Leonard and Sheldon's friendship is put to the test when Leonard wants to present a paper they co-authored at a physics convention, but Sheldon doesn't.
Leonard finds a letter in the trash can, the letter an invitation for him and Sheldon to speak at an upcoming conference on the topic of their latest joint research findings. Sheldon threw the letter out since he didn't want to do it. This brings to the forefront several issues. Has Sheldon thrown out any other important letters to Leonard? Who has the right to their joint intellectual property, especially if Leonard wants to present? Whose idea was the research to begin with? In Penny's eyes, does Leonard own anything appropriate to wear to the conference? Can Leonard and Sheldon come to a compromise so that they will speak to each other and be friends again?
Leonard is dismayed when he finds a letter in the trash can asking he and Sheldon to present a paper at a lecture. Sheldon says he threw it out because he feels that giving a lecture before inferior minds is pandering and undignified. This sets off an argument that has the two not speaking with one another and Leonard deciding to give the lecture without him. Sheldon crashes the lecture and the two end up in a sissy fight that (thanks to Howard) becomes a featured video on YouTube.
- Sheldon and Leonard are asked to a physics conference to present their work together, but that leads to a feud because Sheldon's too arrogant to share the honor. Penny does her best to mediate, but only makes things worse.