AI Mathematicians

[John Clark]

The Chinese AI DeepSeekMath-V2, is not only the first open source AI to win a gold medal at the International Mathematical Olympiad, it also got a score of 118 out of 120 points on the Putnam Mathematical Competition; 3,988 humans took that test and all of them were math majors at prestigious universities, but the test was so difficult that the highest score any human got on it was 90 and the median score was zero. 

DeepSeek’s self-correcting AI model aces tough math proofs

You might also find the following to be of interest: 

Nvidia CEO Says Within 3 Years 90% Of The Worlds Knowledge Will Be Generated By AI

And to think, some people are still getting all hot and bothered over trivialities like illegal immigration and deficit spending and the war on Christmas. 

John K Clark

[Tomasz Rola]

On Sun, Dec 07, 2025 at 03:13:31PM -0500, John Clark wrote:
> *The Chinese AI DeepSeekMath-V2, is not only the first open source AI to

> win a gold medal at the International Mathematical Olympiad, it also got a
> score of 118 out of 120 points on the Putnam Mathematical Competition;
> 3,988 humans took that test and all of them were math majors at prestigious
> universities, but the test was so difficult that the highest score any

> human got on it was 90 and the median score was zero. *

So, a pretty good problem solver. But I think that a mathematician
should be also capable of formulating problems and theories. Consider,
for example, Hilbert's problems [1] or Millenium Prize Problems [2].

Would this AI mathematician be capable of inventing Turing machine
after being loaded with state of the art as it was in 1936? I doubt
it. I also doubt that it will happen soon.

[...]
> *You might also find the following to be of interest: *
>
> *Nvidia CEO Says Within 3 Years 90% Of The Worlds Knowledge Will Be
> Generated By AI*
> <https://www.youtube.com/watch?v=Mrx19bIc_Js&list=WL&index=6&t=8s>

I will keep wondering how did he measure amount of "Worlds Knowledge"
and what made him say about its future value.

[1] https://en.wikipedia.org/wiki/Hilbert's_problems
[2] https://en.wikipedia.org/wiki/Millennium_Prize_Problems

--
Regards,
Tomasz Rola

--
** A C programmer asked whether computer had Buddha's nature. **
** As the answer, master did "rm -rif" on the programmer's home **
** directory. And then the C programmer became enlightened... **
** **
** Tomasz Rola mailto:tomas...@bigfoot.com **

[John Clark]

On Mon, Dec 8, 2025 at 12:05 AM 'Tomasz Rola' via Everything List <everyth...@googlegroups.com> wrote:

> The Chinese AI DeepSeekMath-V2, is not only the first open source AI towin a gold medal at the International Mathematical Olympiad, it also got a score of 118 out of 120 points on the Putnam Mathematical Competition;3,988 humans took that test and all of them were math majors at prestigious universities, but the test was so difficult that the highest score any human got on it was 90, and the median score was zero. 

> So, a pretty good problem solver.

Pretty good? A 118 score on the Putnam and just pretty good? The rate of improvement is astounding, one year ago the smartest AI in the world would've gotten a zero on the Putnam.

> But I think that a mathematician should be also capable of formulating problems and theories. Consider, for example, Hilbert's problems  or Millenium Prize Problems . Would this AI mathematician be capable of inventing Turing machine after being loaded with state of the art as it was in 1936? I doubt it.

Grigori Perelman got a gold medal at the International Mathematical Olympiad in 1982, but he had his 16th birthday only a few days before so he was not yet a good enough mathematician to make a significant contribution to mathematics, however he kept getting better and a few years later he proved one of the Millenium Prize Problems, the Poincare "Conjecture", so now it is no longer a conjecture, it is a fact. I think AIs will follow a similar, but steeper, trajectory.
 

> I also doubt that it will happen soon.

I think that right now AIs are as stupid as they're ever going to be, and human beings are as smart as they're ever going to be.   

