The increasing perception that public communication in science and technology is an important tool to create a knowledge society is encouraging numerous public engagement activities. However, too little is known about scientists' opinions of and attitudes towards the public with whom they interact during these activities, especially in southern European countries such as Spain. If we want to establish an effective dialogue between science and society, we need to be aware of the opinions and perceptions that both parties have of each other. In this study, we address this issue by focusing on 1022 responses to a survey conducted among scientists in Spain to discover their views of the public, and we then compare these responses with data from other national surveys on the public's understanding of science. The results show that approximately 75% of Spanish scientists think that the general public has a serious lack of knowledge and understanding of scientific reasoning, although scientists do recognize that science interests the public (73%). Scientists believe that the public values the scientific profession to a lesser extent than suggested by public surveys: on a scale of 1-5, survey respondents rate their valuation of the scientific profession at 4.22, whereas scientists rate the public's valuation of the profession at 3.12, on average. Significant differences were detected between scientists' perceptions of how citizens are informed about science and what citizens report in surveys. The challenge for the future is to narrow this gap in order to help scientists gain a better understanding of the public and their interests and to make public engagement activities more effective.