I have named seven Millennium Prize Problems. There are other such lists, but they are not without drawbacks: Prior to the compilation of this collection, the Clay Mathematics Institute has named seven CMI Millennium Prize Problems. It is a bit disappointing that there is little overlap between these problems and my research interests. Then there is Barry Simon's list of 15 open questions about Schrödinger operators (Schrödinger operators in the 21st century), but, unfortunately, here the pecuniary incentive is missing.

Therefore, I designated a $70.- prize fund for the solution of the Christian Remling Millennium Prize Problems, with $10.- allocated to each. I myself, and no other persons or body, have the authority to authorize payment from this fund or to modify these stipulations.

The Christian Remling Millennium Prize Problems are problems on one-dimensional Schrödinger operators which are not widely known. (The mere fact that there are many problems left in this area is perhaps not widely known, either.) Still, I think that these are interesting and difficult questions.

I will consider a proposed solution to a Millennium Prize Problem if it is a complete mathematical solution to one of the problems. In the case that someone discovers a mathematical counterexample, rather than a proof, the question will be considered in the same way as described below. A proposed solution to one of the Millennium Prize Problem may not be submitted directly to me.

Before consideration, a proposed solution must be published in a refereed mathematics journal like Annals of Mathematics, and it must also have general acceptance in the mathematics community two years after that publication. Following this two-year waiting period, I will decide whether a solution merits detailed consideration. In the affirmative case, I will try to understand the solution and check it.

I will come to a decision within a reasonable time. I may give a prize to one person. I may also decide that a particular prize be divided among multiple solvers of a problem or their heirs. I will pay special attention to the question of whether a prize solution depends crucially on insights published prior to the solution under consideration. I may (but need not) recognize such prior work in the prize citation, and I may (but need not) include the author of prior work in the award.

All decision-making procedures concerning the Christian Remling Millennium Prize Problems are private.