A warped pan rests on only a single point of its base on the stove; that makes it spin and rock, and oil runs to the edge, leaving the center dry. You can tell whether it is warped with a straight edge, not by looking at it. Here is the bad news: a thin-bottomed pan cannot be unwarped at home. Hammering it will ruin the base completely.
The bottom of a pan almost always looks flat to the eye; the warping is submillimeter, but its effects are significant. Checking it is simple: turn the pan upside down, hold a straight ruler or the back of a knife against its base, and look for light from behind. A gap where light shows in the center means the base is concave; a gap at the edges means it is convex. There is also a tool-free method: put a finger’s depth of water in an empty, cold pan. If the water gathers at just a single edge instead of spreading evenly over the base, the base is not flat.
On the stove, warping causes heat loss. On a gas stove, the pan rocks on the grate and the oil always runs to the same edge; one side of the food browns while the other steams. The effect is more pronounced on a glass-ceramic or induction cooktop because heat transfers through contact. If the base does not sit flush against the surface, an induction cooktop may not recognize the pan at all, or may heat it only through the ring it touches; the user blames the cooktop. A rocking pan is also a safety issue: a full pan can turn when pushed.
The cause is almost always a sudden temperature change. Putting a hot pan into cold water or setting it on a wet counter while hot makes the bottom and top contract at different rates; the metal responds to this stress with a permanent bend. The second cause is heating the pan empty over high heat for a long time. The third is using a burner much wider or narrower than the pan’s base; when heat is concentrated in a narrow ring, the metal expands differently around that ring. Thin aluminum and single-layer steel bases warp most easily.
The honest answer to whether it can be fixed is no, for most pans. Warping leaves permanent stress in the metal’s internal structure; hammering the base may flatten one spot while lifting another, and it can also crack the coating on a coated pan. A thick, multi-layer base can be corrected only under a press, which is not a home repair. Cast iron almost never warps; at that thickness, the metal cracks instead if cooled suddenly. Enamel-coated cast iron behaves the same way.
The decision depends on how you use the pan. A slightly warped pan can still work on a gas stove; it can cook a sauce or eggs, and it may not cause much trouble. You cannot use the same pan on a glass-ceramic or induction cooktop because its rocking base can scratch the surface and will not heat evenly. Protect a new pan by letting it cool after removing it from the stove, not setting it on a wet counter, not leaving it empty over high heat, and using it on a burner that matches the size of its base.