OpenAI published the research on August 1, using the name Astra for its next major model family. The work spans several areas of advanced mathematics, including group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography and extremal combinatorics.
The research was released as a 249-page collection of manuscripts, accompanied by machine-checkable certificates for each of the 10 results. The problems were not routine mathematical exercises: several had remained open for decades and were regarded as significant questions within their respective fields.
Among the reported breakthroughs are a construction demonstrating the existence of non-sofic groups, a disproof of Connes's rigidity conjecture in the theory of von Neumann algebras, and an improved general upper bound for sphere-packing density in high dimensions. The latter improves upon a bound that had remained in place since 1978.
Three of the problems also came from the extensive collection of unsolved questions associated with mathematician Paul Erdős.
The announcement builds on a result reported in May, when the same model family was said to have disproved the Erdős unit distance conjecture, an 80-year-old problem in discrete geometry that had resisted sustained efforts since 1946. Fields Medalist Tim Gowers said he would have recommended the proof for publication in a leading mathematics journal without hesitation. A group of nine mathematicians, including Gowers and Noga Alon, subsequently published a companion paper presenting the proof in a more accessible form for human mathematicians.
Thomas Bloom, who maintains the ErdÅ‘s problem catalogue, described the August results as “big news” and said they were even more significant than the earlier unit distance result. OpenAI researcher Noam Brown offered a more cautious assessment: “Sadly, no Millennium Prize Problems (yet).”
AI research announcements have frequently faced questions over whether reported achievements can be independently evaluated. Benchmarks can be influenced by training data, demonstrations can be selectively presented, and external researchers may have limited ways to reproduce proprietary results.
Astra's mathematical work takes a different approach because the reported proofs were formalized using Lean, a proof assistant designed to verify mathematical arguments step by step. OpenAI also released the certificate files on GitHub under an open license, allowing researchers to download them and run the verification process themselves.
If an individual step does not logically follow from what came before it, the checker rejects the proof. The process therefore does not depend on trusting the organization that produced the result or on subjective interpretation of the argument.
Traditionally, a major mathematical proof goes through peer review, with human experts potentially spending months examining its reasoning before the wider community accepts the result. Machine verification can dramatically shorten the technical verification stage, allowing the validity of a formalized argument to be checked almost immediately.
That distinction makes the Astra announcement different from a conventional AI benchmark. A machine-verified proof can be independently checked even when the underlying model itself is not publicly available.
There are, however, important limitations to the claims.
The selection of the 10 problems was controlled by OpenAI, meaning the published results may not represent the full range of problems the model attempted. The reported $2,000 figure also relates to the successful results rather than the total cost of all experimentation, making it more accurately a measure of the cost of producing the published results than the complete cost of mathematical discovery.
OpenAI researchers also participated in preparing the papers and formalizing the arguments, while the company maintains that Astra generated the mathematical content. Because Astra itself is not available to external researchers, independent reproduction of the model's discovery process is not currently possible.
AI critic Gary Marcus described the release as impressive but substantially oversold. Some mathematicians have also suggested that further scrutiny could reveal that only a portion of the 10 problems represent genuinely unexpected breakthroughs, while others may prove to have been problems that were technically approachable but had not yet received the necessary attention.
Even with those qualifications, one feature remains significant: the results can be mechanically verified. Whether or not the problem selection was optimized for success, a result accompanied by a formal certificate is fundamentally different from an AI-generated claim that cannot be independently checked.
The larger implication may extend well beyond mathematical research.
AI systems can generate large quantities of content and technical output, but organizations often struggle to validate that output at the same scale. Human review may work for a handful of documents or analyses, but it becomes increasingly impractical as AI-generated output grows.
Some industries have already addressed this challenge by building automated verification into their workflows.
Chip design is a prominent example. Formal verification systems can mathematically establish whether a circuit meets its specifications, providing an automated layer of assurance that existed well before generative AI became widely used.
