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There is no largest prime number — and the proof is about 2,300 years old.
Euclid showed that if you multiply any list of primes together and add one, the result has a prime factor that is not on your list. So the primes never end.
Why it matters: Large primes now help keep online banking secure through encryption.
Elements — Euclid (c. 300 BCE)
Book IX, Proposition 20
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Zero is a number — and someone had to write down its rules.
In 628 CE the astronomer Brahmagupta gave rules for calculating with zero, such as a number minus itself is zero. These numerals later reached Europe through Arab scholars.
Why it matters: Our place-value number system, and all digital computing, depends on zero.
Brahmasphutasiddhanta — Brahmagupta (628)
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The words "algebra" and "algorithm" both come from one Baghdad scholar.
Around 820 CE, al-Khwarizmi wrote a book on solving equations by al-jabr (restoring) and balancing. Algebra is named after it, and "algorithm" comes from his own name.
Why it matters: Every computer program is an algorithm — a step-by-step method like the ones he wrote down.
The Compendious Book on Calculation by Completion and Balancing — Muhammad ibn Musa al-Khwarizmi (c. 820)
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