Generating conjectures on fundamental constants with the Ramanujan Machine

Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics to physics, biology chemistry. For centuries, new formulas relating fundamental have been scarce usually discovered sporadically. Here we propose a novel systematic approach that leverages algorithms for deriving help reveal their underlying structure. Our find dozens well-known as well previously unknown continued fraction representations $\pi$, $e$, Catalan's constant, values the Riemann zeta function. Two example conjectures found by our algorithm so far unproven are: \begin{equation*} \frac{24}{\pi^2} = 2 + 7\cdot 0\cdot 1+ \frac{8\cdot1^4}{2 1\cdot \frac{8\cdot2^4}{2 2\cdot 3 \frac{8\cdot3^4}{2 3\cdot 4 \frac{8\cdot4^4}{..}}}} \quad\quad,\quad\quad \frac{8}{7 \zeta(3)} 1 - \frac{1^6}{3\cdot 7 \frac{2^6}{5\cdot 19 \frac{3^6}{7\cdot 37 \frac{4^6}{..}}}} \end{equation*} We present two proved useful finding conjectures: Meet-In-The-Middle (MITM) Gradient Descent (GD) tailored recurrent structure fractions. Both based on matching numerical thus they conjecture without providing proofs requiring prior knowledge any This is especially attractive which no known, it reverses conventional sequential logic formal proofs. Instead, work supports different research: utilizing data unveil structures, trying play role intuition great mathematicians past, leads research.