Conventional beamforming methods for intelligent reflecting surfaces (IRSs) or reconfigurable intelligent surfaces (RISs) typically entail the full channel state information (CSI). However, the computational cost of channel acquisition soars exponentially with the number of IRSs. To bypass this difficulty, we propose a novel strategy called blind beamforming that coordinates multiple IRSs by means of statistics without knowing CSI. Blind beamforming only requires measuring the received signal power at the user terminal for a sequence of randomly generated phase shifts across all IRSs. The main idea is to extract the key statistical quantity for beamforming by exploring only a small portion of the whole solution space of phase shifts. We show that blind beamforming guarantees a signal-to-noise ratio (SNR) boost of Theta(N^{2L}) under certain conditions, where L is the number of IRSs and N is the number of reflecting elements per IRS. The proposed conditions for achieving the optimal SNR boost of Theta(N^{4}) in a double-IRS system are much easier to satisfy than the existing ones in the literature. Most importantly, the proposed conditions can be extended to a fully general L-IRS system. The above result significantly improves upon the state of the art in the area of multi-IRS-assisted communication. Moreover, blind beamforming is justified via field tests and simulations. In particular, as shown in our field tests at 2.6 GHz, our method yields up to 17 dB SNR boost; to the best of our knowledge, this is the first time that the use of multiple IRSs gets verified in the real world.