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1Oct 8, '23In the heart of World War II, as the Nazis took control of Copenhagen, a peculiar situation took place at the Institute of Theoretical Physics, led by physicist Niels Bohr. Two Nob41.4×8.7M21k2k2.4k
2Sep 30, '24MIT Entrance Examination for 1869-187031.9×6.7M45k3.6k13k
3Oct 21, '242¹³⁶²⁷⁹⁸⁴¹−1, discovered today, is the largest known prime. It's a Mersenne prime (2ᵖ-1), which are easier to find. It took nearly 6 years for the GIMPS software to find it after t24.2×5.1M33k5k3.7k
4Jan 12, '23How do Maxwell's equations predict that the speed of light is constant20×4.2M14k1.5k1.1k
5Jan 1, '25Happy New Year! 🎉 2025 will be the only square year (45²) in many of our lifetimes.17.3×3.6M62k6.7k3.5k
6Dec 25, '22Newton was born 380 years ago on Christmas Day. His 3 laws laid the foundation for classical mechanics.16.5×3.5M11k1.1k298
7Aug 13, '23In 2000, Faber and Faber offered a $1,000,000 prize to anyone who proved Goldbach's conjecture: every integer greater than 5 can be written as the sum of three primes (21=11+7+3). 16.5×3.5M9.7k9212k
8Jul 23, '25Ramanujan said that he received his formulas from God12.1×2.5M26k2.2k3.7k
9Jan 7, '19Here's a useful counterintuitive fact: one 18 inch pizza has more 'pizza' than two 12 inch pizzas10.5×059k25k1.5k
10Nov 5, '25Andrew Wiles on the morning he discovered how to fix his proof of Fermat's Last Theorem9.5×2M12k1.5k3.4k
11Jan 14, '23How many π digits do we need? 3.1415 ➡️ design the finest engines 3.1415926535 ➡️ obtain the circumference of the Earth within a fraction of an inch 3.141592653589793238462643383279.4×2M9.1k759428
12Aug 12, '23This is the last photo taken from the surface of Venus, 40 years ago. The Venera-14 lander reached the surface in 1982, lasting 52 minutes in Venus' temperature of 450°C (847°F).8.5×1.8M12k1.3k516
13Sep 3, '23On November 12, 1833, there was a meteor shower so intense that it was possible to see up to 100,000 meteors crossing the sky every hour. Many at the time believed it was the end o8.4×1.8M16k1.9k1.2k
14Aug 1, '25Mathematicians searched up to N = 10⁴⁰ for solutions to this equation and found only the original ones Ramanujan discovered: N = 3, 4, 5, 7, 15. It’s recently been proven - there a7.9×1.7M19k2.1k2.6k
15Jan 14, '23The following formula yields the correct decimal digits of π to 42 billion digits7.9×1.7M11k1.2k716
16Sep 13, '23The following formula yields the correct decimal digits of π to 42 billion digits6.9×1.4M9.1k867963
17Dec 19, '22Which is greater 1000¹⁰⁰¹ or 1001¹⁰⁰⁰?5.5×1.2M9.3k777635
18Jun 25, '23Prime Numbers in Polar Coordinates 5,000 (left) Prime Numbers and 50,000 (right) Prime Numbers plotted in polar coordinates.5.5×1.2M8.1k1k734
19Apr 7, '23In the fall of 1972, President Nixon announced that "the rate of increase of inflation was decreasing". Probably the first time a sitting president used the 3rd derivative to incre5.3×1.1M10k1k481
20Aug 20, '18Cancellation of Momentum: A ball is fired at 50 mph, out of a cannon from a truck that is going at 50 mph. The two momenta cancel each other and in the Earth reference frame the ba5.2×037k10k401
21Dec 13, '23Ramanujan's most beautiful formula5.1×1.1M8.8k8651k
22Dec 24, '23The length of the Christmas tree lights to wrap around the tree perfectly4.8×1000k12k1.6k1.4k
23Oct 18, '20From Ramanujan4.4×040k4.3k817
24Nov 9, '19A demonstration of the conservation of angular momentum using a Hoberman sphere. Angular momentum depends on the rotational velocity of an object, and on its rotational inertia. Wh4.3×035k6.3k924
25Aug 2, '25In the fall of 1972, President Nixon announced that "the rate of increase of inflation was decreasing". Probably the first time a sitting president used the 3rd derivative to incre4.3×901k23k1.3k2.2k
