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🚨 FULL CONVERSATION Fields medalist Terry Tao sits down with Math Inc's Jesse Michael Han and Jared Duker Lichtman for a conversation on the future of mathematics. "I got convinced that this was the future of mathematics [...] It's a different style of writing proofs that actually is in... show more

Math, Inc.

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332,836 views • 7 months ago •via X (Twitter)

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💎 FULL CONVERSATION 💎 Renowned professor of mathematics Emily Riehl at Johns Hopkins University sits down with Math Inc's Jesse Michael Han and Jared Duker Lichtman for a conversation on the future of mathematics. “Formalization has completely changed my view of what mathematics is.” “It acquainted me with a different approach to the foundations of mathematics.” “It helps you think and speak more precisely, often at this dream stage where new ideas are being developed.” “This is what I think the future of mathematics could be.” Watch the full video on YouTube:

💎 FULL CONVERSATION 💎 Renowned professor of mathematics Emily Riehl at Johns Hopkins University sits down with Math Inc's Jesse Michael Han and Jared Duker Lichtman for a conversation on the future of mathematics. “Formalization has completely changed my view of what mathematics is.” “It acquainted me with a different approach to the foundations of mathematics.” “It helps you think and speak more precisely, often at this dream stage where new ideas are being developed.” “This is what I think the future of mathematics could be.” Watch the full video on YouTube:

Math, Inc.

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💎 Emily Riehl, renowned professor of mathematics at Johns Hopkins University: “Formalization has completely changed my view of what mathematics is. Actually most of that is because it acquainted me with a different approach to the foundations of mathematics.” Full conversation with Math, Inc.’s Jesse Michael Han and Jared Duker Lichtman soon.

💎 Emily Riehl, renowned professor of mathematics at Johns Hopkins University: “Formalization has completely changed my view of what mathematics is. Actually most of that is because it acquainted me with a different approach to the foundations of mathematics.” Full conversation with Math, Inc.’s Jesse Michael Han and Jared Duker Lichtman soon.

Math, Inc.

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🚨 BREAKING: Fields medalist Terry Tao on how mathematics will change: “When these tools are perfected, we will change the way we do mathematics. If there's a drudgery or a big computation, we'll just hit it with all our technology and say: 'By Gauss, you can get from here to there,' and now we just keep going. So we can blast through all these obstacles that we avoid almost subconsciously. If you look at what we miss, it's the missed opportunities, and that percentage of the overall opportunities is huge.” Full conversation with Math, Inc.’s Jesse Michael Han and Jared Duker Lichtman coming soon.

🚨 BREAKING: Fields medalist Terry Tao on how mathematics will change: “When these tools are perfected, we will change the way we do mathematics. If there's a drudgery or a big computation, we'll just hit it with all our technology and say: 'By Gauss, you can get from here to there,' and now we just keep going. So we can blast through all these obstacles that we avoid almost subconsciously. If you look at what we miss, it's the missed opportunities, and that percentage of the overall opportunities is huge.” Full conversation with Math, Inc.’s Jesse Michael Han and Jared Duker Lichtman coming soon.

Math, Inc.

137,679 views • 7 months ago

Is math something humans invent—or something we discover? And why does it describe the universe so uncannily well? In this episode of Uncommon Knowledge, Peter Robinson sits down with mathematicians David Berlinski, Sergiu Klainerman, and Stephen C. Meyer to explore one of the deepest mysteries in science and philosophy: the reality of mathematics. From the simple certainty that 2 + 2 = 4 to the mind-bending mathematics behind black holes and quantum physics, the conversation asks why abstract numbers—created in the human mind—map so perfectly onto the physical world. Is mathematics purely logical, or does it point to a deeper structure of reality that isn't material at all? Along the way, the panel explores beauty in science, the "unreasonable effectiveness" of math, and whether the concept of materialism can really explain the world we live in. This wide-ranging discussion blends mathematics, physics, philosophy, and metaphysics into a fascinating conversation about truth, beauty, and the nature of reality itself. Watch the full episode of Uncommon Knowledge on X:

