Tired-Taiku (TT) is really more of an approach than a definitive answer. Teiku is actually roshei tevos for "Tishby Yetaretz Kushyas Ushailos" (Elijah will answer all questions). I have heard various discussions about what that means exactly, but in a contemporary setting, when someone says "Taiku is the answer", they generally mean one of the following:
- We have some reasonable answers, but no way of knowing which is correct, so lets just leave it.
- Any hope of finding any answer seems remote, so lets just leave it.
- I don't know enough about this topic, so lets just leave it.
- The obvious answer is clear, but we really don't like it, so lets just leave it.
- I can't be bothered to discuss this anymore, so lets just leave it.
- I don't want to to discuss this at all, so lets just leave it.
- This is not worth discussing, so lets just leave it.
- For some unrelated reason, I don't wish to answer right now, so lets just leave it.
For example, your average yeshivah bochur, after only a few moments on a science vs torah discussion will lose patience and say "Why do you bother with all this stuff anyway ! Just go learn a daf Gemoroh and forget about it, It has no practical halachic ramifications anyway. Lets just say taiku !". (True Story). Probably a 5 or 7 above.
When Rav Mattisyahu Solomon says "Taiku is an answer", he probably means to say that "I don't really know enough about it, the science seems pretty strong but I cannot possibly take Torah non literally, so lets not go there" i.e. Number 2 above. He may also mean 3 above, or maybe 6.
So is Tired-Taiku the correct answer to questions of Science & Torah ?
Taiku V8 !