The no boundary wavefunction is a proposal for the wavefunction of the universe, which involves a four-dimensional geometry with no boundary into the past. It is used to compute the wavefunction of the universe as a function of the three-dimensional spatial geometry and the values of various fields living on that geometry. The proposal is elegant and theoretically compelling, but it gives a prediction for the curvature of the universe that is in disagreement with observations. In the context of slow roll inflation, it gives a result proportional to exp(24π²Mp⁴/V(φ*)), which gives a very large weight to values of φ where the potential is very small. This leads to a probability that dominates by an amount of order exp(10¹²⁰), the exponential of the cosmological constant problem. The paper reviews this proposal and describes how it applies to slow roll inflation. It gives a prediction for the probability that the spatial sections of the universe have positive scalar curvature, predicting that the curvature should be much larger than what is observed. The paper also discusses various proposals for resolving this disagreement, including the possibility that the path integral is ill defined, that we are not in the Hartle-Hawking state, that we should consider a tunneling wavefunction, that we should apply a selection principle, or that quantum corrections become important. The paper concludes that the no boundary proposal is a natural and mathematically elegant proposal for the wavefunction of the universe, but it is unsettling that it disagrees with observations.The no boundary wavefunction is a proposal for the wavefunction of the universe, which involves a four-dimensional geometry with no boundary into the past. It is used to compute the wavefunction of the universe as a function of the three-dimensional spatial geometry and the values of various fields living on that geometry. The proposal is elegant and theoretically compelling, but it gives a prediction for the curvature of the universe that is in disagreement with observations. In the context of slow roll inflation, it gives a result proportional to exp(24π²Mp⁴/V(φ*)), which gives a very large weight to values of φ where the potential is very small. This leads to a probability that dominates by an amount of order exp(10¹²⁰), the exponential of the cosmological constant problem. The paper reviews this proposal and describes how it applies to slow roll inflation. It gives a prediction for the probability that the spatial sections of the universe have positive scalar curvature, predicting that the curvature should be much larger than what is observed. The paper also discusses various proposals for resolving this disagreement, including the possibility that the path integral is ill defined, that we are not in the Hartle-Hawking state, that we should consider a tunneling wavefunction, that we should apply a selection principle, or that quantum corrections become important. The paper concludes that the no boundary proposal is a natural and mathematically elegant proposal for the wavefunction of the universe, but it is unsettling that it disagrees with observations.