Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
John W. Tukey, The Future of Data AnalysisWhat Would Count as Proof?
The evidence depends on the question being asked
Development of Move 1
Reasoning, in the extended sense in which I use the term, and in which it is synonymous with Inference, is popularly said to be of two kinds: reasoning from particulars to generals, and reasoning from generals to particulars; the former being called Induction, the latter Ratiocination or Syllogism.
John Stuart Mill, A System of Logic, Ratiocinative and InductiveDevelopment of Move 2
For deductive proof to succeed, the axioms, inference rules, and machinery to sequence steps to a conclusion must already exist.
Yet, to reach true statements for which that machine doesn't yet exist, induction remains the only path. This maps directly to how formal discovery actually works: mathematics is built deductively, but it is discovered inductively. Srinivasa Ramanujan recognized deep numerical patterns through inductive intuition. The deductive machinery to prove them had to be invented later.
Moreover, some true statements simply aren't reachable by a sequence of inference steps. In 1931, Kurt Gödel invalidated the assumption that formal deduction could eventually capture all mathematical truth, showing that truth and provability are not the same. As Gödel later put it, in a note added in 1963:
It can be proved rigorously that in every consistent formal system that contains a certain amount of finitary number theory there exist undecidable arithmetic propositions…
Because formal systems are bounded by their initial parameters and subject to incompleteness, inductive reasoning is not only a preliminary heuristic. It is a structural necessity for advancing knowledge and identifying valid propositions that reside strictly beyond the operational limits of deductive logic.