At Computex in May, Cadence said it had expanded its design agent toward full autonomy. The system reportedly runs hundreds of simulations through the company's Jasper formal verification engine, reducing a validation cycle that previously took around five weeks to less than a day. Synopsys offers a similar category of technology through VC Formal, which uses static analysis to verify designs rather than relying solely on individual test cases.
The economics are straightforward: when a machine-generated answer can be checked automatically and inexpensively, mistakes become far easier to detect and correct.
The same principle applies to areas such as cryptography, safety-critical software and hardware verification, where formal proof or automated checking is already part of the development process.
As AI systems become capable of generating increasingly sophisticated output, the ability to verify that output may become more important than the ability to generate it.
The central shift is therefore not simply that AI can produce difficult answers more cheaply. It is that the bottleneck is moving from generating an answer to proving that the answer is correct.
Phishing is no longer limited to technically skilled criminals building fraudulent campaigns from scratch. Through phishing-as-a-service (PhaaS), attackers can rent ready-made infrastructure and tools that allow them to impersonate trusted organisations, harvest credentials and target victims at scale.
Phishing attacks use social engineering to persuade victims to surrender sensitive information. The lure can arrive through an email, text message, phone call, QR code, fake website or malicious application, often impersonating a bank, employer, delivery company or another trusted entity. Stolen passwords, financial details and authentication information can then be used for account takeovers, fraud, identity theft or further attacks.
The emergence of PhaaS has made this process considerably easier.
PhaaS lowers the barrier for cybercriminals
Instead of developing an operation independently, criminals can purchase packages containing fake login pages, legitimate-looking email templates, phishing-site hosting, target lists and setup instructions. Some providers also offer technical assistance and campaign-management capabilities.
The model mirrors legitimate software-as-a-service businesses, except the product is designed to facilitate cybercrime. Microsoft describes the wider cybercrime-as-a-service economy as increasingly commercialised, with specialised services allowing criminals to outsource different parts of an attack.
This creates a multiplier effect. Criminals with limited technical expertise can deploy infrastructure developed by more experienced operators, allowing phishing campaigns to reach far more people than a small group of skilled attackers could target independently.
The threat is therefore not simply that individual phishing messages are becoming more convincing. It is that the number of people capable of launching campaigns is increasing.
PhaaS is evolving beyond password theft
Modern phishing services can also target authentication sessions rather than simply collecting usernames and passwords.
Adversary-in-the-middle attacks, for example, place attacker-controlled infrastructure between a victim and the legitimate authentication service. The victim may still complete the expected login and MFA process, while the attacker attempts to capture authentication information or session tokens that can later be used to access the account.
Microsoft has documented phishing campaigns in which attackers captured tokens generated during legitimate authentication, demonstrating why stolen credentials are not the only concern.
The scale of these operations was illustrated in March 2026 when authorities disrupted Tycoon 2FA, a PhaaS platform that facilitated phishing attacks against nearly 100,000 organisations. Europol said the service generated tens of millions of phishing emails each month and, by mid-2025, accounted for roughly 62% of phishing attempts blocked by Microsoft.
AI is making familiar warning signs less reliable
Artificial intelligence is adding another advantage for attackers by making social-engineering content faster and easier to produce.
Poor grammar and spelling mistakes were once common indicators of phishing. Generative AI can now produce polished messages in seconds, allowing criminals to create more convincing communications and adapt them to different targets. Microsoft has reported that cybercriminals are using AI to automate phishing and generate synthetic content.
Users therefore need to focus less on whether a message is grammatically correct and more on what it is asking them to do.
Unexpected requests for passwords, payment information, verification codes or urgent account actions should be independently verified. Links should be inspected before opening, while sensitive websites are safer to access directly rather than through unsolicited messages. Unexpected attachments should also be treated cautiously.
Defence must account for stolen credentials
Basic security practices remain important, but organisations should also assume that phishing attempts will occasionally succeed.
Unique passwords stored in a password manager can limit the damage caused by credential reuse, while multifactor authentication adds another layer of protection. However, phishing-resistant authentication such as passkeys and FIDO-based methods provides stronger protection against attacks designed to capture authentication information.
Microsoft says phishing-resistant MFA can stop more than 99% of attacks of this type even when attackers possess the password.
