Machine learning in trading: theory, models, practice and algo-trading - page 3746

 
fxsaber #:

The publication of unsolved mathematical problems provided a tremendous stimulus for the development of new mathematical theories, the discovery of previously unknown branches of mathematics and other research findings. Mathematicians tried their hand at tackling well-known problems.


AI marketing is destroying this mechanism. Unfortunately, this is a fact. It was precisely the unsolved problem that brought enormous benefits to mathematics worldwide. It is a pity that this is not unfolding according to Perelman’s scenario, but to suit the purposes of AI marketing. A dark day for mathematics.

In my humble opinion, all means are valid when it comes to solving problems. The use of computers to advance pure mathematics already has a rich history. It has been half a century since the four-colour problem was solved in this way. A complete classification of simple finite groups would have been impossible without computers.

In itself, the emergence of new possibilities in this field with the development of AI can only be welcomed. But using this for PR that fills people’s heads with all sorts of absurd ideas is utterly repugnant.

 
Aleksey Nikolayev #:

The emergence of new opportunities in this area as a result of developments in AI can only be welcomed in itself.

It seems they’ve squandered 15 million USD on solving the Millennium Problem. That’s probably a record-breaking waste.

They’ve destroyed the growth of one of the most beautiful branches of mathematics for the sake of PR. And they’re ready to keep chipping away at the tree of maths. Blasphemy met with applause.


Perelman’s autistic approach to mathematical research no longer seems quite so abnormal, given his natural secrecy. Aggressive AI marketing is now creating gags as well...

 
fxsaber #:

It seems they’ve blown 15 million USD on solving the Millennium Problem. That must be a record-breaking waste.

They’ve destroyed the growth of one of the most beautiful branches of mathematics for the sake of PR. And they’re ready to carry on chipping away at the tree of maths. Blasphemy met with applause.

There’s also been a bit of a scandal over the possible theft of results by an OpenAI employee who was working on the problem privately (but using AI).

fxsaber #:
Perelman’s autistic approach to mathematical research no longer seems so abnormal, given his natural secrecy. Aggressive AI marketing is now even creating gags…

In my humble opinion, Perelman is autistic only in relation to mainstream society. His mathematical socialisation is perfectly normal. That is precisely why, in my view, the attempt to steal his results failed.

However, with the current level of AI development, the possibility of scientific results being stolen is reaching a whole new level. And it is completely unclear how one can stand up to corporate thieves – solidarity amongst scientists may well prove useless here.

 

I asked the AI chatbot to explain the Navier-Stokes equations:

What about OpenAI’s solution to the Navier–Stokes problem? Is it a genuinely original solution, or is it a compilation of the vast body of literature on the subject?

AI chatbot’s response:

The situation surrounding OpenAI’s solution to the Navier–Stokes problem, announced in September 2026, is a complex mix of a major technological breakthrough and a serious ethical scandal within the scientific community. [1, 2, 3]
It is impossible to give a definitive answer as to whether this is an ‘original solution’ or a ‘compilation’, as it combines features of both approaches. Mathematicians agree that the proof contains a genuine mathematical result; however, the path to it was effectively paved by the people whose work the AI utilised. [1, 2]
How does OpenAI’s solution work?
The company stated that its in-house model (which outperforms GPT-6 Astra) solved the problem in just 88 hours by running a multi-agent system comprising 10,000 autonomous AI agents. The agents exchanged millions of messages, sifting through billions of tokens and testing hundreds of proof variants. [1, 2, 3, 4]
  • What has been proven: The existence of a ‘blow-up’ (singularity) within a finite time in the three-dimensional Navier–Stokes equationshas been demonstrated . In other words, under certain conditions, the flow velocity can tend towards infinity, which mathematically refutes the constant smoothness of the solutions. [1, 2, 3]
  • Verification: The result has already undergone automatic verification in the Lean proof formalisation system , which makes it mathematically rigorous and correct. [1, 2, 3]

