Hardy
G. H. Hardy — Rigorous & Shy
Beauty is the first test: There is no permanent place in the world for ugly mathematics. — GH Hardy in A Mathematician’s Apology
Mathematics
Ramanujan
Ramanujan’s Early Work on Continued Fractions
“I had never seen anything in the least like [it] before” — G.H. Hardy On or about the 31st of January 1913, mathematician G.H. Hardy (1877-1947) of Trinity College at Cambridge University received a parcel of papers from Madras, India. The package included a cover letter where a young
Mathematics
The Martians of Budapest
The Martians of Budapest”, sometimes referred to as simply “The Martians” is a colloquial term used to describe a group of prominent Hungarian physicists and mathematicians who emigrated to the United States following the Great Purge of 1933.
Group Theory
The Power of Invariants
We can find invariants in many branches of mathematics. Let us try to use the theory of invariants to solve a few popular brainteasers.
Analysis
Cantor’s Diagonal Argument
“Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén…
Geometry
Exploring the geometric ratios in Rick’s paradox
The math behind a popular zentangle pattern: from special triangles to trigonometry.
Analysis
Pythagorean Triples and Other Beasts
I never thought that I would write math stories in English, but I also never thought that I would live in the UK either.
Gödel
Kurt Gödel's Brilliant Madness
Hungarian polymath John von Neumann (1903–1957) once wrote that Kurt Gödel was “absolutely irreplaceable” and “in a class by himself”.
Ramanujan
Ramanujan’s First Letter to G.H. Hardy (1913)
On or about the 31st of January 1913, mathematician G.H. Hardy (1877-1947) of Trinity College at Cambridge University received a parcel of papers from Madras, India which included a cover letter from an aspiring young Indian mathematician by the name of Srinivasa Ramanujan (1887–1920).
Mathematics
The Duties of John von Neumann’s Assistant in the 1930s
The year is 1933. A 26 year-old former graduate student at Columbia University, Edgar R. Lorch (1907–1990) has just completed his Ph.D. in mathematics and is, in his own words “by some miracle” awarded a National Research Council Fellowship for a year of postdoctoral studies at Harvard University.
Set Theory
What Is Zorn’s Lemma?
The quick and dirty guide to one of the stranger mathematical curiosities.
Analysis
Mathematical Induction: The Domino Effect in Natural Numbers
We discuss the concept of mathematical induction on the natural numbers and give some examples.