Looking for a word that expresses "Area of Interest", "Sphere of Interest" basically a word that expresses everything a person may be interested in. Google translate says "Rem" means interest, but translating "rem" back to English says "business". Is this correct?
Let me comment on the translation offered by Google Translate. Rem is an accusative form of res. Unless there is more context, I would recommend using the nominative.
The noun res is perhaps the broadest noun in Latin. It can be reasonably translated as "interest" or "business" in a suitable context, but the basic translation is often given as "thing". I might even give the rule of thumb that when you need a Latin noun and don't know which one would be appropriate, use res.
See a dictionary entry for res to get an impression of its breadth. (There are a number of online Latin dictionaries to choose from.) These are the translations the linked entry gives: thing, object, being, matter, affair, event, fact, circumstance, occurrence, deed, condition, case, something, reality, truth, effects, substance, property, possessions, benefit, profit, advantage, interest, weal, cause, reason, ground, account, business, case, lawsuit, cause, suit, battle, campaign, military operation, act, state, republic, civil affairs, administration, power, political changes, revolution.
Here is an example where res would stand for "area of interest":
– Mea interest lingua Latina. Et tua?
(I am interested in Latin. How about you?)
– Res meae sunt historia et musica.
(My areas of interest are history and music.)
The bottom line is that res (which looks the same in singular and plural) can be used for "area of interest" and is idiomatic, but on its own it would not be understood as "area of interest" without proper context. You could say res meae to mean "my area of interest" just like the literal translation "my things" can mean it. The Latin res is more formal than the English "thing(s)". If you want something unambiguous, you will need something else.
It might also be worthwhile to look at this question about the meaning of rem.
One option could be
Materia is "subject, argument, course of thought, topic", whereas curiositatis is the genitive of curiositas, curiosity. So, the above would be "topic of curiosity". Res curiositatis is probably also fine, but res seems to be much broader than materia. Finally, area, although a Latin word itself (and the origin of the English one, it seems), did not have the equivalent English meaning intended in the phrase.
Another possibility is studium, which would denote more keenly felt interest than a general word such as res – one's area of particular interest, one's pet interest, or one's passion. Definition 3 in the Oxford Latin dictionary is:
That which forms the object of one's interest or energy, an aim or concern
For example, in book 14 of Ovid's Metamorphoses, orchard trees are Pomona's area of special interest:
rege sub hoc Pomona fuit, qua nulla Latinas
inter hamadryadas coluit sollertius hortos
nec fuit arborei studiosior altera fetus;
unde tenet nomen: non silvas illa nec amnes,
rus amat et ramos felicia poma ferentes;
nec iaculo gravis est, sed adunca dextera falce,
qua modo luxuriem premit et spatiantia passim
bracchia conpescit, fisso modo cortice virgam
inserit et sucos alieno praestat alumno;
nec sentire sitim patitur bibulaeque recurvas
radicis fibras labentibus inrigat undis.
hic amor, hoc studium, Veneris quoque nulla cupido est;
vim tamen agrestum metuens pomaria claudit
intus et accessus prohibet refugitque viriles.
Pomona lived in good king Proca's reign
And none of all the Latin woodland-nymphs
Was cleverer than she in garden lore
Nor keener in the care of orchard trees.
Thence came her name. For in her heart she loved
Not woods nor rivers, but a plot of ground
And boughs of smiling apples all around.
She had no spear, only a pruning-knife
To check too greedy growth and trim to shape
The spreading shoots, or slit the bark and set
A slip for sap to feed a foreign stock.
She never let them thirst; her trickling rills
Watered the twisting fibres of their roots.
This was her love, her passion. Venus' charms
Meant nothing; yet for fear of rustic force
She walled her orchard in to keep away
The sex she shunned.
(Trans. A.D. Melville)
Charles Burnett De Eodem et Diverso introduction, writes,
The contrast between res, the perceptible realities with which Philocosmia deals, and verba, the mental concepts of Philosophia, runs through the whole work.
The five serving girls attending Philocosmia in Adelard are drawn from Boethius, III prose 2 Consolation:
Habes igitur ante oculos propositam fere formam felicitatis humane: opes, honores, potentiam, gloriam, voluptates,
...the epitome of human happiness: wealth, honours, power, fame, pleasures.
So if your interest is one of these, and why not? then the translation is res.
But if your interest has more in common with the seven attendants of Philosophia:
grammar, rhetoric [eloquence], dialectic; arithmetic, music, geometry, astronomy then choose (quotations from *De Eodem Et Diverso,' last three paragraphs)
artes, artium, artibus
studiosius singulis artibus animum applicavi.
I put my mind more intensely to the areas of interest one by one.
lectio, lectionis, lectione.
eum asserentem audivi, lectiones [scilicet disciplinares earumque labores] penitentiam non
I heard him insisting that the areas of interest [particularly the discipline and hard work] were not a matter of regret.