We broke the story ... the literary piece -- titled "Deductive Logic" -- was what first drew Belichick to Hudson way back in 2021 -- when they had their initial encounter on a plane ride from the Boston area to Florida.

Our sources say the ex-New England Patriots head coach was intrigued by the work that Hudson was studying on the flight ... and sparked up a conversation with her over it all.

We're told the talk led to an autograph, which led to an exchange of numbers -- which ultimately led to the duo dating.

Warren Goldfarb -- the Harvard professor who authored "Deductive Logic" -- said in a message to us on Wednesday he's stoked his work played a role in their love story ... joking, "I'm delighted to see that logic, so often derided as a dry subject, has finally been recognized for its romantic potential!"

We're sure Belichick and Hudson would share similar sentiments ... as the two have been going strong for a while now -- even looking quite smitten at Tom Brady's Patriots Hall of Fame induction ceremony earlier this month.