A Conversation with Antal Fekete – Quotient Sets and Stepnumbers

The following is the second in a series of interviews with Professor Antal E. Fekete.

The reader is encouraged to start here:

  1. A Conversation with Antal Fekete — Introduction
  2. A Conversation with Antal Fekete — Real Linear Algebra
  3. A Primer on Quotient Sets and Stepnumbers

Professor Fekete, here is a quote from the Symposia on the Foundations of Mathematics, held at Birkbeck College, University of London, on January 12-13, 2015.

“The focus of this conference is on different approaches to the foundations of mathematics. The interaction between set-theoretic and category-theoretic foundations has had significant philosophical impact, and represents a shift in attitudes towards the philosophy of mathematics. This conference will bring together leading scholars in these areas to showcase contemporary philosophical research on different approaches to the foundations of mathematics. To accomplish this, the conference has the following general aims and objectives. First, to bring to a wider philosophical audience the different approaches that one can take to the foundations of mathematics. Second, to elucidate the pressing issues of meaning and truth that turn on these different approaches. And third, to address philosophical questions concerning the need for a foundation of mathematics, and whether or not either of these approaches can provide the necessary foundation.”

What comes up for you as you read the above quote?

The organizers have missed the point of the conference. They must revise their program to include the antinomies (paradoxes) of mathematics and plans how to eliminate them.

Continue reading A Conversation with Antal Fekete – Quotient Sets and Stepnumbers

A Primer on Quotient Sets and Stepnumbers

Introduction

The following primer has been assembled from various notes I have collected written by Professor Antal E. Fekete on the subject of quotient sets, and stepnumbers — a new number system invented by Fekete in 1997.

My purpose in assembling this information is twofold:

  1. To whet the reader’s appetite for quotient sets and stepnumbers, two absolutely fascinating subjects that could easily slip by unnoticed;
  2. To serve as a primer for an interview with Prof. Fekete about these subjects.

From here, the interested reader is strongly encouraged to go directly to the source and delve into Fekete’s writings on quotient sets and stepnumbers (and other mathematics subjects) which can be found on his website.

Continue reading A Primer on Quotient Sets and Stepnumbers

A Conversation with Antal Fekete – Real Linear Algebra

The following is the first in a series of interviews with Professor Antal E. Fekete.

The reader is encouraged to start here:

Professor Fekete, thank you for agreeing to this interview. As a long-time student of yours, I’m honored (which, I suppose, makes me an honored student.)

In this first installment I would like to discuss everyone’s favorite subject: mathematics.

Now gentle readers, before you stampede for the fire exits, recognize there are good reasons why I’ve chosen to being this conversation with mathematics.

  1. Fekete is a professional mathematician, and if we are to know anything about the man behind his incredible insights into gold dynamics and the Greatest Depression through which we are now struggling, we must understand from where he has come. And he has come from the mathematics department.
  2. Despite being a mathematician, Fekete, unlike the proverbial fellow with a hammer who only sees a world bristling with nails, understands the limits of mathematics, and refuses — unlike armies of economists — to be lured into applying mathematics to monetary economics where it is neither applicable nor ethical. There is much to be learned in this.
  3. His innovations in mathematics are profound in their own right, and well worth a peek for the novice, and some serious pondering for the pro.
  4. Mathematics undergraduate and graduate students should seriously consider mining Fekete’s work for superb deep thesis ideas. They are hanging low, ripe for the picking!

Continue reading A Conversation with Antal Fekete – Real Linear Algebra