Mind Matters Natural and Artificial Intelligence News and Analysis

TagG. H. Hardy (1877-1947)

new-ideas-stockpack-adobe-stock
New ideas

Do Mathematicians Think Differently From Other People?

A math teacher illustrates some ways in which creative ones do but it’s really about imagination, not just getting the figures right

Math teacher Ali Kayaspor has thought a lot about how mathematicians have come up with fundamental ideas about the nature of reality and he shares anecdotes that give us a glimpse. But first, the cold shower: Unfortunately, there is no clear way to answer the question of how a mathematician thinks. But we can approach this question as follows; if you watched any chess tournament, the game’s analysis is shared in detail at the end of the match. When you examine the analysis, you will see a breaking point in each game. Similarly, mathematicians also experience a breaking point while working on a problem before finding a solution. Ali Kayaspor, “How Does a Mathematician’s Brain Differ from Other Brains?” at Read More ›

Logical Diagrams
Making business plan. Businessperson drawing diagrams. Many graphs and hand drawn diagrams.

Why Impractical Things Like Philosophy Are Actually Quite Useful

Chaitin argues that the human spirit is capable of doing both practical things and impractical things which may have practical consequences later

In last week’s podcast,, “The Chaitin Interview V: Chaitin’s Number,” Walter Bradley Center director Robert J. Marks continued his conversation with mathematician Gregory Chaitin, best known for Chaitin’s unknowable number. Last time, they looked at how Chaitin’s unknowable number relates to computer pioneer Alan Turing’s vexing halting problem in computer science. This time, they look at the way pure mathematics has a way of being highly practical: It creates a basis for new understanding, leading to technical breakthroughs: This portion begins at 09:50 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: There are always going to be a few of us who like to do practical things. That’s part of my personality too, but there’s also, Read More ›

black-mathematics-board-with-formulas-stockpack-adobe-stock.jpg
black mathematics board with formulas

Why Don’t We See Many Great Books on Math Any More?

Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books.

In our most recent podcast, “The Chaitin Interview III: The Changing Landscape for Mathematics,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on many things mathematical, including whether math is invented or discovered. This time out, Chaitin talks about why he thinks great books on math, advancing new theorems, aren’t written much any more: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 02:49 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: You don’t hear the word “scholarship” very much anymore in academia. Gregory Chaitin: And people don’t write books. In the past, some wonderful mathematicians like G. H. Hardy (1877–1947, pictured in 1927) would write wonderful books like A Mathematician’s Apology (1940) Read More ›