The hallmark of materials science is the ability to tailor the microstructure of a given material to provide a desired response. Carbon mixed with iron provides the steel of buildings and bridges; impurities sprinkled in silicon single crystals form the raw materials of the electronics revolution; pinning centres in superconductors let them become powerful magnets. Here, we show that either adding a few parts per million of the proper chemical impurities to indium antimonide, a well-known semiconductor, or redesigning the material's structure on the micrometre scale, can transform its response to an applied magnetic field. The former approach is purely quantum mechanical(1-3); the latter a classical outgrowth of disorder(4-7), turned to advantage. In both cases, the magnetoresistive response-at the heart of magnetic sensor technology-can be converted to a simple, large and linear function of field that does not saturate. Harnessing the effects of disorder has the further advantage of extending the useful applications range of such a magnetic sensor to very high temperatures by circumventing the usual limitations imposed by phonon scattering.