Substance and Dynamics:

'Two Elements of Aristotelian-Thomistic Philosophy of Nature in the Foundation of Mathematics in Physics' by Fr. Rudolf Larenz at Studia Gilsoniana

#mathematics #physics

How to write proofs: a quick guide

Eugenia Cheng, Department of Mathematics, University of Chicago, posted this at the University of Sheffield.

"Writing a good proof is not supposed to be something we can just sit down and do. It’s like writing a poem in a foreign language. ...

"Even when you know how to do it, writing a proof takes planning, effort and inspiration. ..."

#mathematics

The mathematical world

James Franklin at Aeon

"To the question: ‘Is mathematics about something?’ there are two answers: ‘Yes’ and ‘No’. Both are profoundly unsatisfying.
...
"Nominalists and Platonists have fought each other to a standstill, each convincingly revealing the fatal flaws in their opponents’ views, each unable to establish their own position. Let’s start again."

(via Great Conversation Reading Group)

#mathematics

Sphere Packing Solved in Higher Dimensions:

'A Ukrainian mathematician has solved the centuries-old sphere-packing problem in dimensions eight and 24.' By By Erica Klarreich at Quanta

(via The Great Conversation)

From the Center: Adler on rhetoric, and on mathematics

Recent communications with members of the Center for the Study of The Great Ideas included:

• Mortimer Adler on the use of rhetoric
• Adler on mathematics as one of the Great Ideas

Here at the weblog, added the Journal of the History of Ideas' JHIBlog to the sidebar blogroll.

Why Do Americans Stink at Math?

Elizabeth Green reported in The New York Times.

"To cure our innumeracy, we will have to accept that the traditional approach we take to teaching math — the one that can be mind-numbing, but also comfortingly familiar — does not work. We will have to come to see math not as a list of rules to be memorized but as a way of looking at the world that really makes sense."

The sum of its parts

David Guaspari reviews An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, by James Franklin, in The New Criterion.

"The mathematician and philosopher James Franklin is a leader of the 'Sydney School,' which has developed an account of mathematics that he sets out in An Aristotelian Realist Philosophy of Mathematics. 'Aristotelian' means not that it strictly follows or develops Aristotle, but that it is recognizably in the same ballpark. He presents it as a middle way between two poles—broadly classifiable as Platonist and nominalist—that have dominated the subject and dictated the terms in which it is discussed."

Thinking Inside the Box

Jenny Price introduces an excerpt from How Not to Be Wrong: The Power of Mathematical Thinking, by Jordan Ellenberg, at On Wisconsin.

The 10 Algorithms That Dominate Our World

Listed and explained by George Dvorsky at io9. (via New Advent)