"A more modern attempt to explain the fruitfulness of mathematical reasoning is that of Poincaré, who finds it all due to the principle of mathematical induction. This principle of mathematical induction is undoubtedly of wide application, though there are many regions even in arithmetic where it is difficult to see its application, e.g., the science of prime numbers, a science dealing entirely with non-recurring individuals. But the important thing to observe is that this principle of mathematical induction is entirely different from the induction that prevails in the physical sciences."