Organisations should also monitor unusual account activity, remove unnecessary accounts and minimise user privileges so that compromised credentials do not automatically provide extensive access.
PhaaS has therefore changed more than the technical mechanics of phishing. It has changed who can conduct these attacks and how easily they can be scaled. As criminal infrastructure becomes increasingly commercialised and AI reduces the effort required to produce convincing lures, defending against phishing can no longer depend solely on recognising suspicious messages.
The stronger strategy is to combine user awareness with authentication and access controls designed to limit what happens when a phishing attempt succeeds.
Starting a consulting business can look deceptively simple. You have expertise, you know there are businesses that need it, and unlike a product company, you do not need a warehouse full of inventory before you can start selling.
But turning expertise into a functioning consulting business is another matter.
There is a point when consulting stops being an idea and becomes a business.
It is usually somewhere between sending the first proposal and realizing that knowing how to solve a client's problem is only one part of the job. The founder now has to find the right customers, decide what the work is worth, manage contracts and finances, build a reputation and keep the pipeline moving, often while delivering the work alone.
That makes the first 90 days particularly crucial.
For a new consulting firm, those months are not simply about landing the first client. They are a testing period for the entire business model. Who actually needs the service? What are they willing to pay? Which prospects are worth pursuing? How should projects be priced? And can the founder deliver the work efficiently without creating an operation that collapses as soon as demand increases?
Market research is one of the earliest safeguards. The U.S. Small Business Administration recommends examining demand, market size, competition, economic conditions and the prices customers already pay before committing to a business idea. Competitive analysis can then help a company identify where it can establish an advantage.
For consultants, that process starts with getting specific.
Know exactly what you are selling
"Consulting" is not a niche.
A prospective client needs to understand what expertise is being offered, what problem it addresses and why this particular consultant is equipped to solve it.
That is why specialization can matter so much during the early stages. A consultant who focuses on regulatory compliance for fintech companies, for example, enters the market with a much clearer proposition than one advertising a general ability to "help businesses grow."
A narrow focus also makes research easier. The founder can identify competitors, understand the language customers use to describe their problems and determine whether there is enough demand to support the business.
The goal is not to permanently lock the consultancy into one category. It is to give the market a clear reason to remember it.
The same attention should go to the business name before significant money is spent on branding. Founders should check whether the name is already being used, whether an appropriate domain is available and whether matching social-media accounts can be secured. Legal and trademark availability should also be checked in the relevant jurisdiction.
A polished identity built around a name that cannot be used is an expensive problem to discover after launch.
Your first clients may already know you
A new consultant's first sales pipeline may be much closer than expected.
Former colleagues, previous clients, mentors and professional contacts can become referral sources, particularly when they understand exactly what the new business does.
Consulting Success has reported that 60% of consultants get their first client through referrals from their existing network.
That figure should not be treated as a promise that networking will automatically produce business. It does, however, point to an important reality for new consultants: relationships can be an early commercial asset.
The first 90 days should therefore include deliberate outreach. Reconnect with former colleagues. Tell people what service you are offering. Attend relevant industry events. Join professional or business-owner groups. Speak to people who understand the market you are trying to enter.
The objective is not to turn every conversation into a sales pitch.
It is to make sure that when someone in your network encounters the problem you solve, they know who to call.
Keeping track of these relationships can help, too. A basic customer relationship management system or even a structured contact database can record conversations, potential opportunities and follow-up dates. Networking becomes considerably more useful when it is treated as an ongoing business process rather than a collection of business cards.
Pricing your expertise is harder than selling it
The first proposal can create an uncomfortable question for almost every new consultant: What should this actually cost?
There is no single answer.
Some consultants charge by the hour. Others set a fixed fee for a defined project. Retainers can provide recurring revenue for continuing advisory work, while value-based pricing attempts to connect the fee to the business outcome being created rather than the number of hours spent producing it.
Each approach carries a different risk.
