Tau Koopa (Τ, τ, or Tau for short) is a fanon Koopaling created as a foil to a previous joke Koopaling, Pi Koopa. Unlike Pi, who is portrayed as laid-back despite his intelligence, Tau Koopa feels the need to be overly pretentious and self-centered because he feels he is less popular.
In the failed invention by Aiva Forte and Iggy Koopa that created Pi, a byproduct was formed that soon settled into physical form as Tau Koopa. Tau became friends with Pi at first, but could not put their differences behind him and started to develop misanthropic tendencies toward Pi. One day, Tau decided to spy on Pi and saw him having fun with Iggy and Thomas Koopa. Tau did not know that these were Pi's only remaining friends and assumed that Pi was more popular than him.
In 2010, Tau Koopa left home to "inform the world of his existence and his point". While he became relatively well-known in the following years, he never garnered much real attention. Tau started wondering if his efforts were all for six-point-two-eight-three-one-eight-five-three-naught. He returned to Bowser's Castle hoping to apologize to Pi, the closest thing he had to a brother. However, he could not tell whether Pi accepted the apology because Pi Koopa speaks like a freaking Pokémon and that is something I will never understand.
Unlike most Koopalings, Tau Koopa goes around wearing a τ-shirt with the number 6.28 screen-printed on and black dress pants instead of a shell. He has a duck-egg blue head topped with very clean, well-combed goldenrod hair. Tau wears a futuristic single-lens goggle with the symbol τ in the middle. Tau has a line of short teeth on his upper lip that ends with a duo of protruding canines on each side.
Tau Koopa is often self-important and pompous, though not to the point of constant annoyance. His thirst for recognition and popularity has resulted in his having a bit of a victim complex. Deep down, Tau just wants to be loved, due to his lack of a father and his continued friendlessness. However, he masks this desire to the point that he ends up driving away people who try to bond with him.
In this sense I think we can all relate to Tau.Tau is also irritated by the world around him. He sees it as "mathematically inefficient and worthless". This implies that Pi Koopa and he are able to see their surroundings as the code and filestructures they are, though while Pi doesn't appear to worry about its mistakes, Tau takes issue with potential bugs and poor level design.