On Tuesday, OpenAI released solutions to three significant mathematical problems that have long puzzled researchers. One of these solutions was particularly surprising: it refuted the "exponential time hypothesis" ( Exponential Time Hypothesis, abbreviated as ETH ). This hypothesis has been a long-standing one in computer science and plays an important role in our understanding of which problems are difficult to compute.

Similar to the reaction from the forefront laboratories when they announced their proof results earlier, the scientific community is both excited and uneasy about this. Mathematicians Levent Alp, ge hinted that the solution proposed by OpenAI was built upon existing research; a few hours later, Anthropic also released their own rebuttal to ETH.

However, there has been a change in the approach taken by OpenAI this time. For the three disciplines involved, the laboratory adopted different arrangements for publishing the results: the materials from the mathematics community were directly posted on GitHub; the computer science community formed a working group that demanded the public sharing of proofs and requested OpenAI to fund a conference to discuss these results; the physics community also established a working group to decide how their findings should be published.

Professor Ryan Williams from the Massachusetts Institute of Technology is responsible for organizing the computer science community's response to this new discovery. Williams's research focuses on computational complexity issues. He has previously criticized the practices of OpenAI, and referred to that company's "proof dumping" earlier this October as a "DDoS attack" on mathematicians.

However, he told TechCrunch that he agreed to collaborate with these cutting-edge laboratories to help guide ideas that are crucial to that field. OpenAI asked him to work with computer scientists Russell Impagliazzo and Ramamohan Paturi from the University of California, San Diego to help interpret this research findings; the latter two first proposed ETH in 1999.

Their first step was to issue an open letter, calling on scientists interested in these issues to provide feedback and to discuss the guidelines that AI should follow when participating in related research.

Williams to TechCrunch said: 'Some parts of the OpenAI evidence might be considered routine, but there are indeed one or two sections that seem to have been written by 'extraterrestrial visitors'. It is these parts that make me think, wow, this requires the entire community to study together.'

Do you understand P vs NP?

ETH belongs to a broader class of problems, namely P vs NP. For decades, this problem has been driving the development of computer science and many other fields. Simply put, researchers want to figure out: for any problem whose answer can be easily verified (NP), can it also be easily solved (P)?

A simple example is the Sudoku game: once the puzzle is solved, people can quickly verify whether it is correct, but finding the solution in the first place is quite time-consuming. This situation exists in many important problems, and this understanding is also the basis of cryptographic systems: when you have a key to encrypted information, you can decrypt it; however, cracking an effective password usually takes too long, making it impractical.

However, scientists have not yet proven whether this is always the case. Williams says, "P = NP means that not only can you verify a Sudoku solution when it exists, but you can also generate it directly. What P = NP argues is that for every problem you can verify quickly, if you can verify it quickly, you can also solve it quickly. That sounds incredibly good."

This is also why most scientists assume that P ≠ NP, and ETH is one of the pieces of evidence supporting this conclusion. It essentially means that for a certain type of tricky logical puzzle, even the fastest computer algorithms will take an exponentially longer time to find a solution as the number of variables increases.

According to OpenAI and Anthropic, their models propose algorithms that can solve these puzzles in "sub-exponential time," which is faster than what was previously thought to be possible. If this is true, they may have proven that ETH is incorrect – in scientific terms, they have "refuted" it – and perhaps opened up a path towards a more general implementation of the P = NP algorithm.

Williams said, "Perhaps every computer scientist should slightly increase the weight given to the possibility of P = NP, but the amount by which each person increases it may vary. I indeed believe that this has, to some extent, shaken our past intuitions about how manageable these difficult NP problems really are. I also think that this is most likely not the final answer yet. I don't believe that the algorithm OpenAI will be the best algorithm you can ultimately obtain."

The next steps for computer scientists

Williams indicates that the long-term stability of ETH is due to the fact that many scientific papers over the past decade have incorporated it as a fundamental assumption; if the claims made by AI laboratory regarding their own proof of its errors ultimately hold water, then these papers will need to be re-examined.

He said, "This is also one of the reasons why I am requesting, or rather, pushing for OpenAI to support the holding of a related meeting – it will affect the work of many researchers. In addition to understanding these algorithms, we also need to figure out what will happen next; we also need to understand what those foundations on which we have built our work up to now should be now."

Before the concerns at the scientific level, there are also issues related to network security. Williams indicates that the improved algorithm may mean that some password systems that rely on a specific key length can be considered obsolete. Therefore, one of the first questions he raised to OpenAI, the scientific leader Dan Roberts, was, "Have they checked whether this will affect any password systems... Is there anything that has become insecure now? Obviously, they have checked, and they are quite confident that this does not... mean that any cracking has occurred."

This brand-new paradigm of scientific discovery, driven by AI, is still in the process of development. However, Williams states that despite genuine concerns, especially regarding how to cultivate the next generation of scientists, he remains optimistic. As a computer scientist specializing in advanced mathematics, this transition may be easier for him to adapt to than for pure mathematicians.

However, he still stated that AI "is forcing people to become more ambitious in the type of work they engage in and to think more deeply: if what I studied in the past has now become what AI considers low-hanging fruit, then how can I raise the bar to ask the kind of scientific questions I truly want to ask?"