If by interim goals you mean goals along the way, short of the ultimate goal, then such often are called milestones. Wiktionary shows two senses either directly or figuratively applicable:
A stone milepost (or by extension in other materials), one of a series of numbered markers placed along a road at regular intervals, typically at the side of the road or in a median.
An important event in a person's life or career, in the history of a nation, in the life of some project etc.
Also consider the terms waymark ("A sign or symbol marked in a prominent position in an off-road location to show the track of a footpath or route") and benchmark ("A standard by which something is evaluated or measured") and synonyms including landmark and signpost.
The terminology mentioned above is less applicable in a mathematical context. There, consider terms such as lemma ("A proposition proved or accepted for immediate use in the proof of some other proposition"), or for arithmetic, subtotal.
The process of setting goals is called planning or might be referred to as scoping.