John K Clark    See what's on my new list at  Extropolis

 

[Tomasz Rola]

On Mon, Dec 08, 2025 at 08:29:55AM -0500, John Clark wrote:
> On Mon, Dec 8, 2025 at 12:05 AM 'Tomasz Rola' via Everything List <
> everyth...@googlegroups.com> wrote:
>
>

> > *>** The Chinese AI DeepSeekMath-V2, is not only the first open source AI
> >> to**win a gold medal at the International Mathematical Olympiad, it also
> >> got a **score of 118 out of 120 points on the Putnam Mathematical
> >> Competition;**3,988 humans took that test and all of them were math
> >> majors at prestigious **universities, but the test was so difficult that
> >> the highest score any **human got on it was 90, and the median score was
> >> zero. *

> >
> >
> > > So, a pretty good problem solver.
>
>

> *Pretty good? A 118 score on the Putnam and just pretty good? The rate of

> improvement is astounding, one year ago the smartest AI in the world

> would've gotten a zero on the **Putnam.*

Yeah, yeah... I wondered what was the whole fuss about this Putnam, so
I browsed a bit and downloaded tasks from last year. I have taken
2024/A6 and 2024/A1, scored max i.e. 24 points for the two (i.e. my
solutions were correct, achieved with pen and paper only and no
looking up in the books etc). Only it took me about ten hours total,
so I would have been disqualified from real P. But I hope I can be cut
some slack, because:

- I am at least twice as old as typical contender

- I took them without preparation, while some (many, all?) prepare
for a year or some (and there is even a textbook for them, for this
specific contest)

- I have to take care of my stuff and so on

- I would not called myself mathematician, or a student of subject,
most of the time, while I felt the affect to maths, maths did not
return the feeling... not too much.

So, anyway, while my performance was not stellar, would I say that
getting score required any kind of superhuman abilities? Nope. It was
quite a fun, however.

> > But I think that a mathematician should be also capable of formulating
> > problems and theories. Consider, for example, Hilbert's problems or
> > Millenium Prize Problems . Would this AI mathematician be capable of
> > inventing Turing machine after being loaded with state of the art as it
> > was in 1936? I doubt it.
>

> *Grigori Perelman got a gold medal at the International Mathematical

> Olympiad in 1982, but he had his 16th birthday only a few days before so he
> was not yet a good enough mathematician to make a significant contribution
> to mathematics, however he kept getting better and a few years later he
> proved one of the Millenium Prize Problems, the Poincare "Conjecture", so
> now it is no longer a conjecture, it is a fact. I think AIs will follow a

> similar, but steeper, trajectory. *

The problem is not about trajectory of some automaton going via
existing road (built by humans, mind you) - this is merely solving a
task of optimisation, so it does not boom into trees. The problem is
about automaton choosing to build a wholly new road. This is what I
expect from a mathematician.

[Tomasz Rola]

On Tue, Dec 09, 2025 at 12:40:31PM +0100, 'Tomasz Rola' via Everything List wrote:
[...]

> I browsed a bit and downloaded tasks from last year. I have taken
> 2024/A6 and 2024/A1, scored max i.e. 24 points for the two (i.e. my

[...]

I meant to write 2024/A5, not A6.

[John Clark]

On Tue, Dec 9, 2025 at 6:40 AM 'Tomasz Rola' via Everything List <everyth...@googlegroups.com> wrote:

> while my performance was not stellar, would I say that getting score required any kind of superhuman abilities? Nope.

I would say that getting a score of 118 on the Putnam is FAR beyond the abilities of 99.99+% of the humans on this planet; so "superhuman" would not be a completely inaccurate word to describe such an ability. 

>> *Grigori Perelman got a gold medal at the International Mathematical
>> Olympiad in 1982, but he had his 16th birthday only a few days before so he
>> was not yet a good enough mathematician to make a significant contribution
>> to mathematics, however he kept getting better and a few years later he
>> proved one of the Millenium Prize Problems, the Poincare "Conjecture", so
>> now it is no longer a conjecture, it is a fact. I think AIs will follow a
>> similar, but steeper, trajectory. 

>The problem is not about trajectory of some automaton going via existing road (built by humans, mind you) - this is merely solving a task of optimisation, so it does not boom into trees.The problem is about automaton choosing to build a wholly new road.

