|
|
|
|
Mathematics, history and philosophy
The article Infinitesimal Knowledges appeared in Axiomathes (2022). In the 17th century, mathematicians were using new methods and the notion of
indivisibles. This led to paradoxes that undermined earlier mathematical certainty. This article considers these issues with reference to Amir Alexander's book Infinitesimal, and to language, history, pedagogy and knowledge.
|
|
|
|
|
|
Fourier analysis research
Let ${\mathbb T}$ be the set of complex numbers of modulus $1$. A function $g\in L^2({\mathbb T})$ is called a difference if there is $b$ in $\mathbb T$ and a function $h\in L^2({\mathbb T})$ such that $g(x)=h(x)-h(bx)$ for almost all $x$ in $\mathbb T$. In 1972, Gary H. Meisters and Wolfgang Schmidt proved for a function $f\in L^2({\mathbb T})$ that
$\int_{\mathbb T}f(t)\,dt=0$
if and only if $f$ is a sum of $3$ differences.
Building on this work, Difference Spaces and Invariant Linear Forms identifies a new phenomenon in Fourier analysis. Read more about Fourier analysis research.
|
|
|
. . . and how hast thou plentifully declared the thing as it is?
Job 26:3
***
"All truly liberating acts are genuinely altruistic and involve freely accepted renouncement of some freedoms" -- Igor Kluvánek.
Read about the mathematics and ideas of Igor Kluvánek, and some more of his quotations.
***
"If one stops oneself from thinking about all this, one makes oneself an accomplice of what is happening" -- Simone Weil.
Read a review of Robert Zaretzsky's book on Simone Weil.
***
"Integrity requires us to view things in their organic reality, not their mechanical reality." Read more about integrity in teaching and learning.
***
"...... postmodern thought, for all its 'radical' and 'subversive' pretensions, is merely an application of the ideas of market forces ... to the world of the intellect. Of course, both [postmodernism and market economics] have the same effect of trivialising the serious life of the mind."
Read more about changing intellectual culture.
***
Read a review of Everywhen: Australia and the language of deep history, Ann McGrath, Laura Rademaker and Jakelin Troy (eds),
NewSouth Press, published in The Journal of
the Royal Australian Historical Society 2023.
***
This page updated 7th August, 2026
|
