Confession as an AI researcher; seeking advice
I&#x27;ll try to reply to the frustrations of
the author of the OP.<p>I&#x27;ll give some high level views and also
outline the math topics mentioned, high
school through much of a Ph.D. in parts of
applied math.<p>I respond in three parts:<p>Part I<p>I have a good pure&#x2F;applied math Ph.D. and
work in applied math and computing; while
I call my work applied math and not
artificial intelligence (AI), machine
learning (ML), or computer science, it
appears from the OP that there is
significant overlap between my background
and work and what the OP is concerned
about.<p>The Reddit post by the guy in Germany was
terrific although easy to parody as a big
feature of old German <i>culture</i>!  :-)!
That post is maybe a bit over organized.<p>I&#x27;ve posted too often that the best future
for computer science was pure&#x2F;applied
math, e.g., that someone seriously
interested in the future of computing
should as an undergraduate just major in
pure math with some applied math and,
essentially f&#x27;get about anything
specifically about computer science.<p>Or, for the <i>essential</i> computer science,
write some code in some common procedural
programming language for some simple
exercises, check out at the library D.
Knuth&#x27;s <i>The Art of Computer Programming,
Volume 3, Sorting and Searching</i>, learn
about big-O notation, the heap data
structure and heap sort, as an exercise
program, say, a priority queue based on
the heap data structure, learn about the
Gleason bound and how heap sort achieves
it so is in an important sense the fastest
possible sort algorithm, as a side
exercise look at AVL trees, and call
computer science done for an
undergraduate!  This is partly a joke but
not entirely.<p>Well, it appears that the OP has started
to discover some of why I&#x27;ve said such
things about math.<p>This role for math is just a special case
of the old standard situation that, in
nearly all fields, the best work
<i>mathematizes</i> the field as in, e.g.,
mathematical physics.  Indeed, there is
the old joke that good coverage of the
math needed for theoretical physics is so
much about just the math that can do the
physics just in the footnotes.<p>It is a standard situation that nearly
everyone in the STEM fields is convinced
that they need to know more math.  As I
read papers by computer science
professors, I tend to agree!<p>Here I&#x27;ll try to help the person with
their lament in the OP:<p>(1) Start at about 50,000 feet up and
begin to identify in what fields, broadly
on what problems, you want to work.
Remember:  One of the keys to success is
good, early work in problem selection.<p>(2) If you want to work in AI, I suggest
you try to regard the current headline
topics in AL&#x2F;ML as nearly irrelevant.
Sure, for political reasons, might have to
keep up, and maybe there are some current,
hot applications, but I don&#x27;t see that
work -- first-cut, ballpark, basically
empirical curve fitting to huge quantities
of data -- as much of a start on AI.<p>E.g., at one time I was hired to work in
an AI project, specifically expert
systems.  My first reaction was that
expert systems -- rule based programming,
working memory and the RETE algorithm,
rule firing conflict resolution -- were
junk and, in particular, nothing like a
good start on AI, programming style, or
anything else.  After 20 years my opinion
has changed:  Expert systems were worse
than junk, as a style of programming, for
much of anything, and in particular on
anything like AI.<p>Maybe I got some revenge:  We were trying
to use expert systems for the monitoring
and management of large server farms and
networks.  For the monitoring, for
essentially <i>health and wellness</i>, they
were using essentially just thresholds set
by hand on single variables one at a time.
