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In the Bronx, the city’s chief executive accused the GOP nominee of governing by punishment, with the Nov. 3 vote nearing

• Terence Tao, now a UCLA professor, earned his doctorate in mathematics at 20.
• The prodigy said his work is changing in the age of AI.
• With AI tools doing the legwork, math is no longer "heroic," Tao said.

AI is upending mathematics. For one top professor, the issue is just as spiritual as it is practical.

Terence Tao, a renowned professor at UCLA, said in a recent podcast appearance that the "romantic era" of math is over, thanks to AI tools capable of solving hundreds of problems with some simple prompting.

Now, he said, even leading scholars like him are reduced to sorting through reams of AI-generated proofs, instead of doing the "heroic" solving themselves.

"We are moving to an industrial era where math will become much more large-scale," Tao said in an interview this week on Numberphile, a YouTube channel dedicated to math.

"We are entering an era where exciting new things are possible, but some things are being lost," he added.

OpenAI began its brusque push into the field by solving the Navier-Stokes equation in early September, one of math's millennium problems.

The revelation that AI had cracked it caused consternation from many a math geek. Some mathematicians also expressed frustration that while the AI model might have solved the problem, it didn't show its work, leaving them with the less celebratory task of verifying it.

Then, earlier this month, OpenAI said it cracked another 700 outstanding problems. A math professor at New York University told CNBC that the company's release had derailed work by early-career mathematicians.

"We've had whole research programs wiped out on Tuesday by their dump," the professor, Tristan Buckmaster, said at the time.

In a separate brouhaha in September, OpenAI backed out of a sponsorship for a so-called AI "mathathon" — an event organized by undergraduates at Caltech, where participants were encouraged to use AI to solve equations — after complaints from a group of more senior academics.

Event organizers told Business Insider at the time that their professors were sorely out of touch with the field's trajectory.

"We look to the future, and we don't even know if there's going to be grad school open positions by the time we get to Ph.D," one organizer, Caiman Moreno-Earle, said.

Though OpenAI has said it is taking steps to ensure human academics retain their role in this new era, some researchers and professors are already forecasting their possible obsolescence.

Tao isn't as much of a doomer as some of his colleagues in the field. However, he did say in the interview that the stories math nerds tell themselves may not mean so much in the future.

"We have these sort of mythological stories," he said in reference to the tale of Sir Andrew Wiles, who famously spent seven years isolated in his attic solving a single difficult equation.

"There was something romantic about sort of the heroic age," Tao said.

The G.O.P. will not always be focused around the strong personality and charisma of Trump.

The European Union and Turkey are preparing high-level talks before the end of October in an attempt to revive negotiations over Cyprus, following an initiative by United Nations Secretary-General António Guterres.

Cypriot President Nikos Christodoulides announced the planned meeting on 16 October during the European Council summit in Brussels, saying discussions would address both the resumption of negotiations over the island’s division and the possibility of improving relations between Ankara and the EU.

The initiative follows diplomatic contacts in New York involving Guterres, European institutional leaders and the Cypriot government. However, renewed differences over the conditions for negotiations have already cast doubt on whether the process can produce substantial progress.

On Sunday, 18 October, Christodoulides accused Turkish Cypriot leader Tufan Erhürman of imposing preconditions before formal negotiations could resume, particularly concerning arrangements for a rotating presidency in a reunited Cyprus.

The disagreement underlines the difficulties facing an initiative intended to reconnect the UN peace process with the EU’s broader relationship with Turkey.

Brussels seeks a negotiating role

Christodoulides said the planned meeting between the EU and Turkey would examine how to establish the necessary conditions for negotiations to restart within the previously agreed UN framework.

He indicated that any improvement in EU–Turkey relations would be linked to progress over Cyprus.

The president’s announcement in Brussels follows months of diplomatic consultations involving the Commission, European Council and UN.

European Commission President Ursula von der Leyen and European Council President António Costa have urged Turkish President Recep Tayyip Erdoğan to support the renewed peace initiative.

Turkey’s relationship with the EU encompasses trade, customs cooperation, migration and regional security. Ankara remains an EU candidate country, although accession negotiations have been effectively stalled for years.

Cyprus remains one of the principal obstacles to any substantial improvement in that relationship.

The island has been divided since Turkey’s military intervention in 1974. The internationally recognised Republic of Cyprus joined the EU in 2004, but EU law remains suspended in areas where its government does not exercise effective control.

The self-declared Turkish Republic of Northern Cyprus is recognised only by Turkey.

Disagreement over political equality

The UN has traditionally sought a settlement based on a bizonal, bicommunal federation with political equality between the Greek and Turkish Cypriot communities.

Negotiations collapsed at Crans-Montana in Switzerland in 2017 amid unresolved disputes over security guarantees, political representation, territory and the presence of Turkish troops.

Erhürman, who became Turkish Cypriot leader in 2025, has expressed support for renewed negotiations within a federal framework. However, he wants assurances about political equality and the structure of future talks.

The latest dispute concerns whether the principle of a rotating presidency between the two communities should be accepted before negotiations resume.

Christodoulides rejected that demand on 18 October, arguing that substantive questions should be negotiated together rather than settled in advance.

The Turkish Cypriot leadership regards rotating executive power as an essential element of political equality, while the Greek Cypriot side objects to making agreement on that arrangement a prerequisite for restarting discussions.

The disagreement has emerged despite recent efforts by the United Nations to improve relations between the communities.

In a statement issued on 13 October, the UN confirmed that Christodoulides and Erhürman had met in Nicosia and agreed to continue discussions, including participation in bicommunal initiatives.

The two leaders subsequently attended a joint event in Pyla, although their public differences persisted.

Turkey’s position remains decisive

A Cyprus settlement would require agreement not only between the island’s communities but also on Turkey’s military presence and the system of security guarantees established at independence.

Ankara has long maintained that Turkish Cypriots require effective political equality and credible security arrangements.

Greek Cypriot leaders argue that the continuation of foreign intervention rights and Turkish military deployments would be incompatible with a fully sovereign and reunited state.

The EU cannot resolve those differences independently of the UN process, but it can influence the economic and institutional framework within which a settlement might operate.

A comprehensive agreement would affect property ownership, trade, customs arrangements, border administration and the application of European law throughout the island.

The European Commission has sought a greater role in supporting the UN-led peace process, reflecting Brussels’ interest in progress towards a settlement.

Negotiations face immediate test

The UN Secretary-General’s personal envoy, María Ángela Holguín, has warned that the opportunity for renewed negotiations may be narrowing.

Disagreements over diplomatic representation, contacts with foreign missions and the status of Turkish Cypriot institutions have complicated relations between the two communities.

Christodoulides has also referred to a series of proposals intended to advance discussions, including the future of the fenced-off area of Varosha. Their full contents have not been publicly disclosed.

The proposed EU–Turkey meeting offers a separate diplomatic channel through which Brussels can assess Ankara’s willingness to support renewed negotiations.

No final date, detailed agenda or list of participants had been publicly confirmed by 18 October.

The immediate test will be whether the parties can agree on the basis for formal talks without attempting to settle disputed constitutional questions before negotiations begin.

"The trend this year continues," Zelensky said, "Since the start of fall, our warriors have liberated more territory than the Russians have managed to capture. The same was true at other points this year."