Data science presents new opportunities but also new challenges. In this talk we will focus on three separate challenges for data science: 1. Paradoxes of the Data Society, 2. Quantifying the Value of Data, 3. Privacy, loss of control, marginalization. Each of these challenges has particular implications for data science. The paradoxes relate to our evolving relationship with data and our changing expectations. Quantifying value is vital for accounting for the influence of data in our new digital economies and issues of privacy and loss of control are fundamental to how our pre-existing rights evolve as the digital world encroaches more closely on the physical. One of the goals of open data science should be to address these challenges to ensure that we can avoid the pitfalls of the data driven society, allowing us to reap the benefits of data science in applications from personalized health to the developing world.