The problem of landmine detection has been studied for decades. Mine detection systems have typically been developed by first identifying a sensor technology, then testing on particular manmade testbeds, then deploying the sensor on a vehicle or manportable device. Despite much effort, current systems still exhibit gaps between existing and desired capability, e.g., in terms of rate of advance, detection rate, and false alarm rate within demonstration testbeds. In this paper, we propose a new system-level approach to landmine detection. We argue that 'the landmine detection problem' cannot be attacked in a piecewise fashion: system-level solutions must simultaneously consider functional requirements, sensor technologies, models of sensors, the method of sensor application, and the platforms from which sensors are applied. This perspective allows us to shift our focus from the previous emphasis on novel sensor technology, and to go somewhat beyond traditional doctrines governing standoff or manportable detection. We first propose a new theory of geometric sensing and probing in the mine detection context. Specifically, we propose new formulations of 'object identification by probing' which correspond to various sensing modalities. We demonstrate that multiple agents can achieve probe classes that are not serializable for emulation by a single probe agent. With this in mind, our second main contribution lies in proposing a new paradigm for landmine detection, based on (i) close-in observation with simple spectra, and (ii) small, inexpensive, networkable robotic sensing platforms which can act in a cooperative fashion to implement powerful multi-agent probing strategies.