So would it be correct to say that Grigori Perelman, who happens to be a human being, did not build a wholly new road into the mathematical frontier, all he did was locate the end of a road that was built by others?  

 

>This is what I expect from a mathematician.

There were hints of calculus before Newton or Leibniz, and before Cantor Jain mathematicians in ancient India had a similar idea about multiple infinite sizes. Can you name any human mathematician who discovered an entirely new field of mathematics completely on his own with no previous mathematician even coming close? I can't. 

 John K Clark    See what's on my new list at  Extropolis

xx9

 

[Brent Meeker]

Having "hints" of a new mathematical field doesn't preclude discovering the whole new field.  Aristotle's finding areas by limits didn't include the idea of derivatives and anti-derivatives; much less differential equations.  I doubt Cantor ever heard of Jain musings about infinities.  Newton, Leibniz, and Cantor did build wholly new roads into the mathematical frontier; even if there was a hint of the possibility beforehand.  I will be interesting to see whether AI's will become innovative in mathematics and if we can understand them when they do.

Brent

[John Clark]

On Tue, Dec 9, 2025 at 4:11 PM Brent Meeker <meeke...@gmail.com> wrote:

> I will be interesting to see whether AI's will become innovative in mathematics 

It's not a question of whether it will happen but how many years it will take before it happens; I'm not sure what that number will be but I am certain it will be in the single digits. It took Grigori Perelman about 20 years to go from winning a gold medal at the International Mathematical Olympiad to solving a Millennium Prize Problem, but electronics operates much faster than biology.  

> and if we can understand them when they do.

I'm not sure of that at all. 

 John K Clark    See what's on my new list at  Extropolis

cdv

 

[Tomasz Rola]

On Tue, Dec 09, 2025 at 07:49:09AM -0500, John Clark wrote:
> On Tue, Dec 9, 2025 at 6:40 AM 'Tomasz Rola' via Everything List <
> everyth...@googlegroups.com> wrote:
>

> *> while my performance was not stellar, would I say that getting score
> > required any kind of superhuman abilities? Nope.*
>
>
> *I would say that getting a score of 118 on the Putnam is FAR beyond the

> abilities of 99.99+% of the humans on this planet; so "superhuman" would
> not be a completely inaccurate word to describe such an ability. *

Sure, solving more problems should be more difficult and would require
bigger ability - in this particular field, i.e. problem solving. This
says nothing about one's ability in other fields until one is tried in
those other fields. And besides, while a horse is stronger than me, so
it has bigger ability in the field of moving a ton of cargo, it is
still no reason to treat a horse as some kind of demigod. Even if
someone discovers that a horse may kick a baseball into neighboring
town. Of course, some people will inevitably elevate such a horse into
demigod position and I will inevitably make remarks how they will eat
salami of demigod once it gets too old.

This is not to mean that there has been no progress - there was a
progress, quite impressive progress, happened during more or less
single lifetime. However, each technology has limits, and if there is
no breakthrough, then there is no more dramatic improvement. In
particular, assuming they run LLM on computing cluster (and I cannot
imagine anything else for such task, but I had not dug for the
information, so I can assume only) - it is very hard to double
performance of a cluster. You may see an example in wikipedia article
about scalability, where is is shown how doubling cpus from 4 to 8
only gives 22% of speed increase (for very specific kind of
computation, as described there). [1]

Or, to put it another way, throwing more and more resources into
cluster is going to give smaller and smaller performance
improvements. Improving algorithms will change the serial part of
computation to be smaller and will make parallel part to give faster
results with more cpus. But algorithms cannot be improved infinitely.

The whole talk about building nuclear plants for powering cluster to
run bigger model on it seems (IMHO) to indicate "they" have hit the
wall and cannot easily improve anymore. Mind you, this is a single
computer (ok, cluster is your new computer, right), running a single
application (LLM), and they need it to have its own power plant.

