We present an $\\mathcal{O}^\\star(2^{0.5n})$ time and\n$\\mathcal{O}^\\star(2^{0.249999n})$ space randomized algorithm for solving\nworst-case Subset Sum instances with $n$ integers. This is the first\nimprovement over the long-standing $\\mathcal{O}^\\star(2^{n/2})$ time and\n$\\mathcal{O}^\\star(2^{n/4})$ space algorithm due to Schroeppel and Shamir (FOCS\n1979).\n We breach this gap in two steps: (1) We present a space efficient reduction\nto the Orthogonal Vectors Problem (OV), one of the most central problem in\nFine-Grained Complexity. The reduction is established via an intricate\ncombination of the method of Schroeppel and Shamir, and the representation\ntechnique introduced by Howgrave-Graham and Joux (EUROCRYPT 2010) for designing\nSubset Sum algorithms for the average case regime. (2) We provide an algorithm\nfor OV that detects an orthogonal pair among $N$ given vectors in $\\{0,1\\}^d$\nwith support size $d/4$ in time $\\tilde{O}(N\\cdot2^d/\\binom{d}{d/4})$. Our\nalgorithm for OV is based on and refines the representative families framework\ndeveloped by Fomin, Lokshtanov, Panolan and Saurabh (J. ACM 2016).\n Our reduction uncovers a curious tight relation between Subset Sum and OV,\nbecause any improvement of our algorithm for OV would imply an improvement over\nthe runtime of Schroeppel and Shamir, which is also a long standing open\nproblem.\n