Fermat's Library @fermatslibrary

A platform for illuminating academic papers. We annotate and share a paper every week. Save, annotate and share papers with anyone: https://t.co/0o2Pls3jmo fermatslibrary.com Joined September 2015

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Fermat's Library @fermatslibrary

2 days ago

The integral symbol ∫ introduced in 1675 was based on the ſ (long S) character, and was chosen because Leibniz thought of it as an ∞ sum

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Fermat's Library @fermatslibrary

2 days ago

The human eye can detect flashes of light as minute as a single photon

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Fermat's Library @fermatslibrary

3 days ago

On this day in 1928, Alexander Fleming noticed a mold growing on one of his petri dishes at St. Mary’s Hospital in London. This contaminated petri dish led to the discovery of penicillin - the world's first antibiotic that has saved millions of lives.

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Fermat's Library @fermatslibrary

4 days ago

Here's a good mnemonic to convert Miles to Kilometers using Fibonacci (0,1,1,2,3,5,8,13...) numbers: 3 mi ≈ 5 km 5 mi ≈ 8 km 8 mi ≈ 13 km The ratio between 1 mi and 1 km is very close to the Golden Ratio ≈1.61

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Fermat's Library @fermatslibrary

5 days ago

Joseph-Louis Proust was born 271 years ago today! His law of definite proportions was a foundational principle for modern chemistry. The idea that a given compound always contains the same elements in the same mass ratio helped establish chemistry as a quantitative science rather…

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6 days ago

Circular primes are numbers where every rotation of their digits also produces a prime number. For example, 193939 is a circular prime because all of its digit rotations are also prime: 193939 → 391939 → 939193 → 391939 → 939391 → 193939 All six of these rotations are…

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a week ago

FUN FACT Astronauts can grow up to 2 inches taller when they’re in space. In the absence of gravity vertebrae in their spines get a chance to spread out and expand. This expansion leads to the increase in height. The height increase is not a permanent! Once astronauts return…

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Fermat's Library @fermatslibrary

a week ago

Today we're sharing one of the most cited papers in psychology: "The Magical Number Seven, Plus or Minus Two". In his 1956 paper G.A. Miller showed that our short-term memory can only handle about 7 "chunks" of information at once. This limit shaped how things like phone numbers…

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a week ago

Principia Mathematica takes over 360 pages to prove 1+1=2. It's not because the authors were unsure of the answer, but because they were trying to prove that all of mathematics could be built from the ground up using nothing but pure logic.

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a week ago

Water is densest at 4°C. This property is the reason why lakes freeze from the top down. 💧 water at 4°C is denser than water at both lower and higher temperatures ❄️ as water cools from room temperature toward 4°C, it becomes denser and sinks but as it cools further from 4°C…

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2 weeks ago

Here's a surprising appearance of e: the limit when n approaches infinity of the nth root of the least common multiple of 1,2,…,n = e

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2 weeks ago

Michael Faraday was born 234 years ago today 🎉. In 1846, Faraday gave a lecture suggesting that lines of force and their vibrations produced light. Maxwell later stated that this lecture marked the beginning of Electromagnetism. These are the original notes of that lecture.

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2 weeks ago

FUN FACT The chemical element Berkelium takes its name from the lab it was discovered in at UC Berkeley which is named after the city of Berkeley which is named after philosopher George Berkeley who argued matter has no mind-independent existence.

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2 weeks ago

WWII story: When Nazis invaded Copenhagen, chemist George de Hevesy dissolved two Nobel Prize gold medals in acid rather than let them be stolen. The orange solution sat unnoticed on a lab shelf throughout the occupation. After the war, he recovered the gold & the medals were…

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Fermat's Library @fermatslibrary

2 weeks ago

Happy Pythagorean Triple Square Day! Today’s date is made of 3 perfect squares and they form a Pythagorean triple: 3² + 4² = 5² This only happens once a century.

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2 weeks ago

Penrose Stairs A square staircase that keeps going up forever but never actually takes you anywhere. An impossible figure where every step seems normal until you notice you're back where you started.

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2 weeks ago

St Mary’s Cathedral in SF is shaped like a hyperbolic paraboloid - a surface with negative curvature everywhere. Cut it vertically: you see a parabola. Cut it horizontally: you see a hyperbola. Geometry turned into architecture!

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2 weeks ago

A pi-prime is a prime number that appears in the decimal expansion of π. The largest known pi-prime was discovered on May 29, 2016, by A. Bondrescu and contains 613,373 digits.