Who came up with martial arts?

That is a very insightful way to express this question because contrary to popular opinion, that is exactly the most accurate way to describe the human relationship to the knowledge of the Martial Art (singular term is more accurate) - - it was discovered, not created or invented. For example, Benjamin Franklin did not "create" or "invent" electricity. He "discovered" it's natural abilities and characteristics, and found a way to harness it, and others since have discovered many ways to use it to the advantage of humans (or to the detriment). Likewise, man did not create or invent fire - - humans discovered it, and learned how to utilize it, and re-create it through natural means.

The Martial Art is a concept of understanding natural forces, and learning how to appreciate the value of life, nature, and the universe, and how to apply the various laws of nature in ways to benefit ourselves and others. This discovery has been an ongoing process since the beginning of human existence in the fields of physical combat, social interactions, and spiritual enlightenment. It is a harmonious balance of body, mind and spirit, and can not truthfully be attributed to any one person, race, or exact time period. Conversely, many people have been credited for creating systems for teaching the philosophy and concept of Martial Art under different system names with variations on strategy, tactics, and techniques of each school of thought.

Like fire, we may never know who the first people were to initially discover the nature of the martial art; however, it is possible to trace the origins of some of the more modern systems or schools of Martial Arts.