Hourly pricing is relatively straightforward, particularly when the scope of a project is uncertain. Fixed-fee work gives clients greater predictability, but the consultant can lose money if the project expands beyond the assumptions used to calculate the fee. Retainers can create more predictable revenue but require a clear understanding of what ongoing access or services the client is actually receiving.
Value-based pricing can potentially capture more of the economic value created for a client, but it is harder to establish when a new consultancy has limited evidence of its results.
The important thing is not to choose a pricing model simply because another consulting firm uses it.
New founders should track how much time projects actually consume, including meetings, revisions, administration and unpaid communication. They should also account for software, professional services, taxes and other operating expenses.
The SBA recommends calculating startup costs and using break-even analysis to understand how pricing, costs and sales volume interact.
That turns pricing from a guess into a business calculation.
And the model does not have to remain fixed. As a consultancy gains experience, it can adjust its pricing based on the type of work clients value most and the economics of delivering it.
Not every potential client is a real prospect
A large prospect list can look impressive while contributing very little to revenue.
Consultants need to distinguish between companies that could theoretically benefit from their expertise and companies that are actually positioned to buy it.
That means asking whether the organization has the problem, whether the problem is urgent, whether it has a budget, who makes the purchasing decision and whether the consultant has a credible route into the organization.
Financial and business research can make that process more informed.
For U.S. public companies, the SEC's EDGAR system provides access to company filings that can reveal information about financial performance, operations, risks and other corporate developments.
Private companies require different sources of information, including company websites, industry publications, professional networks and available business databases.
The objective is not to conduct an exhaustive investigation of every lead. It is to avoid spending valuable time chasing prospects that are unlikely to become paying clients.
For a solo consultant, that distinction can directly affect revenue. Time spent pursuing an unsuitable prospect is time that cannot be spent delivering client work, improving an offer or finding a better-qualified lead.
The tools behind the expertise matter too
Consulting is often presented as a knowledge business, but much of the actual work happens inside ordinary productivity software.
Spreadsheets, presentations, project-management platforms, customer relationship systems and document-management tools can become part of a consultant's daily workflow.
Management Consulted COO Namaan Mian has said consultants can spend around 80% of their day working in Excel and PowerPoint.
The exact proportion will vary considerably between consulting disciplines, but the underlying lesson is useful. A consultant who is excellent at strategy but inefficient at turning analysis into a financial model, presentation or client deliverable can lose considerable time.
Technology also introduces a responsibility that is easy for new consultants to overlook.
Clients may hand an independent consultant confidential business strategies, financial records, employee information, intellectual property or customer data. Secure authentication, controlled access, encrypted storage where appropriate, reliable backups and careful file-sharing practices therefore belong in the business plan from the beginning.
For a technology or cybersecurity consultant, that expectation is even higher. The consultant's own security practices become part of their credibility.
Do not try to be the lawyer and accountant too
Running a consultancy independently does not mean every business function needs to stay with the founder.
Legal and accounting professionals can help establish the structures that allow the consultant to concentrate on client work.
The right business structure can affect taxation, paperwork and personal liability, while contracts can determine how payment, confidentiality, intellectual property and responsibilities are handled between the consultant and client. The SBA recommends considering these structural questions when setting up a business and notes that professional advisers can help with the process.
An accountant can also help establish bookkeeping practices and make sure income and expenses are being tracked properly.
These advisers do not necessarily need to be permanent employees. For a small consultancy, external professionals can often provide support when specific legal or financial questions arise.
What matters is establishing those relationships before a problem forces the issue.
Build accountability into the business
There is one final problem unique to many solo consultants: nobody else is waiting for the work to get done.
The founder may have promised to follow up with prospects, update the website, send invoices, improve a presentation, review finances and develop a new service. Then a client deadline arrives and everything else moves down the list.
An accountability partner can provide a simple counterweight.
That person could be a former colleague, mentor, fellow entrepreneur or another professional encountered through an industry association or business group. A short weekly conversation can be enough to review what was completed, what was missed and what needs to happen next.
The point is not necessarily to find another person who has all the answers.
It is to create a system in which the founder has to answer to someone besides themselves.
