Ejection of Computer Science from Mathematics

[dennis.hamilton at acm.org]

We can all play this game (below).

> From: José Manuel Rodríguez Caballero
> Sent: Sunday, March 5, 2023 23:08
> Subject: Re: L. E. J. Brouwer and the Sub-Axiomatic Foundations of 
> Mathematics

> Patrik wrote:
> > I am very much in favour of separating  mathematics and theoretical
> > computer science, for the simple reason that theoretical computer
> > science upholds approaches allowing to use one language to manipulate
> > another.

Sidenote: Umm, isn't that what Gödel, Post, and Quine did with arithmetization 
and scriptization?  Don't knock the stored-program concept and what it 
demonstrates about the reach of computability.

> So, I asked a fully technological entity to play devil's advocate and defend 
> Patrik's thesis. The result was as follows (original text, unmodified, 
> decide for yourself whether that has already passed the Turing test).

Below, my questions are in all-caps, the responses are in regular text.

PS: I thought the citation of Chomsky's paper on his phrase-structure 
languages was pretty amusing, considering how much it has played in the 
development of computer science, starting in the 1960s.

 - - - - - - - - - - - - - -

Hello, this is Bing.  How can I help? ??

HOW SEPARATE ARE MATHEMATICS AND COMPUTER SCIENCE?

Searching for: mathematics and computer science relation.

Mathematics and computer science are related fields that share some common 
foundations, such as logic, algorithms, and abstract structures[1,2]. However, 
they are also separate disciplines that have different goals, methods, and 
applications[3,4]. Mathematics is more concerned with discovering and proving 
general truths, while computer science is more focused on designing and 
implementing systems that solve specific problems[4].

What are you interested in learning more about? The similarities or the 
differences between mathematics and computer science? Or maybe a specific 
topic or application that involves both fields?

[I am omitting the citations provided as references, but showing their 
references in brackets]

THE SIMILARITIES BETWEEN MATHEMATIC AND COMPUTER SCIENCE

Some of the similarities between mathematics and computer science are:

 * They both use logic, algorithms, and abstract structures to model and solve 
problems[1,2].
 * They both rely on formal languages and notation to express and communicate 
ideas[1,2].
 * They both have applications in various domains, such as science, 
engineering, cryptography, and artificial intelligence[1,3].
 * They both benefit from the use of computing tools and software, such as 
SageMath, MATLAB, and Python[1.3].

Is there a specific similarity that you want to know more about? Or do you 
have another question related to mathematics and computer science?

[Each of the Bing responses has separate citations for "Learn more."]

TELL ME MORE ABOUT LOGIC IN MATHEMATICS AND COMPUTER SCIENCE.

Searching for: logic in mathematics and computer science

Logic is the study of the principles and methods of reasoning[1,2]. Logic is 
used in mathematics to construct and verify proofs, to define and manipulate 
abstract concepts, and to explore the foundations of mathematics[2]. Logic is 
also used in computer science to design and analyze algorithms, to model and 
verify systems, and to implement and automate reasoning[3,1].

Some of the branches of logic that are relevant to both mathematics and 
computer science are:

 * Propositional logic: the study of the truth values of simple statements and 
their combinations[1].
 * Predicate logic: the study of the truth values of statements that involve 
variables, quantifiers, and predicates[1].
 * Modal logic: the study of the truth values of statements that involve 
modalities, such as necessity, possibility, knowledge, and belief[1].
 * Computability theory: the study of the limits and capabilities of 
computation and algorithms[1].
Do you want to learn more about any of these branches of logic? Or do you have 
another question related to mathematics and computer science?

TELL ME MORE ABOUT THE DIFFERENCES OF MATHEMATICS AND COMPUTER SCIENCE

Searching for: differences between mathematics and computer science

Some of the differences between mathematics and computer science are:

* Mathematics is the study of abstract structures, patterns, and 
relationships, while computer science is the study of computation, 
information, and systems[1,2].
* Mathematics is more focused on theory, proof, and rigor, while computer 
science is more focused on application, implementation, and 
experimentation[1,2].
 * Mathematics is more general and universal, while computer science is more 
specific and contextual[1,2].
 *  Mathematics has a longer and more established history, while computer 
science is a relatively newer and more dynamic field12.

Of course, these are not absolute distinctions, and there are many overlaps 
and interactions between the two fields. For example, some branches of 
mathematics, such as discrete mathematics, computational mathematics, and 
applied mathematics, are closely related to computer science. Similarly, some 
branches of computer science, such as theoretical computer science, artificial 
intelligence, and cryptography, are heavily influenced by mathematics.

Do you want to learn more about any of these branches of mathematics or 
computer science? Or do you have another question related to mathematics and 
computer science?

MORE ABOUT DISCRETE, COMPUTATIONAL, AND APPLIED MATHEMATICS WAS OFFERED.  I 
ENDED THIS HERE, WITH MY OWN CONCLUSION.

Some of us need to get out more.

 - Dennis