Most people are pretty easy to convince, that they need mathematics, but they mostly underestimate what kind of mathematics they need. At the moment there are some people around Leo Dorst, who develop a framework from geometric algebra, which could make things easier to program. But the mathematical core is something pretty new. It looks unfamiliar, because school mathematics doesn’t even go near this kind of mathematics.
The things you will need in any case are vectors, with a throughout knowledge of dot and cross product. Trigonometry, this is sinus and cosinus, because you need this stuff to find out for example, if your avatar is facing the right direction. And translation and rotation matrices. The later because, if your avatar is facing the wrong direction you will have to rotate him. Translation is needed, because you want your figures to move. If you want to do animation you need quaternions too, they are used to interpolate rotations.
Then there are splines, which are mathematically defined and even if DirectX has most of the common ones build in, you need to know the differences and how they work.
If you work with the camera you need to know projection, different kind of projections, what is field of view and what happens, if you set it on 90 degree (bad things mostly in DirectX).
And there is collision detection, which uses a lot of mathematics.
And you need a working knowledge of calculus, which will also help in physics.
And some statistics can come handy too.
The more you know the more you can control and knowledge opens new doors. In the games industry it is important to do new things and knowing a lot of mathematics can make new things possible.
I always though that the need of physics in games is self evident, but some questions I get, made me think that maybe it isn’t.
Because there are physics engines nowadays, people often assume that you need physics only if you use these. Or said differently you use these and you need no physics knowledge. Naturally using a physics engine is easier, if you have an idea what it does. But every simple game has a lot of physics, only people are so used to it in normal meat space, that they don’t recognize it as such. If your figures and objects are on the terrain or floor, you use your knowledge that on earth there is gravity. So even this simple assumption that things are on the floor, is actually already part of physics and obeys natural laws stated by Newton.
Things like how do projectiles work, how does a cannon work, how high can a human being jump, how fast can he run all this is part of almost every game I know and is actually by a large part determined by physics.
Then there is the visual part, how does material look like. How does it react to light is part of optics and this is a part of physics. Bump mapping or the playing around with surface normals only makes sense, if you know how light reacts on surfaces. If you want to write new shaders, with new effects, it pays to know how this works. Transparency and refraction for glass and water are important too. Shadows, which are used to to make games feel more realistic, are part of physics.
You can even program a real sunset, if you know how light works.
Every time you have water in your game, you need physics to make it look real, to find out when it is a mirror, when it is transparent and how waves look. If you have things in water ships or even your avatar you need to know how buoyancy (that’s the one with Archimedes in his bath tube) works.
Every time you have a vehicle or something flying around it helps to know physics to make it look and react in a way the player can understand and use.
And then physics is a great source of inspiration. Mario Galaxy for Wii or Crazy Machines uses it for game play. Especially in Mario Galaxy, the levels are very much inspired by crazy physics. There are cool things to find, if you make the effort and go looking.
By the way talent is not necessary. If you can program you can learn mathematics. It is just a question of training. And if you do sports or just move around, you know quite a lot about physics already. The only thing to do is to put it into a framework, formalize it and find the connections.
And yes, it is just this easy, no matter what your school experience may tell you.
Physics is the glass that falls every time there is nothing beneath it and the insight that this is the same thing that keeps the earth rotating around the sun. It is the connection, that the funny feeling you get in a fast elevator downwards, is the same that keeps people on the ISS weightless. This connection to things we instinctively know, only breaks down in quantum mechanic, relativity and beyond, where everyday experiences give no valid clue. Until then physics is the stuff that happens all around you all the time (time included).