Assuming they get there, can they have even bigger cluster, say, 20
times as big, powered by another 20 plants? This is going to be
ridiculous, or pathetitc improvement. There should be a better
way. And if no such way is found - there will be long stagnation, I
suppose.

[1] https://en.wikipedia.org/wiki/Scalability

Of course there are going to be some interesting new uses for this
stagnated tech. Some more click-baity titles. LLM will kick a
football, too, always scoring perfect goal.

Wild prophecies about coming era of artificial intelligence were
happening for a very long time - the earliest I have read about was in
1954, if memory serves (I do not want to dig out this book right
now). This means 71 years of unfulfilled prophecies. Color me bored.

This time, it may be different. But so far, the only thing which seems
different is the fact prophecy makers are not very trustworthy. If
they were less wealthy, I would have been prone to think some of them
were small time grifters. Since I have been tracing the field of tech
for a certain number of years, I think I have read about CEOs giving
testimonies in front of court, which I would say were not aligned with
the truth too much, maybe even knowingly so, and getting away with
it. Or selling product while probably knowing it was faulty. Frankly,
guys similar to those earlier guys are now promising me a better
future. Oh really.

About mathematician being able to start a wholly new road - I think we
had miscommunication. I never meant a road built nowhere, disconnected
from other roads - this would have been useless. I meant more like it
is easy to build road around the mountains, but one day someone builds
one road straight throu them and thus a new way of mathematics is
born. Or extends one road even further. Existing roads are not
nullified, AFAIK. I think I am with Brent except I do not wait for
coming of AI. But I will be glad to be wrong.

[John Clark]

On Fri, Dec 12, 2025 at 7:37 AM 'Tomasz Rola' via Everything List <everyth...@googlegroups.com> wrote:

>>I would say that getting a score of 118 on the Putnam is FAR beyond theabilities of 99.99+% of the humans on this planet; so "superhuman" would not be a completely inaccurate word to describe such an ability. 

> Sure, solving more problems should be more difficult and would require
bigger ability - in this particular field, i.e. problem solving.

Problem solving is more than just a "particular field";  intelligence is a measure of how good something is at problem solving.    

> while a horse is stronger than me, so t has bigger ability in the field of moving a ton of cargo, it is still no reason to treat a horse as some kind of demigod.

Do you really believe that is a good analogy for what we are currently observing in the field of AI?!  

 

> This is not to mean that there has been no progress - there was a
progress, quite impressive progress, happened during more or less
single lifetime.

Over a single lifetime? There has been quite impressive progress in AI during the previous month!  

> it is very hard to double performance of a cluster. You may see an example in wikipedia article about scalability, where is is shown how doubling cpus from 4 to 8 only gives 22% of speed increase (for very specific kind of computation, as described there). 

Recent developments have proven that one of the following things must be true: 

1) The article is flat out wrong. 

2) The article is correct but AI it's not one of the "very specific kinds of computation" that it's referring to. 

>The whole talk about building nuclear plants for powering cluster to run bigger model on it

That's because no matter how smart and efficient an AI is, more power will always enable it to perform more computations and therefore become smarter. 

 

> seems (IMHO) to indicate "they" have hit the wall and cannot easily improve anymore.

Interesting theory, but it's wrong because it disagrees with observations. As Richard Feynman said "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."

> This time, it may be different.

 

It is. This time nobody talks about the Turing Test anymore because AI blew past that benchmark about 3 years ago, and it was considered the gold standard for AI. It took about 70 years to go from the first primitive electronic computer to beating the Turing Test, but since then, during the previous 3 years, I have observed the rate of AI improvement accelerate dramatically.  

John K Clark 

[John Clark]

 Less than two months ago Google introduced Gemini 3.0 and it blew past all previous benchmarks and became the smartest AI in the world, then just a few weeks later Anthropic introduced Claude opus 4.5 and it blew past all the previous benchmarks and became the smartest AI in the world, then just yesterday GPT 5.2 was introduced and it blew past all the previous benchmarks and became the smartest AI in the world. If that's not what the start of the Singularity is supposed to look like then what in the world is it supposed to look like?

John K Clark