An algorithm is an unambiguous sequence of steps that leads to the solution of a given problem. Over time, with the expansion of science and human understanding of the laws of nature by the aid of mathematics, algorithms have seen improvements. More often than not, nature has inspired solutions to complex problems. A neural network is probably the most talked-about, nature-inspired algorithm in the present day.
When computer logic began with multiple if-else ladders, no one would ever have thought that one day we'd have computer programs that would learn to produce results similar to the if-else ladder without the need to write conditions manually. What's more, we have computer programs today that generate other programs that can simulate AI!
Surely, with each passing day, algorithms developed by humans and now, by machines too, are getting smarter and more powerful at performing their tasks. This has directly impacted the rise of neural networks, which, in their rudimentary form, seem to be a time-consuming super-nesting of loops to solve matrices and vector arithmetic problems.