26Nov 20, '19Start with 82 and go backwards to 1 8281807978777675747372717069686 7666564636261605958575655545352 5150494847464544434241403938373 6353433323130292827262524232221 20191817161514133.3×029k4.1k411
27Jun 19, '23A Proof withouth words (a+b)² =a² + 2ab + b² ⬛️3.2×671k7.9k1.2k585
28Dec 26, '20The time period of a pendulum with infinite length is 84.6 minutes.2.9×027k2.4k1k
29Dec 24, '24The length of the Christmas tree lights to wrap around the tree perfectly2.9×600k10k1.4k1.7k
30Feb 6, '22In linguistics, Escher sentences are sentences which initially seem acceptable but upon further reflection have no well-formed meaning.2.8×023k2.9k1.6k
31Jan 11, '20A visual proof why 1+3+5+...+(2n-1)=n² ⚪⚫⚪⚫⚪⚫ ⚫⚫⚪⚫⚪⚫ ⚪⚪⚪⚫⚪⚫ ⚫⚫⚫⚫⚪⚫ ⚪⚪⚪⚪⚪⚫ ⚫⚫⚫⚫⚫⚫2.7×022k4k598
32Jun 30, '19Here's a demonstration that concave mirrors invert images pass their focal point more here:2.6×022k3.7k403
33Nov 8, '19Here's an interesting approximation for the number 82.5×023k2.9k328
34Jan 20, '25In the fall of 1972, President Nixon announced that "the rate of increase of inflation was decreasing". Probably the first time a sitting president used the 3rd derivative to incre2.5×530k15k1.2k1.5k
35Nov 14, '21List of people that have walked on the Moon: Neil Armstrong 🇺🇸🪦 Buzz Aldrin 🇺🇸 91 yo Pete Conrad 🇺🇸🪦 Alan Bean 🇺🇸🪦 Alan Shepard 🇺🇸🪦 Edgar Mitchell 🇺🇸🪦 David Scott 2.5×023k1.8k433
36Feb 6, '20How to derive Electromagnetic Waves from Maxwell's eq. in 1 Tweet 1)∇.B = 0 2)∇.E = 0 3)∇xE = -∂B/∂t 4)∇xB = μ₀ε₀∂E/∂t Using ∇x(∇xA) = ∇(∇⋅A)-∇²A for E & B ∂²E/∂t² = 1/μ₀ε₀∇²E 2.4×018k3.3k697
37Aug 14, '19Here's why the sun turns red near the sunset on Earth2.3×016k4k666
38Apr 1, '18FUN FACT J.J. Thomson won the Nobel in Physics in 1906 when he showed electrons were particles. His son G. P. Thomson won the Nobel Prize in Physics in 1937 for showing that electr2.1×015k4.3k74
39Jan 2, '20Beautiful shapes created by simple harmonic motion 🧐2.1×015k3.6k750
40Mar 5, '17A visualization of chaos: 41 triple pendulums with very slightly different initial conditions2.0×010k5.9k25
41Jun 22, '19In 1683 the Swiss mathematician Jacob Bernoulli found the first approximation of the mathematical constant e while studying continuous compound interest. e is one of the most impor1.9×017k2.4k249
42Dec 17, '17The Geneva Drive: a mechanism that translates a continuous rotation movement into intermittent discrete motion. (used in mechanical watches, movie projectors, banknote counting mac1.9×013k4.5k10
43Sep 11, '19The Tsiolkovsky Rocket Equation derived by the Russian schoolteacher Tsiolkovsky in 1898 describes how rockets move in space - expelling part of its mass. "Mankind will not forever1.8×015k2.5k283
44Nov 23, '19Universe ↑ ↑ 10²⁴ ↑ ↑ 🌌 Milky Way ↑ ↑ 10¹⁸ ↑ ↑ 10¹⁵ ↑ ↑ 💫 Solar System ↑ ↑ ☀️ Sun ↑ 🌍 Earth 10⁶ ↑ ↑ 🏔 Mountains ↑ 🐋 Whales 👫 Humans ↓ 🐞 Ladybug 10⁻³ ↓ ↓ 10⁻⁶ 🦠 Virus ↓ 🧬 D1.8×013k3.7k390
45May 8, '19These diagrams show the paths traced by Mercury, Venus, Mars, Jupiter and Saturn as seen from Earth.1.8×012k3.5k376
46Jun 2, '22The first time Albert Einstein wrote down E=mc²1.8×016k1.8k419
47May 2, '20Here's a great photo of the ISS by J. Mccarthy. The reason why the ISS keeps its relative size against both the Sun and the Moon is due to a remarkable coincidence: the diameter of1.8×014k2.7k293
48Jun 15, '19Mars' Olympus Mons, the tallest known volcano in the solar system, has such a gradual slope that someone standing at the base couldn't see the summit because it's beyond the horizo1.7×013k3.2k172
49Dec 25, '21Newton was born 378 years ago on Christmas Day. His 3 laws laid the foundation for classical mechanics.1.7×016k1.8k261
50Dec 25, '19Newton was born 377 years ago on Christmas Day. His 3 laws laid the foundation for classical mechanics.1.7×014k2.7k139
51Feb 10, '20Highest points on Earth 1 - Mount Everest🇳🇵: Highest altitude above sea level 2 - Mauna Kea 🇺🇸: Highest altitude from base to summit 3 - Mount Chimborazo 🇪🇨: Highest distance1.7×013k2.9k394
