Rrerku

1. Programming language, after removing loss for you, reverses time (6)


2. Complex arithmetic begins, Turing tests start beforehand (7)


3. Quadruply male doctor Einstein, familiarly (11)


4. Lie on a 100/100 imaginary item (9)


5. Between 3.14 and 2.718 is originally risky mathematics (5)


6. Arctan maps every other arccot into an embankment, too (8)


7. 
   Heated rant with part of Ulam spiral (7)


8. Curse without Germain’s initial initial (4)

Solve these cryptic clues (no definitions), then find the answer to this question: what role does math play in our daily lives?

^{Remember: when in doubt, always consult OEIS!}

No time to finish, but a partial...

2. Complex arithmetic begins, Turing tests start beforehand (7)

C(omplex) + A(rithmetics) + T(ests) + ALAN (Turing) = CATALAN

3. Quadruply male doctor Einstein, familiarly (11)

TETRA (quadruply) + HE + DR + AL(bert) = TETRAHEDRAL

4. Lie on a 100/100 imaginary item (9)

FIB (lie) ON A C/C (100/100) I (imaginary item) = FIBONACCI

5. Between 3.14 and 2.718 is originally risky mathematics (5)

PI (3.14) + E (2.178) with R(isky) M(athematics) inside = PRIME

Adding to answer by @jafe

1. Programming language, after removing loss for you, reverses time (6)

SQ L (replaced by) U (you) + ARE (era reversed) = SQUARE

Partial answer

(Omitting clues that other people have also solved.)

Arctan maps every other arccot into an embankment, too (8)

I haven't solved this one, but I'm fairly sure about one tricky element of it:

I think "every other arccot" -> RCT (alternate letters) and the idea is to replace ("map") the RCT inside "arctan" with something else. However, I've failed to find a good something else.

Heated rant with part of Ulam spiral (7)

NATURAL. (Anagram of RANT ULA).

Curse without Germain’s initial initial (4)

PELL. (SPELL without the initial letter Sophie Germain's first, i.e., initial, name.)

So, what's next? Well,

all the answers are names of particular sets/sequences of integers, and the question directs us to OEIS. So here's a little table, which has not yet been of much use to me:

A000290 squAre Programming language, after removing loss for you, reverses time (6)
A000108 cataLan Complex arithmetic begins, Turing tests start beforehand (7)
A000292 tetrAhedral Quadruply male doctor Einstein, familiarly (11)
A000045 fibonaCci Lie on a 100/100 imaginary item (9)
A000040 priMe Between 3.14 and 2.718 is originally risky mathematics (5)
 Arctan maps every other arccot into an embankment, too (8)
A000027 Natural Heated rant with part of Ulam spiral (7)
A000129 pell Curse without Germain’s initial initial (4)

The capital letters in the answers are in positions corresponding to the position in the clue of the italicized word; that doesn't seem like it leads anywhere. I also considered using digits of the OEIS indices to index into the italicize words (ignoring out-of-range ones), which yields E T ALA M I 8 [?] E IN, which also seems unpromising.

... so right now I'm stuck.