The Legend:

On the campus of Murray State College in Murray, Kentucky, there is a stone memorial which commemorates the day in 1902 that Nathan B. Stubblefield first publicly displayed a wireless means of transmitting voices between two points. Stubblefield’s wireless telephone was first demonstrated in 1892, years before Guglielmo Marconi developed his wireless telegraph; but that had been a demonstration for just one man, one Rainey T. Wells.
Stubblefield, a farmer and telephone repairman living in Calloway County, Kentucky, claimed he could send messages through the air without wires, a claim which attracted a huge crowd of spectators to the front of the Calloway County Courthouse in Murray on January 1, 1902. At points about two hundred feet apart on the lawn, Stubblefield and his son Bernard had set up two boxes that were not connected in any visible way. Each box was about two feet square and contained a telephone, through which Stubblefield and his son talked as if they were standing next to each other, their voices being perfectly audible to the crowds gathered around each box. It's said that his demonstration was greeted by hoots and snickers, causing the inventor to angrily gather up his equipment and leave.
However, word of the demonstration reached the St. Louis Post Dispatch, which then wrote to Stubblefield to request another demonstration. Weeks later, the newspaper received a simple postcard: "Have accepted your invitation. Come to my place any time. Nathan Stubblefield". The Post Dispatch reporter arrived at the farm in the second week of January, 1902. In the article written after the demonstration, the reporter described how he traveled about a mile from the inventor's farm and stabbed the rods attached to the wireless telephone into the ground, with the result that he could hear what Stubblefield's son spoke and played into the transmitter (Bernard played his harmonica some). According to one source, Stubblefield claimed in the same article that his apparatus worked by using the electrical field which permeates all matter.
The newspaper article won Stubblefield an invitation to demonstrate his invention in Washington, DC. At this demonstration one of his boxes was placed on a steamship, the Bartholdi, on the Potomac River, while a number of other boxes were positioned along the shore at sites of the users' choosing. Communication between the boxes -- including the one on the ship -- was fantastically clear. Stubblefield also demonstrated his wireless telephone in Philadelphia and New York that same year.
Strangely, Stubblefield never marketed his invention, despite applying for patents in several different countries, and definitely getting the patent for his devices in Canada and the United States. After his stunning success in Washington, he packed up and went home, afraid, some said, of having his ideas stolen. Stubblefield dropped out of the public eye and his family left him; he spent the remainder of his life in seclusion in a shack in Calloway County. On March 30, 1928, he was found dead of starvation; the true mystery, his reasons for not promoting his amazing invention and claiming his rightful place in the history of broadcasting, passed away with him.
In 1930, the monument was erected on the campus of Murray State College in memory of Nathan B. Stubblefield, posthumously declaring him the "Inventor of Radio". Before he died, Stubblefield said of himself: "I've lived fifty years before my time".

Variations
Frank Edwards' book, Stranger Than Science, gives the date of the Murray demonstration as 1892 and the date of Stubblefield's death as 1929. These are likely incorrect for the simple reason that the dates given on the memorial mentioned above is 1902 for the Murray demonstration and 1928 for his death, and these agree with my other sources. Perhaps Edwards or his source for the story confused the date of the Murray demonstration for the date of Stubblefield’s 1892 demonstration to Rainey T. Wells (mentioned above). Edwards also sets the date of the demonstration for the Post Dispatch reporter as January 10, 1902.
Let me also note that Edwards tries to add to the sense of mystery surrounding Stubblefield's device by stating that Stubblefield's patents don't make sense to those who examine them, and by stating that the inventors' equipment and records were missing from the scene of his death (which he neglects to mention was caused by starvation), thus implying Stubblefield was killed by someone to get these items.
Edward Lambert in a 1970 article in TV Guide states that Stubblefield had put in "two decades worth of effort" in developing his wireless telephone before his 1902 demonstration.