52Apr 22, '21A proof without words that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1 🤓1.6×014k2k466
53Apr 14, '21Brute-forcing a 256-bit key would require a minimum energy of 590000000000000000000 Suns during 1 year!1.6×014k1.6k501
54Dec 9, '17The fifth hyperfactorial: 5⁵ × 4⁴ × 3³ × 2² × 1¹ = 86400000 milliseconds is exactly 1 day!1.6×09.6k4k10
55Aug 27, '19The infinite gift 🎁is an interesting object where the side of the nth box is 1/√n. As n→+∞, the gift has infinite surface area and length but finite volume!1.5×011k2.5k395
56Apr 21, '22Although Georg Ohm discovered one of the most fundamental laws in the field of electricity, his work was ignored by his colleagues, and he lived in poverty for much of his life.1.5×014k1.3k250
57Dec 5, '19These diagrams show the paths traced by Mercury, Venus, Mars, Jupiter and Saturn as seen from Earth.1.5×011k2.8k369
58Jan 4, '20It was only 282 years ago that Euler presented in his textbooks the exact formula for the volume of a sphere1.5×013k2k144
59Mar 1, '19Geneva Drive: A mechanism that converts continuous motion into discrete motion. The name was derived from its usage in mechanical watches which were popularized in Geneva. This mec1.5×011k2.7k348
60Apr 5, '20FUN FACT J.J. Thomson won the Nobel in Physics in 1906 when he showed electrons were particles. His son G. P. Thomson won the Nobel Prize in Physics in 1937 for showing that electr1.5×011k2.6k209
61Jan 2, '18In 1982, 11,000 people planted 11,000 trees on an artificial mountain near Ylöjärvi, Finland forming a mathematical pattern based on the golden section. The project was conceived b1.4×09.4k3.4k7
62Apr 12, '21Marie Curie was exposed to such high doses of radiation that 100 years later her research notebooks need to be kept sealed in a lead-lined box. She is considered the mother of mode1.4×012k2.3k200
63Sep 21, '19In the fall of 1972, President Nixon announced that "the rate of increase of inflation was decreasing". Probably the first time a sitting president used the 3rd derivative to incre1.4×011k2.3k224
64Dec 28, '20FUN FACT J.J. Thomson won the Nobel in Physics in 1906 when he showed electrons were particles. His son G. P. Thomson won the Nobel Prize in Physics in 1937 for showing that electr1.4×011k2.1k283
65Jul 14, '19John Wallis devised this beautiful formula for π in 1655. It is the infinite product of even numbers squared divided by their two adjacent odd numbers.1.4×011k2.2k326
66Apr 3, '21All the basic trigonometric identities in one figure1.4×010k2k824
67Jun 22, '20Clever algorithm to find out whether or not 2 words are anagrams1.4×010k1.9k734
68Jun 11, '18All the following symbols and notations were introduced by Leohard Euler1.4×011k2.2k56
69Feb 29, '20"Chaos: When the present determines the future, but the approximate present does not approximately determine the future." Edward Lorenz1.4×09.7k2.6k369
70Sep 15, '18Individual dots moving along straight lines. 🧐1.3×09.1k2.8k165
71May 10, '20Here's why the circle has 360 degrees: around 2400 B.C., the ancient Sumerians noticed the Sun's annual path across the sky was ~ 360 days. In order to track the Sun's motion, they1.3×011k1.8k237
72Mar 14, '19Happy π day! π=3️⃣,1⃣4️⃣1592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117451.3×08.3k3.3k45
73Feb 24, '20Euler's identity displays a profound connection between fundamental numbers π, e (the base of natural logarithms), and i (the imaginary unit). It is considered one of the most beau1.3×010k1.9k298
74Jan 27, '18Area of the Circle1.3×08.2k3.1k42
75Aug 24, '19Viviani's Theorem: in an equilateral △, the sum of the distances from any interior point to the 3 sides is equal to the height of the △1.3×010k2.1k316
76Mar 9, '18Here is a visual proof of square binomial: (a+b)²= a²+2ab+b²1.3×08.1k3.2k70
77Apr 7, '21John Nash recommendation letter1.3×011k1.4k255
