Explore the fascinating world of algebraic number theory in this hour-long conference talk. Delve into the intriguing analogy between numbers and shapes, discovering how it serves as a wellspring of inspiration for modern mathematical research. Examine the parallel between the law of quadratic reciprocity and the symmetry of linking numbers in knot theory. Learn how this analogy contributed to resolving Tate's 1966 conjecture on higher-dimensional linking numbers for varieties over finite fields. Gain insights into ongoing research, including a new approach to the motivic Steenrod algebra using prismatic cohomology, presented as joint work with Shachar Carmeli.