It would show Harry as a more intellectual and curious character. His love for math could lead him to explore areas of magic that others haven't. For instance, he might use math to predict the movements of magical creatures, making him seem more of a wizard - scientist.
In this fanfic, Harry could be developed as a problem - solver. Math gives him a different way of thinking, so when faced with challenges in the wizarding world, he approaches them with a mathematical mindset. He might break down a difficult situation into equations and find solutions that way. He could also be seen as a bit of an outcast among his peers at first, as his love for math is not a common trait in the wizarding world, but later they come to respect his unique approach.
He'd be more disciplined. His character would be shaped by military values. He'd be less likely to act impulsively and more likely to think things through strategically.
He'd be tougher. Hiei's no - nonsense attitude would rub off on him. Harry would be more likely to take risks without hesitation.
Harry's character would be more attuned to the deeper magics. He would be less likely to jump into things without thinking. Since Flamel is a master of alchemy, Harry might be more interested in the scientific aspects of magic. He would also have a greater respect for life and magic's power, as Flamel, with his long life, would instill in Harry a sense of wonder and caution about the forces they deal with.
Harry's character would transform significantly. Goku's carefree and positive attitude would rub off on him. He would be less brooding and more open - minded. His magic training might take a backseat initially as he gets immersed in learning martial arts from Goku. But as he grows, he would find a way to balance both. He would develop a new sense of self - worth, knowing that he is part of Goku's family. His relationships with others would also change. He might be more assertive in his friendships, and his leadership skills would improve as he watches Goku lead in battles. His magical abilities would become more fluid, as he adapts to using them in tandem with his newfound physical abilities.
One possibility could be that Harry discovers the magic of math in his wizarding world. Maybe he uses math to solve some complex spells or potion-making ratios. For example, he realizes that a certain spell's effectiveness is related to geometric patterns and uses his newfound math knowledge to enhance it.
Harry's character would be a unique blend of wizard and wolf - like traits. Growing up with wolves, he would be less inhibited by the social norms of the wizarding world at first. He would be more direct in his communication, like the wolves. However, as he enters Hogwarts and interacts more with other wizards, he would start to understand and adapt to those norms while still holding onto his wolf - adopted values. He might be more attuned to nature and magic that is related to the natural world, which could lead him to explore different branches of magic that other wizards might overlook.
As the son of Zeus, Harry would have to grapple with his new identity. He might struggle with feelings of being different from the other wizards. This internal conflict could drive his character development, as he tries to find a balance between his wizarding self and his new Greek - god - related self. He could learn to embrace both aspects and use them to become a more complex and powerful character in the fanfic.
Harry's character could become more reserved as he tries to adapt to Marge's strict household. He might learn to hold his tongue more often.
Harry's character would face a huge transformation. He'd be constantly on edge, having to deal with Umbridge's strict rules and her mean - spirited nature. This would make him more empathetic towards those who are oppressed. He'd also become more resourceful, finding ways to communicate with his old friends and allies despite Umbridge's attempts to isolate him. His experience with Umbridge would be a crucible that forges him into an even more resilient and determined hero, ready to take on not only Voldemort but also the corrupt elements within the wizarding establishment.
Harry Potter's character would likely develop a stronger sense of independence. Since Jack Frost is often portrayed as a solitary figure, Harry might learn to rely on himself more. He could also develop a sense of wonder for the natural elements, especially ice and snow. His values might shift towards a more elemental view of magic, and he might be less interested in the politics and social hierarchy within the wizarding world. His sense of justice could still be strong, but it would be more in line with the unyielding nature of ice, being very firm and unwavering.