One possible plot could be that Harry Potter's long - lost cousin somehow ends up in the world of Bleach. Maybe they have some unique magical abilities that are a blend of the wizarding world and the spiritual powers in Bleach. They could team up with Ichigo to fight against a common enemy, like a dark wizard who has also dabbled in the forces of Hollows. This would bring together the magic of Harry Potter and the action - packed battles of Bleach in an interesting way.
A plot could also involve the cousin being a key to opening a portal between the two universes. The Ministry of Magic in Harry Potter's world and the Soul Society in Bleach are initially suspicious of this new development. However, as the threat of a greater evil looms, they have to work together. The cousin, with the help of Harry and Ichigo, has to navigate the politics and power struggles of both worlds while trying to figure out their own place and powers.
It could be a dark wizard who has somehow managed to gain the power of Hollows. This antagonist would be extremely dangerous as they would combine the dark magic of the wizarding world with the destructive power of the Hollows. They might be after the cousin because of some special power or connection that the cousin has, which could be used to either rule both worlds or destroy them.
One possible plot is that Ichigo is reborn as Harry Potter's long - lost twin. He would then have to deal with the same kind of prophecy and the threat of Voldemort. But being Ichigo, he would approach things in his own way. He might not rely so much on magic wands but use his own spiritual power which could be disguised as a new form of magic in Hogwarts. This would cause a stir among the professors and students alike.
In the fanfiction, Harry might raise his cousin in an attempt to break the cycle of animosity that has always been between them. He could show his cousin a different side of life, full of magic and wonder. Harry could also protect his cousin from the dark forces that are always lurking in the wizarding world, and in the process, his cousin could become a valuable ally to Harry.
Perhaps Harry could be a wizard - geisha hybrid. He might use his magic to enhance the traditional geisha arts, like creating magical illusions during his performances. He could be in a Hogwarts - like school but also trained in the ways of the geisha, with spells and potions being used in the context of geisha traditions.
In this 'harry potter math fanfiction', it might also be that there is a new subject in Hogwarts called 'Magical Math'. The teachers could be magical creatures who are experts in both magic and math. The students would have to learn things like how to use equations to create spells or use geometric shapes to build magical structures. And there could be a big competition where the students use their math skills to win a great prize, like a magical artifact that can enhance their magic power.
A possible plot could be Morgoth's return in a weakened form in the Forbidden Forest. His presence starts to corrupt the magical creatures there. Harry and his friends sense the disturbance and go to investigate. They soon realize it's a much greater threat than they thought and must find a way to either banish Morgoth back to his realm or destroy his essence completely.
Well, perhaps in this fanfiction, Harry Potter uses his magical skills in the context of auditing. He could use spells to detect financial irregularities, like a magical version of auditing software. For example, he might cast a spell that reveals hidden transactions in a company's books.
Well, perhaps the Yautja is on a hunt in its own world but gets caught in a magical portal that leads it to Hogwarts. The students are both scared and intrigued. Hermione starts researching about it, trying to find a way to send it back. Meanwhile, the Yautja sees the Death Eaters as worthy prey and starts stalking them. Harry has to convince the Yautja not to go on a full - out killing spree which might endanger innocent lives as well.
A possible plot could be that a Smilodon escapes from a magical menagerie in the Forbidden Forest. Harry and his friends discover it and try to return it safely without getting hurt or getting in trouble with the Hogwarts authorities.
Well, one possible plot could be that Orochimaru somehow finds his way into the Harry Potter universe. He might be interested in the unique magic there, like the Elder Wand or the Philosopher's Stone. He could try to use his ninja skills and devious ways to steal these powerful magical items, and Harry and his friends would have to stop him using their own magic.