knowing which one describes yours is the actual skill: fixed workload and hard latency target is Amdahl, growing workload and throughput target is Gustafson.