Why is this referred to as ‘compilation’ or even ‘theft’?
The main controversy lies in the fact that OpenAI did not start from scratch, but instead made use of the interim results of real-life mathematicians: [1, 2]
  1. The basic mathematical foundation: Both OpenAI and independent researchers drew on the revolutionary strategy of the Spanish mathematicians Diego Córdoba and Luis Martínez-Soroa, who radically changed the approach to tackling the Navier–Stokes problem. Without their original theoretical framework, AI would not have been able to find this direction. [1]
  2. Data leak scandal (Codex): Twelve hours before OpenAI’s announcement, mathematicians Tristan Buckmaster ( New York University) and Levent Alpöge ( an employee at Anthropic) announced a breakthrough in a related field — the Euler equations. For the past year, they had been carrying out calculations and drafting papers within the OpenAI Codex platform . Buckmaster directly accused OpenAI of having intercepted their ideas from their user session logs, recognised a promising avenue (applying an external force to create an ‘explosion’) and ‘crushed’ the problem with colossal computational power. [1, 2, 3, 4, 5, 6]
  3. OpenAI’s response: OpenAI acknowledged that, a few days before publication, ‘rumours had reached them’ about a forthcoming solution by Bakmaster and Alpöge, after which they urgently mobilised their agents. The company claims that their model did not read the mathematicians’ user sessions directly, but could not rule out the possibility that anonymised log data from Bakmaster and Alpöge had found its way into the training dataset for this new model. [1, 2, 3, 4]
Conclusion: original or compiled?
This is an original analytical proof obtained by brute force based on other people’s ideas. [1, 2, 3]
AI did not invent a new mathematical philosophy. The model took the ready-made strategy of Córdoba–Martínez-Soroa, probably picked up on the direction of travel from Buckmaster and Alpogé, and, with the help of terawatts of energy and 10,000 agents, broke through a barrier in a couple of days that would have taken humans decades to overcome. The mathematical calculations of OpenAI and Buckmaster themselves differ; in other words, the neural network generated its own unique path, but it was ‘guided’ towards the goal by its human authors. [1, 2, 3, 4, 5, 6, 7]
OpenAI has already announced that, due to the controversial nature of the discovery, it does not intend to claim the $1, 000,000 Millennium Prize from the Clay Institute. [1, 2]
If you’re interested, you can check out OpenAI’s official breakdown or read a detailed analysis of the scientific debate in Quanta Magazine. Would you like to find out more about exactly where the evidence presented by the AI and that of human mathematicians diverged?
AI Has Solved One of Math’s $1 Million Millennium Prize Problems | Quanta Magazine
AI Has Solved One of Math’s $1 Million Millennium Prize Problems | Quanta Magazine
  • www.quantamagazine.org
On the morning of Tuesday, September 8, mathematicians at OpenAI announced that a group of 10,000 autonomous AI agents under their direction, running on an advanced model not available to the public, had found a “singularity” in the Navier-Stokes equations in three dimensions — thus resolving one of the six remaining Millennium Prize Problems...
 
fxsaber #:

It seems they’ve blown 15 million USD on solving the Millennium Problem. That must be a record-breaking waste.

The following figures are interesting for comparison.

  • How many man-hours of thinking does that amount to, given the average rate at which the human brain generates ‘tokens’?
  • How many man-hours of existence would that be, given the average energy consumption of the human body?
And if these figures are astronomical, then we can speak of the super-efficiency (perhaps unattainable with current technologies) of human intelligence, as its results would be difficult to explain away as mere statistical anomalies.
 
fxsaber #:

The following figures are worth noting for comparison.

  • How many man-hours of thought does this amount to, given the average rate at which the human brain generates ‘tokens’?
  • How many man-hours of existence would that be, given the average energy expenditure of the human body?
And if these figures are astronomical, then we can speak of the super-efficiency (perhaps unattainable with current technologies) of human intelligence, as its results would be difficult to explain away as mere statistical anomalies.

These are, however, very specific man-hours – those of unique specialists, the training of whom has required a great deal of resources, which must also be taken into account. Moreover, it takes not just one person, but several schools of thought spanning several generations.

In some respects, the difference between ordinary mathematicians and AI mathematicians is small – they both need the same ‘shoulders of giants’ to stand on, and so on.

In my view, the costs will be roughly comparable, but the big question is how to account for the infrastructure costs required to support both mathematicians and AI.

From a statistical point of view, it all depends on the distribution used. And here we might recall Taleb, who argues that some areas of human activity are described by normal distributions, whilst others are characterised by heavy-tailed distributions such as the Pareto distribution.

 
Aleksey Nikolayev #:

These are, after all, specialised man-hours – those of unique specialists whose training has required a great deal of resources, which must also be taken into account.

There’s no need, as we don’t factor in development costs for AI.
 
fxsaber #:
There’s no need, as we don’t factor in development costs for AI.

In that case, we simply need to calculate it based on average grant amounts. For two people solving the problem over the course of a year, that works out at around 0.2 million. That amounts to a nearly hundredfold advantage.

This could be attributed to the novelty of the technology, as was the case, for example, with aluminium, which was initially used for jewellery.

 
Aleksey Nikolayev #:

In that case, you simply need to work it out based on the average grant amounts. For two people who have solved the problem within a year, that works out at around 0.2 million. That works out as a nearly hundredfold advantage.

It’s better to use physical units. For example, in W*h. Or perhaps in ‘tokens’.

 
fxsaber #:

It’s better to use physical units. For example, in W·h. Or in ‘tokens’.

If measured in W·h, the difference is more than 2,000-fold. But if we take into account that energy from food is more expensive than from the mains, then it’s about 25-fold.

If we use ‘tokens’ as a rough measure, then it’s almost 5,000 times.

We’re waiting for artificial OI to reach the level of AI chatbots. It runs on glucose.