Is math something humans invent—or something we discover? And why does it describe the universe so uncannily well? In this episode of Uncommon Knowledge, Peter Robinson sits down with mathematicians David Berlinski, Sergiu Klainerman, and Stephen C. Meyer to explore one of the deepest mysteries in science and philosophy: the reality of mathematics. From the simple certainty that 2 + 2 = 4 to the mind-bending mathematics behind black holes and quantum physics, the conversation asks why abstract numbers—created in the human mind—map so perfectly onto the physical world. Is mathematics purely logical, or does it point to a deeper structure of reality that isn't material at all? Along the way, the panel explores beauty in science, the "unreasonable effectiveness" of math, and whether the concept of materialism can really explain the world we live in. This wide-ranging discussion blends mathematics, physics, philosophy, and metaphysics into a fascinating conversation about truth, beauty, and the nature of reality itself. Watch the full episode of Uncommon Knowledge on X:

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In this explosive episode of The Anchormen Podcast, Matt Gaetz sits down with Jesse Lee Peterson Jesse Lee Peterson for a raw conversation about faith, family, and the future of America. Subscribe to OAN LIVE to watch The Matt Gaetz Show every weeknight

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AI is changing the software engineering craft. Anders Hejlsberg (Anders Hejlsberg) - creator of C#, TypeScript and industry legend - on why code review needs to get more enjoyable in response: #1 - AI is shifting the craft from writing code, to reviewing code: "In a sense, we're all turning into project managers. We can have an army of junior programmers, called agents, that will just spit out reams of code but someone's got to have the big picture and review all of that. And so, increasingly, our craft is going from one of writing the code, to one of reviewing the code and building the architecture of the code and overseeing the work. It's a different kind of craft. It's a different kind of enjoyment. I've always liked writing the code. To me that was the fulfilling part, seeing it work. In a way, AI robs a little bit of that, because I am less interested in reviewing code." #2 - The code review experience should be improved: "I think we could also make the process of reviewing code much more interesting than it is today. I mean, today, you see a list of diffs in alphabetical order and now it's up to you to make heads or tails of it. There are more pedagogical ways of presenting that. And you could have commentary generated by the AI that tells you what the changes are and whatever, and then tries to guide you along. So that symbiotic relationship, I think we need to work on that more and to keep the enjoyment in there."

AI is changing the software engineering craft. Anders Hejlsberg (Anders Hejlsberg) - creator of C#, TypeScript and industry legend - on why code review needs to get more enjoyable in response: #1 - AI is shifting the craft from writing code, to reviewing code: "In a sense, we're all turning into project managers. We can have an army of junior programmers, called agents, that will just spit out reams of code but someone's got to have the big picture and review all of that. And so, increasingly, our craft is going from one of writing the code, to one of reviewing the code and building the architecture of the code and overseeing the work. It's a different kind of craft. It's a different kind of enjoyment. I've always liked writing the code. To me that was the fulfilling part, seeing it work. In a way, AI robs a little bit of that, because I am less interested in reviewing code." #2 - The code review experience should be improved: "I think we could also make the process of reviewing code much more interesting than it is today. I mean, today, you see a list of diffs in alphabetical order and now it's up to you to make heads or tails of it. There are more pedagogical ways of presenting that. And you could have commentary generated by the AI that tells you what the changes are and whatever, and then tries to guide you along. So that symbiotic relationship, I think we need to work on that more and to keep the enjoyment in there."

The Pragmatic Engineer

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Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level that you could get involved in a math project and actually make a real contribution... because of all these AI tools and Lean and everything else." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

Terence Tao: "Previously, you needed a PhD to contribute to math research. Now a high school student can." Dwarkesh asks the world's most famous mathematician: what's your advice for someone considering a career in math, especially in light of AI progress? Tao is honest about uncertainty: "We live in a time of change. A particularly unpredictable era. Things that we've taken for granted for centuries may not hold anymore. The way we do everything... not just mathematics... will change." He admits his preference: "In many ways, I would prefer a much more boring, quiet era where things are much the same as they were 10 or 20 years ago. But one just has to embrace this. There's going to be a lot of change. The things you study... some of them may become obsolete or revolutionized. But some things will be retained." On new opportunities: "Previously, you had to go through years and years of education and get a math PhD before you could contribute to the frontier of math research. But now it's quite possible at the high school level that you could get involved in a math project and actually make a real contribution... because of all these AI tools and Lean and everything else." His advice: "There will be a lot of non-traditional opportunities to learn. You need a very adaptable mindset. There'll be worth pursuing things just for curiosity and for playing around. Still go through traditional education and learn math and science the old-fashioned way for a while... credentials will still be important. But you should also be open to very, very different ways of doing science. Some of which don't exist yet." He concludes: "It's a scary time. But also very exciting."

