Should spaces be used between "" and numbers or letters?

The AMA Manual of Style says:

Thin spaces should be used before and after the following mathematical symbols: ±, =, <, >, ≤, ≥, +, −, ÷, ×, ·, ≈, ∼, ∩, ∫, Π, Σ, and |.

a ± b a = b a + b a − b a ÷ b a × b a · b a > b a < b

Symbols are set close to numbers, superscripts and subscripts, and parentheses, brackets, and braces.

(Highlight mine)

However, this is only one (albeit popular) style guide. Check with the journal/platform/whatever you want to publish in/on what their style guide says.

I have not found a similar statement in the Wikipedia Style Guide, but they consistently also use spaces around (on both sides of) those symbols (with no regard as to what either side is, it may be a number, letter, function or else).

To supplement the AMA's recommendations (noted in Polygnome's answer), I offer the following style guide recommendations.

From The Chicago Manual of Style, sixteenth edition (2010):

12.15 Basic spacing in mathematics. Mathematics isn't simply read left to right in a machine-like manner, and one should be able to see the parts of an equation if it is properly set. Good mathematical spacing helps to indicate grouping: things that are more closely related should be set more tightly than things that are less closely related. Such spacing will vary according to the elements being set. In simple expressions, however, absolute spacing may be called for. Signs for binary operations (i.e., conjunctions); symbols of integration, summation, or union; and signs for binary relations (i.e., verbs) are preceded and followed by medium spaces:

[Relevant example:] xⁿ + yⁿ = zⁿ

From The Oxford Guide to Style (2002):

12.6.2 Symbols Operational signs are of two types: those representing a verb (= ≈ ≠ ≥) and those representing a conjunction (+ – ∨ ×). All operational signs take a normal interword space of the line on either side ; they are not printed close up to the letters or numerals on either side of them.

From Words into Type, third edition (1974):

Spacing. Signs—plus, minus, equality, arrow—are often hair-spaced or thin-spaced, but they may be set closed with accompanying numerals or symbols. (An em dash should not be used for a minus sign.) It may be advisable to send the compositor a sample showing the amount of spacing preferred, because some compositors tend to use more than necessary.

[Relevant example:] x + 3y – z = O

All three of these reference works support at least some degree of spacing on either side of operational signs in equations, although Words into Type, which was published near the end of the era of hand-compositing, seems less inclined than Chicago or Oxford to endorse a uniform approach—and even indicates that a closed-up treatment can be acceptable.