The world’s richest man, in a Twitter showdown that will be seen as one for the history books, is floating a proposal to end the war in Ukraine — only to find himself being swatted down by that war-torn country’s president, Volodymr Zelensky.

The spat with Elon Musk is not just about a clash of ideas and outsized personalities. It also underscores that after nearly eight months of war there is no ceasefire in sight and that social media barbs are no substitute for robust diplomacy. 

Mr. Musk, the founder of Tesla and SpaceX, has more than 100 million followers on Twitter as well as a financial stake in the social media company. He used Twitter Monday to propose an idea for a peace deal that, as he sees it, would mark a new approach.

The idea would involve the United Nations supervising a new round of referenda in the four regions of Ukraine that Russia illegally annexed last week. “Russia leaves if that is the will of the people,” he suggested.

Mr. Musk’s unsolicited plan would also acknowledge Russian sovereignty over the Crimean peninsula, which Russia seized in 2014, and confer on Ukraine status as a neutral country.  Embracing the social aspect of the medium, Mr. Musk generated a poll so that his followers could vote. 

Mr. Zelensky, though, was not having it, brandishing instead some social media bravura of his own. He created his own poll, with the question,  “Which @elonmusk do you like more?”, with two responses from which to choose: “One who supports Ukraine” and “One who supports Russia.”

Mr. Musk, by invoking political neutrality for Ukraine, seems to discredit the possibility of Ukraine’s joining the NATO military alliance, which has long been seen as a red line for Moscow. 

The billionaire knows that Crimea, while stolen territory, was also Russian for much of its history. Crimea was “part of Russia,” he tweeted, “since 1783 (until Khrushchev’s mistake).”

Yet glossing over the reality of how the dissolution of the former Soviet Union reshuffled the map betrays a certain naivete that could easily be construed by Kyiv as insensitive, to say the least. 

Mr. Musk’s concerns about the possibility of Moscow ordering up a full mobilization of troops which could in his view lead to “full war” are also on shaky ground. “Victory for Ukraine is unlikely in total war,” he stated. “If you care about the people of Ukraine, seek peace.” Yet so far, even Mr. Putin’s partial mobilization has been a spluttering failure as young men flee Russia in droves.

Mr. Musk  also fails to understand how his suggestions would be perceived at Kyiv, the resilient capital of a country that is badly fractured, but not broken.  Mr. Zelensky appeared to be peeved by too many cooks in the kitchen. He is also fighting a war, so he left it to others to flesh out their reactions.

The Ukrainian ambassador to Berlin, Andriy Melnyk, was less artful with a tweet of his own: “My very diplomatic response [to Musk] is to get lost.” A top advisor to Mr. Zelensky, Mykhaylo Podolyak, had a more measured if somewhat wry response to the Twitter kerfuffle.

Mr. Podolyak suggested a “better peace plan” in which “Ukraine liberates its territories, including the annexed Crimea,” Russia “undergoes demilitarization and mandatory denuclearization so it can no longer threaten others” and “war criminals go through an international tribunal.”

In the meantime, any kind of dialogue between the Russian and Ukrainian leaders seems as remote as prospect as Mr. Musk reining in his own ego. “Tesla is a nice car for sure,” Mr. Podolyak ribbed the entrepreneur via Twitter, adding “But today I prefer HIMARS.”

HIMARS is an acronym for the high mobility artillery rocket systems with which Washington has supplied to Ukraine. They have thus far proven to be more effective in fending off Russian forces than an eccentric billionaire’s tweets.

On Tuesday, the Kremlin said it “takes two sides to negotiate” and called Mr. Musk’s thoughts on a peace deal a “positive step.”