It started with Donald Trump announcing that the US will pull out of the Paris climate agreement. It ended with Ted Cruz and a Harvard professor in dispute – and calling each other “sad”.

It was an intense dispute over another Paris deal, two centuries old, which featured increasingly heated discussion of patriotism, sexism and – what else? – partisan politics.

Within two hours of Trump’s announcement that the US will withdraw from the historic global deal to combat climate change, historian Joyce Chaplin posted on Twitter that the decision was a betrayal of the international community.

“The USA, created by int’l community in Treaty of Paris in 1783, betrays int’l community by withdrawing from #Parisclimateagreement today,” she wrote.

Chaplin is the James Duncan Phillips professor of early American history and the chair of American studies at Harvard University. She also studies climate history and climate science.

Initially, her tweet sparked a lively but relatively polite debate, among members of the general public. Some weighed in to argue that the US had created itself much earlier, with the Declaration of Independence on 4 July 1776. Others agreed that it took formal recognition under international law, with the signing of the Treaty of Paris, for the United States to be considered officially extant.

Then, just after 11pm and with the boom of a rebel cannon, Cruz entered the arena.

“Just sad”, he tweeted. “Tenured chair at Harvard doesn’t seem to know how USA was created. Not a treaty. Declaration plus Revolutionary War plus Constitution = USA.”

The following morning, Chaplin retorted: “Sad. US senator, Harvard Law degree. Doesn’t know that national statehood requires international recognition.”

The war of words heated up from there. On Saturday, Chaplin told the Guardian via email: “The treaty brought the US into legal existence … as any scholar of early American history will attest.”

Via a spokeswoman, Cruz declined to comment further. But the sour social media exchange remained for all to see. After Chaplin returned his verdict that her opinion was “sad”, the Texas senator – who graduated from Princeton and Harvard Law School in the 1990s, known even then as a polarizing figure – doubled down.

“Lefty academics @ my alma mater think USA was ‘created by int’l community’,” he wrote. “No – USA created by force, the blood of patriots & We the People.”

Not having received another riposte from Chaplin, Cruz posted that the Paris treaty merely memorialised the patriots’ “total victory at Yorktown” and commented: “Her claim is like saying a plastic globe created the Earth.”

Others joined in. One said Cruz had perpetrated “the ‘mansplanation’ of the year”. Another lamented that “sexism somehow had to be played into this”. A man told Chaplin that Cruz “knows a hell of lot more than you, sweet cheeks”.

Fighting broke out in Britain’s American colonies on 18 April 1775, at Concord, Massachusetts. On 4 July 1776, Congress issued the Declaration of Independence. British forces did not surrender until 1781, after the battle of Yorktown, in Virginia.

In 1783, representatives of King George III met in Paris with Americans including founding fathers Benjamin Franklin and John Adams. Representatives of France and Spain also signed the United States of America into formal, internationally-recognised existence.

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Chaplin said: “The Declaration of Independence was necessary but not sufficient. The American patriots knew that they needed international assistance to win the war. Even before [4 July] 1776, they sent a diplomatic envoy to Paris – foreign aid and recognition were top priorities.”

She declined to comment on the tone of Cruz’s criticism and his more personal points, saying: “Personal attacks cannot alter the historical record.”

On the history, she added: “Before they recognised the US, the French referred to the Americans as “insurgents” … not citizens of a separate nation … the full spate of recognitions only came after the treaty. Those who recognised the US before were demonstrating antagonism to Great Britain.”

The 1783 Paris treaty formalised the boundaries of the US: north of Florida to the Great Lakes and east of the Mississippi.

“The treaty … in terms of law created the US as one nation among others,” Chaplin said. “By relinquishing claims to the US, Britain also gave force of law to its territorial boundaries, which had not been clear before, from anyone’s perspective …There is scholarly consensus on this.”

She called 4 July 1776 “a first step” on the road to national independence.

Asked if the US now owes it to the rest of the world to stick with the Paris climate deal, Chaplin said that accord was the culmination of centuries of quid pro quo.

“If we turn our backs on the rest of the world now,” she said, “when climate change requires all hands on deck, we are denying centuries of cooperation in a community of nations.”