Today, the scientific research effectiveness is more and more often determined by the size of grants obtained, the number of publications and the level of their prestige, as well as the ability to attract public attention, and not by well-defined problems and stringent methods of their solutions. This trend is disastrous for science. Bibliometric data, useful as a subsidiary method of evaluation, cannot replace expert opinion based on paper analysis. The pressure making scientists to publish, leads to poor quality of publications. Irreproducibility of papers is now a commonplace, amounting in oncology up to 75%. This results in the incremental character of science, when the research is reduced to a systematic refinement of available data. As a consequence, researchers and financing are focused on known and common research directions, while there are still many white spots avoided by the researchers due to the risk to fail and lose publications. For instance, 1000 of 4000 E. coli genes remain absolutely uninvestigated. Clearly, there are even more white spots in complex multicellular organisms, including humans. All this creates prerequisites to reducing the probability of big scientific discoveries which are often made by chance. Science needs better financing and this is aggravated by that the allocated funds are distributed ignoring the scientific value of research and accidental character of discoveries. The author draws attention to the importance of financial support of scientific schools that are the most probable centers of the obtaining of new scientific knowledge and preparing the ground for scientific discoveries.