regarding algorithms, AL Khwarizmi didn't invent algorithms despite the naming, an algorithm is a broad term that means a step by step process to solve a task, algorithms existed since ancient times:
c. 1700–2000 BC – Egyptians develop earliest known algorithms for multiplying two numbers
c. 1600 BC – Babylonians develop earliest known algorithms for factorization and finding square roots
c. 300 BC – Euclid's algorithm
c. 200 BC – the Sieve of Eratosthenes
263 AD – Gaussian elimination described by Liu Hui
Timeline of algorithms - Wikipedia
Euclid's algorithm for example is a divide and decrease algorithm sharing mechanisms with the sorting algorithms used today
Divide-and-conquer algorithm - Wikipedia
Euclid's elements also was instrumental in the development of logic and modern science
also Heron's algorithm for approximating square roots which is found in his AD60 Metrica
Square root algorithms - Wikipedia
also method of exhaustion which was used by Euclid and Archimedes which is a clear case of iterative converging algorithm, Archimedes himself used a reductio ad absurdum(a proof by contradiction) for it
and there are many other ancient algorithms like ones found in conics and Euclid's elements.
and there are many types of algorithms like: brute force algorithm, Recursive algorithm, Greedy algorithm, Backtracking algorithm, Divide and conquer algorithm, Dynamic programming algorithm, Sorting algorithms and more,
also more than 90% of algorithms were invented after 1900 and most of them by the western world and China
list of algorithms invented in 1950s alone:
Hamming codes , Simulated annealing, Radix sort , Box–Muller transform, Kruskal's algorithm, Ford–Fulkerson algorithm, Prim's algorithm, Bellman–Ford algorithm, Dijkstra's algorithm, Shell sort, De Casteljau's algorithm, QR factorization algorithm, Rabin–Scott powerset construction
there are way way more:
Timeline of algorithms - Wikipedia
again the definition of an algorithm is a step by step set of instructions or rules followed to solve a specific problem or accomplish a task
also most algorithms that power the technologies of today are invented by the western world and china, some of the many algorithms invented in the western world for example:
Bellman-Ford Algorithm, Breadth-First Search (BFS), Depth-First Search (DFS), Boruvka’s Algorithm, Topological Sort, Heap Sort, Radix Sort, Bucket Sort, Counting Sort, Shell Sort, Strassen’s Algorithm, Rabin-Karp Algorithm, Boyer-Moore String Search Algorithm, Sieve of Eratosthenes, Euclid’s Algorithm, Flood Fill Algorithm, Bresenham’s Line Algorithm, Alpha-Beta Pruning, Traveling Salesman Problem (TSP), Bron-Kerbosch Algorithm, Lovász Lattice Reduction Algorithm, Steinhaus–Johnson–Trotter algorithm, Union-Find Algorithm, Kadane’s Algorithm, Knight’s Tour Algorithm, Barnes-Hut Simulation, Cooley-Tukey FFT Algorithm, Quicksort, Merge Sort, Dijkstra’s Algorithm, A* Search Algorithm, Kruskal’s Algorithm, Prim’s Algorithm, KMP String Matching Algorithm, RSA Algorithm, AES (Advanced Encryption Standard), SHA (Secure Hash Algorithm) Family, Diffie-Hellman Key Exchange, Fourier Transform, Fast Fourier Transform (FFT), Simplex Algorithm, Kalman Filter, K-Means Clustering, PageRank, Adaboost, CART (Classification and Regression Trees), Expectation-Maximization (EM) Algorithm, Fibonacci Search Technique, Knuth-Morris-Pratt Algorithm, Levenshtein Distance, Markov Chain Monte Carlo (MCMC), Minimax Algorithm, Newton’s Method, Particle Swarm Optimization, Viterbi Algorithm, Bubble Sort, Insertion Sort, Selection Sort, Bitonic Sort, Shellsort, Bogosort (Stupid Sort), Brent’s Algorithm, Booth’s Multiplication Algorithm, Gauss-Seidel Method, Jacobi Method, Gaussian Elimination, Cholesky Decomposition, LU Decomposition, Integer Factorization Algorithms (Fermat, Pollard, etc.), Euclidean Algorithm, Extended Euclidean Algorithm, Shor’s Algorithm, Grover’s Algorithm, Data Compression Algorithms (Huffman, LZW, Arithmetic Coding, etc.), Fast Multiplication Algorithms (Karatsuba, Toom-Cook, etc.), Miller-Rabin Primality Test, Solovay-Strassen Primality Test, Tarjan’s Strongly Connected Components Algorithm, Knuth-Bendix Completion Algorithm, Schreier-Sims Algorithm, Gröbner Basis Algorithms, Deutsch-Jozsa Algorithm, Simon’s Algorithm, Euclidean Shortest Path Problem Algorithms (Dijkstra, Bellman-Ford, etc.), Floyd-Warshall Algorithm, Johnson’s Algorithm, Hopcroft-Karp Algorithm, Edmonds-Karp Algorithm, Kuhn Munkres Algorithm (Hungarian Algorithm), Needleman-Wunsch Algorithm, Smith-Waterman Algorithm, Lesk Algorithm, N-gram Algorithms, Burrows-Wheeler Transform, BLAST Algorithm, Hirschberg’s Algorithm, Hunt-Szymanski Algorithm, Ukkonen’s Algorithm, Boyer-Moore-Horspool Algorithm, Aho-Corasick Algorithm, Suffix Array Algorithms (Manber-Myers, etc.), Burrows-Wheeler Transform Algorithms (BWT, FM-index, etc.), Shunting Yard Algorithm, Graham Scan Algorithm, Jarvis’s Algorithm (Gift Wrapping Algorithm), Kirkpatrick-Seidel Algorithm.
interestingly there is another term called Algorism which is closer to what Al Khwarizmi worked with