My view was, wrap that data and processing
in all the rules possible, and still the
results won&#x27;t be very good.<p>Sure, for monitoring there are two ways to
be wrong, (A) a false alarm and (B) a
missed detection.  So, right, we&#x27;re forced
into statistical hypothesis testing with
(i) a <i>null hypothesis</i> that the system is
healthy, (ii) a false alarm is Type I
error, (iii) a missed detection is Type II
error.  Quickly decide that need some
statistical hypothesis tests, with the
null hypothesis that the system is
healthy, that are both multidimensional
(treat several variables jointly)
distribution-free (make no assumptions
about probability distributions) and find
that apparently there were none such in
the literature.  So, I invented a large
class of such tests that, really, totally
knocked the socks off expert systems for
much of monitoring.  And what I did was
just some applied math and applied
probability -- some group theory, some
probability theory based on measure
theory, some measure preserving as in
ergodic theory, etc.<p>So, yes, I could say that my monitoring
took in <i>training</i> data, did some <i>machine
learning</i>, was better at its monitoring
than humans so was some <i>artificial
intelligence</i>, was <i>computer science</i>,
etc., but I didn&#x27;t:  I just called my work
some applied math.  E.g., I got real
hypothesis tests where false alarm rate
was adjustable and known in advance and
some useful best possible results on
detection rate.  So, as I wrote in the
paper, take away the mathematical
assumptions, derivations, theorems and
proofs, forget about false alarm rate and
detection rate, and just do the specified
data manipulations and call the work AI.<p>So, such real problems and applied things
are one approach to computer science, AI,
ML, etc.  Then, sure, for such work as in
what I did for detection, need, really,
the Ph.D. coursework in pure and applied
math and some ability to do publishable
theorems and proofs in math -- for both,
net, need a pure&#x2F;applied math Ph.D.<p>So, back to AI and mostly setting aside
the current headlines:  For AI, I&#x27;d
suggest that from 50,000 feet up start by
watching<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vc8MddDFRw4" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vc8MddDFRw4</a><p>with a mommy kitty cat (domestic short
hair tabby) and 6 or so of her kittens,
maybe only 2 days old, and how they learn.
Their learning is astoundingly fast.
E.g., for how they learn to use their hind
legs, can see fairly directly some of just
how they do that.  In just that one video
clip, in real time of likely just a week
or so, those kittens go from nearly
helpless balls of fur to young kitty cats.
Easy to guess that in two months they will
be safely 40 feet up a tree catching
something or other, effortlessly doing
gymnastic feats that would shame Olympic
athletes, etc.  Astounding.<p>Okay for AI from 50,000 feet up, start by
trying to guess how those kittens learn.
Maybe there will be some math in that,
maybe not.  Then if you can implement your
guess in software, if the software appears
from good tests in practice to learn some
things well, and if your guess is fairly
general, then maybe you have some progress
on AI.  Here f&#x27;get about my view and
confirm with some AI profs who would have
to review your work, hire you for a
research slot, give you a research grant,
etc.<p>So, for some research, (i) could do some
math as I did for that monitoring or (ii)
try to do some real AI, e.g., by starting
by watching those kittens learn where
maybe, eventually there will be some math.<p>For both those research directions, notice
that need (i) some overview of the real
problem, (ii) some intuitive insights,
(iii) some good, new ideas.  Maybe the
ideas will be mathematical or use math and
maybe not.  E.g., might go a long way on
what those kittens are doing before use
much math.<p>(3) But for the math as mentioned by the OP,
I&#x27;ll try to give an outline:<p>(i) Start with the real numbers, e.g., as
learned likely well enough by the 9th
grade.  Then, sure, learn about the
complex numbers.  So, net, have a high
school major in math, e.g., everything
short of calculus.<p>(ii) Learn college calculus well.  At
least in part, you can do well alone:  Due
to some circumstances beyond my control,
for freshman calculus I just got a good
book, studied, worked the exercises, and
learned.  Then at a college with a good
math department, I started on sophomore
calculus.  You can do such stuff yourself.<p>(iii) It would be good to take a course in
abstract algebra, especially one where
nearly all the exercises are proofs.  So,
learn about sets, functions, groups,
rings, fields, more about the real and
complex numbers, maybe some basic number
theory, the greatest common divisor and
least common multiple algorithms, and some
about vector spaces.  Might touch on
cryptography and coding theory.<p>Really the more important, maybe main,
value of the course is just learning how
to write proofs.  The math there is nearly
all just so childishly simple that it&#x27;s
easy to learn to write very highly precise
proofs -- crucial stuff if later want to
publish theorems and proofs.<p>Blunt fact of life, politically incorrect
observation:  Without such training in
writing theorems and proofs, and, really,
just in math notation and how to do math
derivations, tough ever to learn how.  So,
can find chaired professors of computer
science at top computer science
departments in top US research
universities who, however, fumble terribly
with just standard math notation and,
especially, with how to write theorems and
proofs.