REFERRING to the review of Hilbert's “Grundlagen der Geometric,” on p. 394 of No. 2066 of NATURE (June 3), may I point out that the commutative law of addition can be proved without the help of any ...

NEITHER Dr. Hilbert nor the reviewer make any suggestion that the commutative law of addition is best proved as a deduction from the laws of multiplication. But the laws of multiplication are so often ...

A new proof illuminates the hidden patterns that emerge when addition becomes impossible. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward ...