Cantor's Archive (Page 2)
From the Big bang to the Heat death of the universe
It’s not because you’re stupid or weren’t concentrating in school
Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty!
Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891).
In a purely logical argument, even if the premises aren’t in any way (semantically) connected to the conclusion, the argument may still be both valid and sound. Professor Edwin D. Mares displays what he sees as a problem with purely formal logic when he offers us the following example
Motion of a moving particle is considered to be one of the most instructive and useful physical systems one can study. In a real world case, such systems may exhibit immense complexity and intractability. But if we are lucky, we may be able to isolate the moving particle from unwanted
The nature of subsymmetries
The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.
A Framework For Defining Geometric Objects In Space
Developing an Intuition for Radicals
The three main contemporary ways to understand the foundations of mathematics.
Why engineers should know their algorithms
Proof Theory
How Mathematical Proofs can Help Unlock the Secrets of the Brain
Computational neuroscience, broadly defined, is the mathematical and physical modeling of neural processes at a chosen scale, from molecular and cellular to systems, for the purpose of understanding how the brain represents and processes information. The ultimate objective is to provide an understanding of how an organism takes in sensory
Philosophy
Who Says Nature is Mathematical?
This piece wouldn’t have been called ‘Who Says Nature is Mathematical?’ if it weren’t for the many other similar titles which I’ve seen. Take these examples: ‘Everything in the Universe Is Made of Math — Including You’, ‘What’s the Universe Made Of? Math, Says Scientist’ and ‘Mathematics
Particle Physics
The Discovery of Spontaneous Radioactivity
Sweety, let me see what you got inside.
Group Theory
Group Theory
The nature of symmetry and the symmetry of nature
Philosophy
Is ‘Philosophy of Mathematics’ somehow useful?
What the philosophy of mathematics is useful for? Max Black, the author of The Nature of Mathematics (1933), thought the main task of the foundation of mathematics (and, consequently the main task of any philosophy of mathematics) would be to elucidate “and analyze the notion of integer or natural number”
Geometry
Horrocks’ Measurements of How Far Away The Sun Is
Understanding the sun-to-planets absolute distances was a long-run investigation proceeding with new scientific-tools and new laws. As a police case requires time and symmetry of action that concatenates all threads within one bracket, space exploration is alike. At the time of Venus transit in 1761, scientists had all to kill
Discrete Mathematics
How Many Distances Must Be Made from N Points?
My most striking contribution to geometry is, no doubt, my problem on the number of distinct distances. This can be found in many of my papers on combinatorial and geometric problems. -Paul Erdős, On Some of My Favorite Theorems, 1996. Erdős is one of the greatest mathematicians from history, and
Relativity
The Lorentz Transformation
And how to repair physics
Poincaré
Poincaré’s Philosophy of Mathematics
Was his philosophy of mathematics underrated?
Series
An Amazing Formula
Generalizing Leibniz’ formula for π, the alternating harmonic series, and the Basel problem
Constructivism
R.L. Wilder’s Constructivist Account of Early 20th Century Mathematics
This is the second part of my piece on Raymond Louis Wilder (1896–1982) and his philosophical, historical and anthropological account of mathematics. I suggest that the reader refer back to the introduction to my ‘Raymond L. Wilder’s Anthropology of Mathematics: Platonism and Applied Mathematics’for Wilder’s biographical
Cryptography
Could We Break RSA Encryption Without A Quantum Computer?
We discuss a range of integer factorization algorithms that can run on classical computers and explore their future in the face of Shor’s algorithm.