The first 90 days are where the business gets tested
A new consultancy does not become sustainable simply because its founder is good at what they do.
Expertise gets the business into the room. Everything else determines whether it can stay there.
The first three months should therefore be used to test the market, sharpen the niche, build relationships, qualify prospects, experiment with pricing and establish the systems needed to deliver work consistently.
That includes the less glamorous work: checking the business name, setting up financial records, understanding legal obligations, learning the software that will be used every day and protecting client information.
The U.S. Small Business Administration describes a business plan as a roadmap for structuring, operating and growing a company, while its startup-cost guidance encourages founders to understand expenses and break-even points before making financial decisions.
For a consultant, the first 90 days can serve the same purpose in practice.
By the end of them, the founder should have more than a website and a client list. They should have evidence about which customers are worth pursuing, which services generate demand, what those services cost to deliver and what the business needs to operate without constantly running on improvisation.
That is the real moment when a consultant gets skin in the game.
The expertise may have been there for years.
Now there is a business behind it.
The researchers conducted an end-to-end experiment involving an attacker-controlled Worker and a victim Worker, with the JWT deliberately stored in the victim's memory. According to the research paper, the experiment did not involve accessing any customer information.
Cloudflare said it has already addressed the issue in its production environment by strengthening Dynamic Process Isolation (DyPrIs), integrating the V8 Sandbox and introducing Memory Protection Keys (MPK)-based in-process isolation. The company also said it found no evidence of active exploitation related to the issue during the past three years.
"We demonstrate that the production implementation of DyPrIs was insufficient," the researchers said in the paper.
Cloudflare Workers executes code belonging to multiple tenants using separate V8 isolates within the same operating-system process. Rather than relying solely on strict process-level separation, the platform uses language-level isolation to help maintain faster startup times.
According to Cloudflare, a memory-read attack within a shared Worker process could potentially enable information to leak across tenants. However, the attack requires both the attacker and victim Workers to be placed in separate V8 isolates within the same Worker process.
The researchers said the attacker must control legitimate code within its own isolate. The technique does not rely on native code execution, a V8 vulnerability or a sandbox escape.
Cloudflare Workers also limits access to local timing mechanisms by freezing or reducing the precision of timers during CPU execution. Worker scripts do not have access to shared memory or multithreading. However, the researchers discovered that WebSocket communications could act as a remote timing channel.
They also found that Durable Objects could keep a Worker isolate running continuously for periods ranging from five hours to more than 20 hours. Under DyPrIs, suspicious scripts are moved into a separate process after an invocation ends. The researchers found that long-running Durable Object invocations could remain active before this isolation mechanism was triggered.
Another weakness involved WebSocket-intensive input/output activity. The researchers observed that such activity increased instruction translation lookaside buffer (iTLB) activity, weakening the normalized branch-misprediction signal monitored by DyPrIs and pushing it below the mechanism's detection threshold.
Cloudflare characterized the problem as a limitation in how DyPrIs was implemented. The research paper, however, argued that the weaknesses represented more fundamental limitations of the detection methodology rather than simple implementation errors. The researchers recommended monitoring for such activity during execution and using signals that cannot be suppressed through I/O activity.
The researchers conducted their production testing on Linux servers powered by AMD EPYC Zen 2 and Zen 3 processors. Measurements were intentionally performed at night, when CPU utilization was between 10% and 25%, to determine the highest achievable leakage rate.
According to the paper, heavier system workloads reduced the amount of data that could be leaked, although the attack remained possible at slower speeds under greater CPU load.
The study recorded a peak leakage rate of 12 bits per second with 99.16% accuracy. By comparison, the earlier attack achieved approximately 2 bits per minute.
The latest disclosure arrives nearly five years after Cloudflare and Graz University of Technology (TU Graz) published research detailing a remote Spectre attack against Workers. That earlier work demonstrated a leakage rate of 120 bits per hour and introduced DyPrIs as a defense mechanism.
The 2021 research reported a false-positive rate of 0.61% and concluded that DyPrIs offered, statistically, security guarantees comparable to strict process isolation against the Spectre attacks evaluated at that time.
