In other quantum-related news, this was the day in 1932 that Albert Einstein received his American visa…
Above: Big Al does the math for the density of the Milky Way…
Ordinary finds
From the latest hit to the wisdom of old...
German physicist Werner Heisenberg was, according to the uncertainty principle, born Dec. 5, 1901 and died in 1976…
Heisenberg got the Nobel in Physics in 1932 “for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen…”
Above: The Formula
Austrian mathematician Kurt Gödel: April 28, 1906 - 1978…
Gödel’s major contribution to logic and mathematical philosophy - more specifically, set theory - came at the tender age of 25 when he formulated his incompleteness theorems, the first of which can be rendered:
If P is ω-consistent, then there is a sentence which is neither provable nor refutable from P.
Photo: LIFE Magazine, 1962
Pierre de Fermat, was born on Aug. 17, 1601 - 410 years ago. A lawyer at the Parlement of Toulouse and a gifted amateur mathematician, he made breakthroughs in several fields of calculus, probability, geometry and number theory, but is best known for a brief note he made in the margin of a book of arithmetic:
“It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.”
Google doodle: Fermat’s Last Theorem: xn + yn ≠ zn
German mathematician Carl Friedrich Gauss - April 30, 1777 - 1855…
Among his many contributions is the formulation of the prime number theorem:
The prime number theorem states that if a random number nearby some large number N is selected, the chance of it being prime is about 1 / ln(N), where ln(N) denotes the natural logarithm of N. For example, near N = 10,000, about one in nine numbers is prime, whereas near N = 1,000,000,000, only one in every 21 numbers is prime. In other words, the average gap between prime numbers near N is roughly ln(N).
Henri Poincaré (April 29, 1854 – 1912) was a French mathematician and theoretical physicist, and a philosopher of science. Poincaré is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
“Mathematics is the art of giving the same name to different things” — H.P.
Austrian mathematician Kurt Gödel was born April 28, 1906 (d. 1978) - his major contribution to logic and mathematical philosophy - more specifically, set theory - came at the tender age of 25 when he formulated his incompleteness theorems.
Basically put:
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.
Or:
“Gödel found a hole in the center of mathematics”
Photo: Alfred Eisenstaedt, 1962 - LIFE
Paolo Ruffini (Sep. 22, 1765 – 1822) was an Italian mathematician and philosopher who developed a quick method for polynomial division - Ruffini’s Rule. Ruffini also made contributions to group theory…
Ruffini’s rule establishes a method for dividing the polynomial
by the binomial
to obtain the quotient polynomial
and a remainder s…
Don’t ask…
A bit of Math:
German mathematician Carl Friedrich Gauss - April 30, 1777 - 1855…
Among his many contributions is the formulation of the prime number theorem:
The prime number theorem states that if a random number nearby some large number N is selected, the chance of it being prime is about 1 / ln(N), where ln(N) denotes the natural logarithm of N. For example, near N = 10,000, about one in nine numbers is prime, whereas near N = 1,000,000,000, only one in every 21 numbers is prime. In other words, the average gap between prime numbers near N is roughly ln(N).
Etching of Gauss by Siegfried Detlev Bendixen, 1828
And a bit of Math:
Henri Poincaré (April 29, 1854 – 1912) was a French mathematician and theoretical physicist, and a philosopher of science. Poincaré is often described as a polymath, and in mathematics as The Last Universalist, since he excelled in all fields of the discipline as it existed during his lifetime.
The Poincaré Conjecture in words:
“Consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?”
A visualization of the proof of the Poincaré Conjecture that the Russian mathematician Perelman produced 100 years after the conjecture was originally formulated…
Two ways of putting the Poincaré Conjecture into words:
“Consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?”
“The Poincare Conjecture says “hey, you’ve got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball.”“
Austrian mathematician Kurt Gödel was born April 28, 1906 (d. 1978) - his major contribution to logic and mathematical philosophy - more specifically, set theory - came at the tender age of 25 when he formulated his incompleteness theorems.
Basically put:
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.
Or:
“Gödel found a hole in the center of mathematics”
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