How many mathematicians does the main protagonist meet in the musical "Fermat's Last Tango"?

The plot is based on the story of the proof of Fermat's Last Theorem by Andrew Wiles, whose name is changed to "Daniel Keane" in the musical. After seven years of isolation in his attic, Keane believes he has found a proof of the theorem. The musical starts with a press conference, where Keane explains his proof to reporters and promises to return to normal life with his wife Anna and his family. After promising to Anna that he is now "done with Fermat", Keane is surprised in his study by none other than Fermat himself. Keane asks Fermat for the secret of his proof but is refused. Instead, Fermat introduces him to the "Aftermath", a "heavenly purgatory" where he meets the famous mathematicians Euclid, Pythagoras, Newton, and Gauss. They inform him that his proof contains a "big fat hole". In a second press conference, Keane is questioned by reporters about a flaw in the proof. Anna wishes for a corrected proof for her birthday. Fermat mocks Keane, and the other mathematicians inform him that "mathematics is a young man's game". Keane returns to his attic to try to fix his proof, while his "math widow" wife is frustrated. Fermat continues to taunt Keane, but he is invisible and inaudible to Anna, and the three dance a "bizarre tango à trois" while Anna is confused by Keane talking to Fermat. The other mathematicians from the Aftermath, after noticing that they can't keep up with the mathematics of the past century, decide to grant admission to Keane even if he is unable to prove the theorem. As Keane finally gives up and declares his attempts a failure, Anna suggests that "within your failure lie the seeds of your success", repeating a line earlier spoken by the mathematicians. This quickly leads to Keane realising how to close the gap in the argument, and the musical ends with another press conference, and Fermat congratulates Keane for his proof.

The main protagonist meets five mathematicians - Fermat, who appears in Daniel's study, and Euclid, Pythagoras, Newton, and Gauss, who appear in the "Aftermath".