Google released AlphaEvolve. I tried to get a sense of whether the problems it solved were hard. I focused on Problem B.1:
B.1. First autocorrelation inequality
For any function $f:\mathbb{R} \rightarrow \mathbb{R}$, define the autoconvolution of $f$, written $f*f$, as \begin{equation} f*f (t) := \int_\mathbb{R} f(t-x) f(x)\ dx. \end{equation} Let $C_1$ denote the largest constant for which one has \begin{equation} \max_{-1/2 \leq t \leq 1/2} f*f(t) \geq C_1 \left(\int_{-1/4}^{1/4} f(x)\ dx\right)^2 \end{equation} for all non-negative $f: \mathbb{R} \rightarrow \mathbb{R}$. This problem arises in additive combinatorics, relating to the size of Sidon sets. It is currently known that \begin{equation} 1.28 \leq C_1 \leq 1.5098 \end{equation} with the lower bound proven by Cloninger and Steinerberger (2017) and the upper bound achieved by Matolcsi and Vinuesa (2010) via a step function construction. AlphaEvolve found a step function with 600 equally-spaced intervals on $[-1/4,1/4]$ that gives a better upper bound of $C_1 \leq 1.5053$.