<p>An original mathematical theory-inspired optimization algorithm, named multi-sequence discrete recursive descent optimizer (MDRDO) is proposed for numerical optimization and engineering issues. The main inspiration is derived from the deterministic recursive descent method, composed of descent directions and step lengths. Firstly, by adopting multiple initial sequences, a multiple-sequence searching framework (MSF) is constructed to explore the feasible space fully. Then, according to the Taylor expansion, the approximate discrete gradient is calculated to form a discrete quasi-Newton direction (BFGS) and the imprecise search step length for each sequence. Furthermore, to enhance the ability to escape local optimums, two random searching strategies are employed to keep the diversity of candidate solutions. Hence, the MDRDO is constructed by merging the quasi-Newton direction, imprecise step length and random strategies, in which suitable descent directions and step lengths help the MDRDO to explore a promising region and exploit the optimal solutions. The effectiveness of the MDRDO is verified by the comparison experiments with other 10 excellent algorithms on two typical test suites. Results reveal that the MDRDO outperforms others for 62.07% among 29 functions of CEC2017 test suite and 80% among 10 functions of CEC2020 test suite. Average convergence curves prove the ability of MDRDO to approach better solutions quickly. The applicability of the MDRDO is tested on 5 engineering problems with the other 9 widely used algorithms, in which the MDRDO ranks first for all problems with excellent comprehensive performance. Overall, the test results demonstrate that MDRDO is a promising tool for addressing practical optimization problems.</p>