78Mar 14, '20Happy π day! 3.14141592653589 793238462643383 27 950 288 4 197 16 939 93 751 05 8 2097 49445 9230 7811.3×09.5k2.5k53
79Apr 22, '20Take the alphabet and do the following conversion: A = 1 B = 2 C = 3 ... Z = 26 Words are sums of the corresponding letter values. The word PRIME is prime.1.3×011k1.2k231
80Oct 14, '22Tupper's self-referential formula is a formula that visually represents itself when graphed at a specific location in the (x, y) plane.1.3×010k1.1k866
81Apr 15, '19Euler was born exactly 312 years ago. All the following symbols and notations were introduced by Euler.1.3×09k2.5k81
82Mar 31, '19René Descartes was born exactly 423 years ago. He is responsible for proposing the use of letters at the end of the alphabet for unknowns and letters at the beginning for known qua1.2×09.7k2.1k87
83Apr 15, '18Today is the 311th year since the birth of Leonhard Euler. Euler published more than 500 books and papers during his lifetime, while 400 more appeared after his death.1.2×09k2.4k41
84Apr 12, '20"You know, people think mathematics is complicated. Mathematics is the simple bit. It's the stuff we can understand. It's cats that are complicated". RIP John Conway1.2×09.3k2.1k164
85Feb 3, '18Comparison between 5,000 and 50,000 prime numbers plotted in polar coordinates1.2×09.2k2.3k10
86Nov 29, '20Euler's number "e" In 1683 the Swiss mathematician Jacob Bernoulli found the first approximation of the mathematical constant e while studying continuous compound interest. e is on1.2×010k1.4k325
87Dec 31, '19Here's a special countdown for 2020. Happy New Year!1.2×08.4k2.5k116
88Apr 24, '21Clever algorithm to find out whether or not 2 words are anagrams1.2×09.2k1.4k660
89May 4, '18Motion produced by fifteen uncoupled pendulums of different lengths. Order and chaos visualized. 😮 Learn more here:1.1×07.9k2.2k82
90Sep 2, '19Here's how to represent the multiplication of two numbers on the real line1.1×08.5k1.6k395
91Jul 21, '19A visual proof that 1/4 + 1/4² + 1/4³ + ... = 1/3 ⚪⚪⚪⚪⚪⚪⚪⚪ ⚪⚫⚪⚪⚪⚪⚪⚪ ⚪⚪⚫⚫⚪⚪⚪⚪ ⚪⚪⚫⚫⚪⚪⚪⚪ ⚪⚪⚪⚪⚫⚫⚫⚫ ⚪⚪⚪⚪⚫⚫⚫⚫ ⚪⚪⚪⚪⚫⚫⚫⚫ ⚪⚪⚪⚪⚫⚫⚫⚫1.1×08.4k1.8k242
92Jun 17, '18Here's a quick method to calculate the square root of a number (√y) by hand1.1×07.9k1.9k272
93Feb 24, '21Start with 82 and go backwards to 1 8281807978777675747372717069686 7666564636261605958575655545352 5150494847464544434241403938373 6353433323130292827262524232221 20191817161514131.1×09.4k1.1k195
94Apr 25, '21This is one of the biggest numbers you can find in a physics paper. It's the expected distance one would travel before encountering another visible-universe-sized region of space w1.0×08.5k1.3k323
95Sep 19, '19It was only 282 years ago that Euler presented in his textbooks the exact formula for the volume of a sphere1.0×08.5k1.5k124
96Jul 18, '20"There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery" 1.0×08.4k1.4k304
97Dec 4, '19Here is how you can fold a piece of paper into an ellipse: 1) Cut a circle from a regular piece of paper 2) Draw a dot inside the paper circle 3) Fold it so that the circumference 1.0×07.8k1.5k316
98Jan 10, '18Here's a cool way to paper-fold an ellipse: 1) Cut a circle and fold it so that the circumference falls on a fixed point inside 2) Repeat this procedure using random folds1.0×07.4k1.9k14
99Nov 5, '22The French mathematician André Weil was imprisoned for failure to report for duty in 1940. While in jail for six months at Rouen, he proved the Riemann hypothesis for curves over f1.0×08.5k946345
100Sep 11, '21"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?" - David Hilbert0.9×08.2k876298
101Sep 28, '18We launched Margins A free online repository where you can 📝 Save and annotate your papers 🗣 Share papers and collaborate with anyone 💻 Annotate using LaTeX, Code, Markdown and 0.9×04.7k1.2k1.1k

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