Abstract. The success of the CDM model on large scales does not extend down to galaxy scales. We list a dozen problems of the dark matter hypothesis, some of which arise in specific models for the formation of structure in the universe, while others are generic and require fine tuning in any dark matter theory. Modifications to the theory, such as adding properties to the DM particles beyond gravitational interactions, or simply a better understanding of the physics of galaxy formation, may resolve some problems, but a number of conspiracies and correlations are unlikely to yield to this approach. The alternative is that mass discrepancies result from of a non-Newtonian law of gravity, a hypothesis which avoids many of the more intractable problems of dark matter. A modified law of gravity is not without formidable difficulties of its own, but it is no longer obvious that they are any more daunting than those facing DM.

Table of Contents

• INTRODUCTION
• MASS DISTRIBUTIONS IN THE INNER PARTS OF GALAXIES
• PROBLEMS CREATED BY THE DARK MATTER HYPOTHESIS
• DISCUSSION
• THE ALTERNATIVE
• CONCLUSIONS
• REFERENCES