This book has focused on Husserl’s thoughts about mathematics and the kind of method he used to approach it. Some words were also devoted to what kind of logic this approach demands. I hope the reader was able to gain a clear enough understanding of all this to make her or him wonder about the next steps, namely, what would phenomenological philosophy of mathematics look like in the twenty-first century?

Extrapolating from Husserl’s approach, I contend that it would use radical Besinnung – that is, it would aim to capture the values and goals of present-day mathematicians, both pure mathematicians as well as those with a logical or “foundational” interest. It might not be focused only on particular areas of inquiry, such as set theory and mathematical logic, but might aim to capture the values guiding different mathematical practices considered more widely.