Cloudflare subsequently outlined additional security hardening measures for Workers in September 2025. The company's mitigations include:
Enhanced DyPrIs: Improvements designed to strengthen the detection capabilities of the existing isolation mechanism.
V8 Sandbox: A security layer designed to restrict transient access to 64-bit pointers.
MPK-based in-process isolation: Worker heaps are placed behind hardware-enforced Memory Protection Keys. Cloudflare said modern x64 systems provide approximately 12 keys that can be used for this purpose. Its architecture combines MPK with the V8 Sandbox and a rotating memory layout to prevent neighboring sandboxes from being assigned the same protection key.
Cloudflare's September 2025 documentation noted that randomly assigning MPK keys would block roughly 92% of cross-isolate access attempts because two isolates could receive the same key. The company said its stricter rotating memory layout eliminates that remaining gap within the threat model covered by the in-sandbox protections.
Microsoft Copilot Personal contains three vulnerabilities that could allow an attacker to execute a malicious prompt with one click and exfiltrate data from connected applications, according to Varonis Threat Labs.
The researchers collectively named the flaws CoSnitch and reported them to Microsoft in December 2025. Microsoft patched the vulnerabilities on August 18, 2026, with the issue tracked as CVE-2026-24301. Varonis said it found no evidence of exploitation in the wild. The research concerns the consumer Copilot service at copilot.microsoft.com and does not establish that the same behavior affected Microsoft 365 Copilot.
Copilot Revealed Its Own Attack Path
Varonis discovered the vulnerability through what it calls "meta-hacking," repeatedly asking Copilot why a prompt could not execute without user interaction. After several refusals containing technical explanations, Copilot eventually disclosed an undocumented "autorun=1" URL parameter, including the conditions and safeguards associated with it.
Researchers constructed the URL as described and found that the supposedly disabled parameter still executed. They combined "autorun=1" with Copilot's existing "q" parameter, which pre-fills the prompt. While "q" alone requires user interaction, the combination automatically triggered the prompt when the page loaded.
Varonis said the prompt then continued executing even if the victim immediately closed the Copilot tab. Its earlier Reprompt research had also used "q" as a one-click Parameter-to-Prompt mechanism.
Existing Permissions Enable Data Theft
The first two CoSnitch flaws form the one-click exfiltration chain. The injected instruction operates with the same capabilities available to a legitimate user prompt and does not grant Copilot additional permissions.
Researchers demonstrated access to connected mail messages, subject lines and sender and recipient metadata; calendar titles, attendees, times and locations; Google Drive filenames and metadata summaries; previous Copilot conversations; and stored memory instructions and user-defined rules.
The retrieved information could be encoded, including with Base64, and transmitted through Copilot's built-in URL-fetching capability to an attacker-controlled webhook. Varonis said the resulting request could resemble Copilot's ordinary web retrieval traffic, potentially making network-level detection difficult.
Separate Memory Poisoning Path
The third vulnerability involves indirect prompt injection through web summarization. A malicious webpage could contain attacker-controlled instructions that Copilot processed and wrote into its persistent memory.
Varonis said such injected memories could survive password changes, session revocation and device re-enrollment until manually removed. The modification reportedly generated no process, file or network activity that conventional security tooling would necessarily flag, although the change remained visible in Copilot's memory interface.
The finding follows earlier Microsoft 365 Copilot memory research by Håkon Måløy and Johann Rehberger. Microsoft has separately said M365 Copilot applies sanitization and prompt-injection checks to memory writes, performs Task Adherence checks on explicit memory updates, and records those changes for security monitoring through audit data and the "MemoryUpdated" field.
Varonis recommends reviewing connected applications, disconnecting unnecessary services, monitoring AI assistants as privileged systems and exercising caution with links that open AI assistants.
The disclosure follows Varonis's RovoBlast research, which identified another one-click attack involving Atlassian's Rovo assistant. Together, the findings demonstrate how URL handling, authorized application access, external content and persistent AI memory can combine into an attack chain without directly compromising the victim's underlying accounts.