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a16z

1,015,035 views • 1 month ago

Cursor CEO Michael Truell on the future of writing code: “ Our goal with Cursor is to invent a new type of programming.” “It looks like a world where you have a representation of the logic of your software that does look more like English.” “You can imagine kind of an evolution of programming language towards pseudocode. You have written down the logic of the software, and you can edit that at a high level.” “It won't be the impenetrable millions of lines of code, it'll instead be something that's much terser and easier to understand and easier to navigate.” Source: Michael Truell (CEO Cursor) with Lenny Rachitsky on Lenny's Podcast

Cursor CEO Michael Truell on the future of writing code: “ Our goal with Cursor is to invent a new type of programming.” “It looks like a world where you have a representation of the logic of your software that does look more like English.” “You can imagine kind of an evolution of programming language towards pseudocode. You have written down the logic of the software, and you can edit that at a high level.” “It won't be the impenetrable millions of lines of code, it'll instead be something that's much terser and easier to understand and easier to navigate.” Source: Michael Truell (CEO Cursor) with Lenny Rachitsky on Lenny's Podcast

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Six Five Media

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📺 Emily Jashinsky is joined again by Michael Malice for a provocative conversation that spans MAGA, Epstein, the future of the Democrats, and the collapse of elite institutions.

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Enough of the fluff. Time for some real advice. Launch your GPT 5.6 Sol Pro. Use the following prompt (feel free to swap the second and third lines for something of your choice): Prove for me that the group of rational points on the elliptic curve (y^2=x^3+17) is finitely generated. I want to tailor the general proof to this particular case to narrow down my understanding to a particular case. Write down a full mathematical proof, step by step, in Leslie Lamport style. Unpack all the definitions and notions so that it is fully self-contained. An example here: Notice how Sol is spawning all the subagents to complete the task. What is "Leslie Lamport style"? It's a technique where you split your proof into short, one-line sentences (claims) that are easy to justify. In a situation where your proof is not a 1-to-1 translation of, e.g., Python code, the Leslie Lamport-style proof can be treated as such. It tremendously improves the possibility of verifying each claim and helps the model structure the arguments in a very clear way. Leslie Lamport, a legendary mathematician and computer scientist, was a promoter of this way of structuring proofs. Partly because of that, he created an extension of Donald Knuth’s typesetting system TeX called LaTeX. Here you can read about "Leslie Lamport-style proofs":

Enough of the fluff. Time for some real advice. Launch your GPT 5.6 Sol Pro. Use the following prompt (feel free to swap the second and third lines for something of your choice): Prove for me that the group of rational points on the elliptic curve (y^2=x^3+17) is finitely generated. I want to tailor the general proof to this particular case to narrow down my understanding to a particular case. Write down a full mathematical proof, step by step, in Leslie Lamport style. Unpack all the definitions and notions so that it is fully self-contained. An example here: Notice how Sol is spawning all the subagents to complete the task. What is "Leslie Lamport style"? It's a technique where you split your proof into short, one-line sentences (claims) that are easy to justify. In a situation where your proof is not a 1-to-1 translation of, e.g., Python code, the Leslie Lamport-style proof can be treated as such. It tremendously improves the possibility of verifying each claim and helps the model structure the arguments in a very clear way. Leslie Lamport, a legendary mathematician and computer scientist, was a promoter of this way of structuring proofs. Partly because of that, he created an extension of Donald Knuth’s typesetting system TeX called LaTeX. Here you can read about "Leslie Lamport-style proofs":

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"Tolerance is not enough, you have to work together." The conversation with Amartya Sen becomes a masterclass in humanity. Among the themes we touched on: - the ancestry of mathematics, - the ideas of freedom and justice, - how mathematics and Sanskrit have shaped his economic thinking, - and even the legendary bicycle that carried him to win the The Nobel Prize in Economic Sciences, for his contributions to welfare economics. One thing I’ve learned is that his knowledge stands upon admiration and affection, admiration for the beauty of mathematics, and affection for the philosophical depth of Sanskrit literature. He's an economist by formation, but a humanitarian by heart and experience. An honor to learn from him. Tune in,

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Sinn Féin's Louise O’Reilly TD for Dublin Fingal West asserts her views on the future of the Irish presidency: 'I think if we're going to have a conversation about how we elect Uachtarán na hÉireann in the future, that conversation has to involve making sure that all of the people on this island have a vote'

