About

Math & AI
Inside

I began working on this site in April 2023, after I had numerous conversations (still having) with AI chatbots on freely accessible websites. In this conversations I focused on two of my main favorite research and teaching topics, namely:

  • Dynamic Programming (DP)
  • Decision-Making Under Severe Uncertainty (DMUSU)

I began these conversations in early March 2023 out of curiosity. After a bit of experimentation, I decided to use these conversations as a supplementary resource for two books that I am writing, whose tentative titles are:

  • Dynamic Programming By Example.
  • Wald’s Might Maximin Paradigm: an introduction to robust decision-making under severe uncertainty.

More specifically, the plan was, still is, to use these conversations as a supplement to the discussions in these books. More on this can be found in the Motivation page where I explain in detail what motivated me to embark on this exciting project.

For various reasons, early on in this project I decided to conduct these conversations mainly with

In short, the main attraction on this site is a collection of conversations I have had (still having) with ChatGPT and Bard, mainly on various aspects of Dynamic Programming and Decision-Making Under Severe uncertainty.

The main objective of this page is to provide some details about the content of the site and the way it is organized. But before I do that,

A bit about myself

I am a retired academic, currently affiliated with the School of Mathematics and Statistics at the University of Melbourne, where I worked from 1989 until my retirement in 2008. Before that, I worked at the CSIR (South Africa), IBM Thomas J. Watson Research Center (USA), Princeton University (USA) and the University of Arizona (USA), where I completed my PhD degree in 1976. My main general area of expertise/interest is Operations Research (OR), particularly mathematical methods for modeling, analyzing and solving decision-making problems under uncertainty.

You can find details on my professional profile on my website. You can also find there a large number of educationally rich interactive online models for a number of OR methods.

I should stress that

  • I am not an AI person.
  • My comments on AI matters in this site are strictly user oriented.

And now that I have clarified all this, let me briefly describe the content of the site and how it is organized.

The main topics discussed in this site are listed in the menu just below the header. Here is the current (April 26, 2023) list:

  • Chatbots
        ChatGPT
        Bard
        AI
        AI detectors
        Hallucinations
  • Dynamic Programming
        Multistage/Sequential decision processes
        Principle of optimality
        Functional equations
        Curse of dimensionality
        DP Algorithms
        Dijkstra’s algorithm
  • Decision-making under severe uncertainty
        Decision-making in the face of uncertainty
        Severe uncertainty
        Robustness
        Worst-case analysis
        Wald’s maximin rule
        Wald’s maximin paradigm
  • Life in general, and chatbots’ lives in particular.

Each topic is discussed in a separate dedicated page and the conversations related to the topic are listed in the sidebar of the page. The sidebar also provides links to other resources that are relevant to the topic.

The conversations vary greatly in length, style, technical orientation, etc. Some are very short, some are very long; some are very relaxed, others are very tense, some deal with abstract non-technical issue, others are highly technical in nature. Some are funny, others are sad. And so on …

When you read these conversations, it is important that you keep in mind that

  • One of the two participants in human the other is a chatbot.
  • The response from the chatbot is essentially instantaneous.

It is also very important to realize that, depending on the topic discussed, the chatbot’s response can be “surprising”. For instance, it can be seriously incorrect, or even fundamentally flawed, it can contradicts previous claims made by the chatbot, etc. It can also be 100% correct and beautifully stated.

And, at present, the citations provided by chatbots for sources of information is extremely unreliable. This important issue is discussed in detail here.

More general details on the conversations, their purpose, style, length can be found in the Conversations

What’s next?

My recommendation is that from here you navigate to the Motivation page where you’ll find details about what motivated me to embark on this project. Alternatively, you may prefer to surf to the Guide page where you’ll find useful details about certain aspects of the discussion here such as the format and layout of the conversations, the display of mathematical notation, etc.

Or you may surf directly to pages page dealing with your specific topics of interest. Whatever yo do, surf carefully and obey the road signs.

Have fun!

Moshe
Melbourne
April, 26, 2023