The Sonnet
"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence."
Stanford mathematician Keith Devlin wrote these words about the equation to the left in a 2002 essay called "The Most Beautiful Equation." But why is Euler's formula so breath-taking? And what does it even mean?
First, the letter "e" represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. In math, the number exhibits some very surprising properties, such as — to use math terminology — being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant "e" pervades math, appearing seemingly from nowhere in a vast number of important equations.
Next, "i" represents the so-called "imaginary number": the square root of negative 1. It is thus called because, in reality, there is no number which can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter "i" is therefore used as a sort of stand-in to mark places where this was done.
Pi, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi So Special?]
Putting it all together, the constant "e" raised to the power of the imaginary "i" multiplied by pi equals -1. And, as seen in Euler's equation, adding 1 to that gives 0. It seems almost unbelievable that all these strange numbers — and even one that isn't real — would combine so simply. But it's a proven fact.
"Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence."
Stanford mathematician Keith Devlin wrote these words about the equation to the left in a 2002 essay called "The Most Beautiful Equation." But why is Euler's formula so breath-taking? And what does it even mean?
First, the letter "e" represents an irrational number (with unending digits) that begins 2.71828... Discovered in the context of continuously compounded interest, it governs the rate of exponential growth, from that of insect populations to the accumulation of interest to radioactive decay. In math, the number exhibits some very surprising properties, such as — to use math terminology — being equal to the sum of the inverse of all factorials from 0 to infinity. Indeed, the constant "e" pervades math, appearing seemingly from nowhere in a vast number of important equations.
Next, "i" represents the so-called "imaginary number": the square root of negative 1. It is thus called because, in reality, there is no number which can be multiplied by itself to produce a negative number (and so negative numbers have no real square roots). But in math, there are many situations where one is forced to take the square root of a negative. The letter "i" is therefore used as a sort of stand-in to mark places where this was done.
Pi, the ratio of a circle's circumference to its diameter, is one of the best-loved and most interesting numbers in math. Like "e," it seems to suddenly arise in a huge number of math and physics formulas. What Makes Pi So Special?]
Putting it all together, the constant "e" raised to the power of the imaginary "i" multiplied by pi equals -1. And, as seen in Euler's equation, adding 1 to that gives 0. It seems almost unbelievable that all these strange numbers — and even one that isn't real — would combine so simply. But it's a proven fact.
The 4-Color Theorem
The 4-Color Theorem was first discovered in 1852 by a man named Francis Guthrie, who at the time was trying to color in a map of all the counties of England (this was before the internet was invented, there wasn’t a lot to do). He discovered something interesting—he only needed a maximum of four colors to ensure that no counties that shared a border were colored the same. Guthrie wondered whether or not this was true of any map, and the question became a mathematical curiosity that went unsolved for years.In 1976 (over a century later), this problem was finally solved by Kenneth Appel and Wolfgang Haken. The proof they found was quite complex and relied in part on a computer, but it states that in any political map (say of the States) only four colors are needed to color each individual State so that no States of the same color are ever in contact.@maths_sorcerer
The 4-Color Theorem was first discovered in 1852 by a man named Francis Guthrie, who at the time was trying to color in a map of all the counties of England (this was before the internet was invented, there wasn’t a lot to do). He discovered something interesting—he only needed a maximum of four colors to ensure that no counties that shared a border were colored the same. Guthrie wondered whether or not this was true of any map, and the question became a mathematical curiosity that went unsolved for years.In 1976 (over a century later), this problem was finally solved by Kenneth Appel and Wolfgang Haken. The proof they found was quite complex and relied in part on a computer, but it states that in any political map (say of the States) only four colors are needed to color each individual State so that no States of the same color are ever in contact.@maths_sorcerer
👨🎓Meeting with Mathematician👨🎓 (Episode 1 with Ken Ono)
Ken Ono is a Japanese-American mathematician who specialises in Algebra, Combinatorics and Number Theory. Especially, his research interests lie in integer partitions, modular forms, Umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan.
This intellectual crucible produced the desired results — Ono studied mathematics and launched a promising academic career — but at great emotional cost. As a teenager, Ono became so desperate to escape his parents’ expectations that he dropped out of high school. He later earned admission to the University of Chicago but had an apathetic attitude toward his studies, preferring to party with his fraternity brothers.
He eventually discovered a genuine enthusiasm for mathematics, became a professor, and started a family, but fear of failure still weighed so heavily on Ono that he attempted suicide while attending an academic conference. Only after he joined the Institute for Advanced Study himself did Ono begin to make peace with his upbringing.
Inspiration✨:- The story of Ramanujan gave him hope that maybe mathematics isn’t the stuff of tests, it isn’t about memorizing figures quickly. It had to be something deeper.
Books written 📖 :- My Search for Ramanujan: How I Learned to Count , Harmonic Maass Forms and Mock Modular Forms: Theory and Applications and others
Join us @maths_sorcerer❣️❣️
Ken Ono is a Japanese-American mathematician who specialises in Algebra, Combinatorics and Number Theory. Especially, his research interests lie in integer partitions, modular forms, Umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan.
This intellectual crucible produced the desired results — Ono studied mathematics and launched a promising academic career — but at great emotional cost. As a teenager, Ono became so desperate to escape his parents’ expectations that he dropped out of high school. He later earned admission to the University of Chicago but had an apathetic attitude toward his studies, preferring to party with his fraternity brothers.
He eventually discovered a genuine enthusiasm for mathematics, became a professor, and started a family, but fear of failure still weighed so heavily on Ono that he attempted suicide while attending an academic conference. Only after he joined the Institute for Advanced Study himself did Ono begin to make peace with his upbringing.
Inspiration✨:- The story of Ramanujan gave him hope that maybe mathematics isn’t the stuff of tests, it isn’t about memorizing figures quickly. It had to be something deeper.
Books written 📖 :- My Search for Ramanujan: How I Learned to Count , Harmonic Maass Forms and Mock Modular Forms: Theory and Applications and others
Join us @maths_sorcerer❣️❣️
Maths Sorcerer 🎩 pinned «👨🎓Meeting with Mathematician👨🎓 (Episode 1 with Ken Ono) Ken Ono is a Japanese-American mathematician who specialises in Algebra, Combinatorics and Number Theory. Especially, his research interests lie in integer partitions, modular forms, Umbral moonshine…»
India's National Game Means "Twenty-Five"
The cross-and-circle board game of Pachisi is a hugely popular game in India dating back centuries, played on a board in which a player throws several cowry shells. Its name translates in Hindi to "Twenty-Five," which refers to the largest score that can be earned through the toss of the shells (there's also a version where the score can reach 30).@maths_sorcerer
The cross-and-circle board game of Pachisi is a hugely popular game in India dating back centuries, played on a board in which a player throws several cowry shells. Its name translates in Hindi to "Twenty-Five," which refers to the largest score that can be earned through the toss of the shells (there's also a version where the score can reach 30).@maths_sorcerer
2 And 5 Are the Only Prime Numbers That End With 2 And 5
A prime number is a natural number greater than one that cannot be created by multiplying two smaller natural numbers. So, to put that in non-math talk, prime numbers are numbers greater than 1 that can only be formed by multiplying 1 by itself. A natural number greater than one that is not prime is called a composite number.@maths_sorcerer
A prime number is a natural number greater than one that cannot be created by multiplying two smaller natural numbers. So, to put that in non-math talk, prime numbers are numbers greater than 1 that can only be formed by multiplying 1 by itself. A natural number greater than one that is not prime is called a composite number.@maths_sorcerer
