Primes, weeds, and military precision

Here’s a quote from Don Zagier that I found in Larry Rolen’s lecture notes on modular forms.

There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision.

Emphasis added.

One thought on “Primes, weeds, and military precision

  1. Hi John,
    thks for the article about “primes, weeds and military precision”.
    Fyi, an article in Quanta Magazine, sept. 21, 2023 by Jordana Cepelewitz, ” Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?” gives also an unforgettable imprint on the subject.
    Nice sunny autumn weather with lovely colours, enjoy the WE.


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