## Fermats Library

Buffer : Superscripts are a mathematical notation used to indicate powers or exponents was first introduced by René Descartes in 1637.

Bio **A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: fermatslibrary.com/librarian**

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Buffer : Superscripts are a mathematical notation used to indicate powers or exponents was first introduced by René Descartes in 1637.

Buffer : Michael Beeler and William Gosper noticed that there is at least one zero in the decimal expression of each power of 2 between 2⁸⁷ and 2²³⁰⁷³⁹⁰¹⁴

Buffer : Heres a popular math misconception: the product of the first N primes + 1 is not necessarily a prime itself

Buffer : J. E. Mills noted that many products and quotients of fundamental constants have values very close to the number 3 multiplied by a power of 10

Buffer : A mathematician is a machine for turning coffee into theorems - Paul Erdös

Buffer : Heres why the sun turns red near the sunset on Earth

Buffer : How can 2 teams excavate a tunnel from both ends and ensure they meet in the middle?

Eupalinos of Megara figured it out in the 6th century BC and built the Tunnel of Samos (over 1km long) in 8 years: fermatslibrary.com/s/the-tunnel-o…

A great paper for your summer ☀️reading list 📚

Buffer : Jeff Roulston has found the following numbers that can self-locate in the decimal digits of π. The digit 1 is found in position 1 in 3.1415, the string 16,470 starts in position 16,470!

Buffer : In 1675, Leibniz introduced the notation df/dx for the derivative and 95 years later Joseph Lagrange was the first person to use the notation f(x) for the first derivative.

Buffer : In 1997, the Texas banker Andrew Beal noticed that for any solution of Aˣ+Bʸ=Cᶻ he could find, A,B,and C had a common factor (e.g. 3⁶+18³=3⁸, 3 is a common factor). Theres currently a $1 million prize for a proof or counterexample of the Beal conjecture.

Buffer : Heres why the circle has 360 degrees: around 2400 B.C., the ancient Sumerians noticed the Suns annual path across the sky was ~ 360 days. In order to track the Suns motion, they decided to divide the circle in 360 degrees.

Buffer : If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. - John von Neumann

Buffer : A human is the geometric mean of the mass of a proton and the Sun

Buffer : Why are some things darker when wet?

Its an interesting question and you just need some basic knowledge about elementary optics to understand it. Learn more here: fermatslibrary.com/s/why-some-thi…

A great paper for your summer ☀️reading list 📚

Buffer : This is the largest number that cannot be represented as the sum of distinct cubes

Buffer : Heres an example of a function that grows faster than polynomials but slower than exponentials

Buffer : The 2nd Law of Thermodynamics states that the entropy - disorder - of a system will increase over time. The Universe is full of irreversible processes that continuously increase its total entropy thus tending to disorder rather than order.

Buffer : The average Gregorian year comes out to be 365.2425 days. That difference causes the Gregorian calendar to advance 1 day every 3333 years.

Buffer : Heres Riveras palindromic approximation for π

Buffer : Heres an interesting surprise: if you write down the digits of e you quickly find a 649 digit prime!