Despite getting off to a rocky start, the friendship between Michael Burnham and Sylvia Tilly on Star Trek: Discovery has become one of the best relationships on the show. Tilly was first introduced in season 1 as Michael's bubbly, socially awkward roommate after Michael was unwittingly recruited to work on the USS Discovery by Captain Lorca. Having just been court-martialed by Starfleet for her mutiny, Michael was not only wary of her new posting but completely closed off to any kind of friendship, perhaps believing she didn't deserve it because of her guilt over the part she played in starting the Klingon War.
It was clear from their first meeting that Michael and Tilly were very different people, and because of this, their connection was not immediate. Michael seemed to only tolerate Tilly, and once Tilly learned who Michael really was, she acted afraid of her. However, when Tilly apologized for her behavior and began to open up more about herself and her ambitions, Michael slowly began to take Tilly under her wing, starting to mentor her in hopes of helping her to accomplish her goals. From there, the mentorship slowly blossomed into a friendship that only got stronger over the course of Discovery's 3 seasons.
Besides the fact that it has been meaningful for many fans to see such a strong and healthy depiction of female friendship, Michael and Tilly's relationship has been especially important to their respective character development. As previously mentioned, Michael was extremely closed-off when she arrived on Discovery, wrapped up in her grief and guilt over her past actions and unwilling to open herself up to human connection. Her upbringing on Vulcan had also made her much less in touch with her emotions than a normal human. By contrast, Tilly was completely in touch with her emotions, likely to say whatever she was thinking or feeling in a given moment. While Michael was technically the one mentoring Tilly for much of season 1, Tilly helped Michael begin to open up and trust people again, as well as become more in touch with her emotional expression.
Along with this, the biggest thing that Michael aided Tilly with was her confidence. While Tilly had big dreams in Star Trek: Discovery season 1, she struggled with feelings of inadequacy and was hindered by a social awkwardness that often left her feeling like an outsider. During the 1st season, Michael helped Tilly to gain confidence and then continued to nurture that confidence through their friendship in season 2. Tilly's newfound self-esteem served her especially well in Discovery season 3 when she was promoted to acting-First Officer under Captain Saru. Without Michael's friendship, it seems unlikely that Tilly would have had the courage to not only accept the position but face the challenges that it presented. Likewise, Tilly's support for Michael in season 3 during her uncertainty about her place in Starfleet was part of what helped Michael ultimately decide to stay on board Discovery.
Michael and Tilly have been through much together over the course of Star Trek: Discovery, and their friendship has not only been enjoyable to watch but also made them both better and more dynamic characters. Now, the end of season 3 has set up Michael as Discovery's new Captain and Tilly as her apparent First Officer, giving the two characters a whole new set of challenges to face together that will hopefully test their friendship but also make it stronger. If season 3 was any indication, fans can expect some great things from Captain Burnham and First Officer Tilly on Star Trek: Discovery in the future.