Summary

World’s Largest Math Proof Solved. And It Takes Up 200 Terabytes

Jan 29, 2021 | 🚀 Fathership

It’s the largest math proof. A supercomputer solved it in just 2 days. And it’s 200 terabytes.

Yes, 200 terabytes. That’s the size of the file containing the computer-assisted proof for a mathematical problem that has boggled mathematicians for decades—known as Boolean Pythagorean triples problem.

The proof was compressed into a 68-gigabyte file, meaning anyone who wants to can download, reconstruct, and verify all the information embedded onto it. And individuals can do so, if they have the space processor time, in just about 30,000 hours.

The 200 terabyte file ultimately beats a previously established record for the largest-ever computer-assisted proof. It had a size of just 13 gigabytes.

PROBLEM BEHIND THE PROOF

According to Ronald Graham, a University of California, San Diego mathematician and previous record-holder of the then biggest proof, having computers assist in creating proofs for combinatorics problems is quite common. He even offered a prize of US$100 for to anyone that could solve it.

As previously mentioned, the 200-terabyte proof solved a combinatorics type of mathematical problem called the Boolean Pythagorean triples. It asks whether each positive integers can be colored either red or blue, so that a combination of three integers a, b, and c, (Pythagorean Triple) can satisfy the Pythagorean equation, a 2 + b 2 =c 2, wherein none of the integers have the same color.

COMPUTER RUN-TIME

Though the problem presented many allowable ways to color integers in different combinations, the scientists took advantage of techniques and symmetries in number theory to lessen the number of checks that the computer had to do. This step minimized the number of runs performed by the computer by almost 1 trillion.

Two days and 800 parallel running processors later, the Stampede supercomputer of the University of Texas produced the 200 terabyte file. A separate computer program was then used to verify the produced proof.

Despite having cracked the infamous Boolean Pythagorean triples problem, the record-breaking file still fails to provide answers as to why the coloring scheme is possible.

The proof revealed that yes, it was possible to color the integers in multiple ways; however, only up to 7,824. After this point, it’s not possible. This raises more questions: Why is there a cut-off point at 7,825? Why is the first stretch possible?

The team’s findings are featured in the Cornell University online library.

PAP members call on party to embrace diversity and be open to opposing views

Nov 29, 2021 | 🚀 Fathership
Two People’s Action Party (PAP) members have called on the ruling party to embrace diversity and listen to opposing views, with one Member of Parliament (MP), Ms Nadia Ahmad Samdin, going as far as to say that PAP has to fix its "empathy deficit and grow more comfortable with understanding views we disagree with".

The MP for Ang Mo Kio Group Representation Constituency (GRC) was among some party activists who spoke at the annual PAP convention on Sunday (Nov 28). There were about 2,000 party activists as well as members from the National Trades Union Congress (NTUC) who attended the event both physically at Suntec Convention and Exhibition Centre and online.

Ms Gho Sze Kee, branch secretary of the party’s Bukit Timah branch, also talked about how the party needed to introduce a diversity of perspectives to avoid the dangers of groupthink and being part of an echo chamber.

Addressing fellow party activists in her speech, Ms Nadia acknowledged that there is a tendency for people to live in “bubbles”, which refer to how individuals are often surrounded by others who look or think the same way as them, and that these “bubbles” have led to social divisions.

And these differences have played out online in the way party members have responded to opposing views as if they were threats.

However, she urged party members to be conscious of their own inherent biases and not view these differences as a threat, but as opportunities to have hard conversations.

“I hope we have them, and in listening, be at least open to the possibility of changing our minds,” she added.

“More than any trait during this time, I call for empathy that goes two ways. Empathy should drive us to amplify voices of others, to join forces for a shared cause, for our future.

“We have always been a party of action, and empathy is how we will continue to stay relevant, and continue to take meaningful action for our fellow Singaporeans.”

Recounting her own experience as a party activist since 2012, Ms Gho, 42, said PAP’s biggest pressing need is to ensure that it renews its members at every level of the party’s hierarchy, and not only in the candidates it fields during a general election.

Citing some branch-level statistics, she said that there are only 12 branch secretaries who are female, compared with 81 who are male.

“We need to ensure our party’s membership at the branch level truly reflects the diversity of Singapore. And we have to make sure that diversity counts when anticipating ground needs, giving inputs to policy formulation, and communicating our messages to our voters,” said Ms Gho.

When asked by reporters later if her point about PAP needing to embrace people from diverse backgrounds extends to people from the lesbian, gay, bisexual and transgender community, Ms Gho agreed.

Recurring theme

The need to embrace people from diverse backgrounds and different viewpoints was a recurring theme at Sunday’s party convention.

PAP’s secretary-general Lee Hsien Loong, who is also Singapore’s Prime Minister, made similar points in his speech.

He had said that the party must show that it is not afraid of opposing views or being challenged, and that voters today want to see more debate, contestation and questioning of established ideas.

“We welcome good ideas, regardless of who proposed them… We also have to rebut wrong views, if possible gently, but when necessary firmly,” said Mr Lee.

Speaking to reporters after the event, MP for MacPherson ward Tin Pei Ling said that embracing diverse viewpoints would strengthen trust.

“It’s not just me pushing things to you and you have to accept it, or I just say things that you like to listen. But I explain to you so that even if we may not see eye-to-eye 100 per cent on everything, you know where I am coming from, that it’s not self-serving,” she added.

“And so, it comes back to what are we in politics for? It’s about serving people. And if that’s the case, then, having that empathy, bridging those differences, listening to people and to willingly engage and see whether we can have a midpoint perhaps, and letting you know where I come from. I think that’s important.”

Also speaking at Sunday’s convention was Mr Ling Weihong, 40, branch secretary of Sengkang Central, which is currently under the Workers’ Party.

He talked about the difficulties operating in an opposition ward, but said that his team would continue to work to win back Sengkang GRC, though he acknowledged that it would be an uphill task.

Representing the trade unions, Mr Sanjeev Tiwari, general secretary of the Amalgamated Union of Public Employees, talked about the need to reinforce the strong ties between NTUC and PAP.

He said the collaboration between both organisations is mostly happening within the leadership level and that it needs to be extended to all members of both organisations.