Sinn Féin's Louise O’Reilly TD for Dublin Fingal West asserts her views on the future of the Irish presidency: 'I think if we're going to have a conversation about how we elect Uachtarán na hÉireann in the future, that conversation has to involve making sure that all of the people on this island have a vote'

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21,666 views • 10 months ago

#WATCH | New York, USA: On Summit of the Future at the UN Headquarters in New York, Former UN President, Maria Fernanda Espinosa, says "I think the Summit of the Future is the outcome of a long process and the collective political will of seeing the UN strengthen its power, delivery capacity, adapt itself to the challenges of the 21st century. I think that some say that it's one in a lifetime opportunity to agree, discuss, and commit to build a better UN. I think that the UN has done a lot of good to the world, prevented many conflicts, provided life-saving support to refugees, to victims of war and an endless list of the good things that the UN has done, but we are living a different reality than 80 years ago, the time has come for a UN refurbishing, retooling, rejuvenating in the opportunities now. We are confident that we will have a strong pact of the future that will put women and gender equality at the centre and that looks at the UN as this very complex ecosystem that is human-made. Therefore, the improvements and the reforms also need to be led by humans, societies and not only governments but societies as a whole. We have to say that member states also have provided a central space to the negotiations and discussions of the pact, Global Digital Compact and the Declaration of Future Generations, which is a single package and we are very much looking forward to seeing the Summit of the Future commit not only to the pact but to the implementation of the actions that are embedded in the pact."

#WATCH | New York, USA: On Summit of the Future at the UN Headquarters in New York, Former UN President, Maria Fernanda Espinosa, says "I think the Summit of the Future is the outcome of a long process and the collective political will of seeing the UN strengthen its power, delivery capacity, adapt itself to the challenges of the 21st century. I think that some say that it's one in a lifetime opportunity to agree, discuss, and commit to build a better UN. I think that the UN has done a lot of good to the world, prevented many conflicts, provided life-saving support to refugees, to victims of war and an endless list of the good things that the UN has done, but we are living a different reality than 80 years ago, the time has come for a UN refurbishing, retooling, rejuvenating in the opportunities now. We are confident that we will have a strong pact of the future that will put women and gender equality at the centre and that looks at the UN as this very complex ecosystem that is human-made. Therefore, the improvements and the reforms also need to be led by humans, societies and not only governments but societies as a whole. We have to say that member states also have provided a central space to the negotiations and discussions of the pact, Global Digital Compact and the Declaration of Future Generations, which is a single package and we are very much looking forward to seeing the Summit of the Future commit not only to the pact but to the implementation of the actions that are embedded in the pact."

ANI

11,166 views • 1 year ago

“So originally, Paint by Numbers was like track one of the album. And at that time, the album was very different. It was like sonically sounding very different. It was like very introspective. I think I was really starting to feel like, you know, I think I loved the idea of opening the album with, oh, what a gift it is to be noticed, but it's nothing to do with me. I just loved, I was like so dedicated to that being the opening line. And I felt so like powerful in a lot of ways to be able to acknowledge that it's not really about me, you know. I mean the opening, the whole opening of the song is, oh, what a gift is to be noticed, but it's nothing to do with me. You've got to wonder if there's a reason to believe it's a lifetime of learning to Paint By Numbers and watching colors run.” - Harry about ‘Paint by Numbers’ on Q

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Klutch Sports CEO Rich Paul weighs in on the future of the NBA and the face of the league conversation. “I don’t think there's going to be a next ‘face of the league’. I think there will be a community.” ✍️ (via Pat McAfee)

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281,470 views • 1 year ago

Mathematician Jacob Tsimerman from University of Toronto has won the 2026 Fields Medal. Tsimerman extended the scope of o-minimal techniques within arithmetic and complex algebraic geometry and proved Griffiths' conjecture on the algebraicity of images of the period maps. He is also a Simons Investigator in Mathematics. Watch his full video and see all of the Fields Medal winners: #math #ICM2026 #FieldsMedal

Mathematician Jacob Tsimerman from University of Toronto has won the 2026 Fields Medal. Tsimerman extended the scope of o-minimal techniques within arithmetic and complex algebraic geometry and proved Griffiths' conjecture on the algebraicity of images of the period maps. He is also a Simons Investigator in Mathematics. Watch his full video and see all of the Fields Medal winners: #math #ICM2026 #FieldsMedal

Simons Foundation

37,992 views • 9 days ago