PodcastsHear the voice. See the shape of the thought.

Dwarkesh Patel interviews Nvidia CEO Jensen Huang on whether the company's dominance in AI compute is sustainable. Huang argues that transforming "electrons to tokens" requires deep system-level engineering that resists commoditization, that CUDA's breadth far exceeds what any TPU or ASIC can match, and that export controls on China hurt American competitiveness more than they help national security. The conversation spans supply chain strategy, Nvidia's investments in OpenAI and Anthropic, and the economics of chip architecture. ## [00:00] Is Nvidia's biggest moat its grip on scarce supply chains? Dwarkesh opens by noting that software company valuations have crashed on expectations that AI will commoditize software — and asks whether the same logic applies to Nvidia, whose designs are ultimately manufactured by TSMC, SK Hynix, and others. Jensen pushes back hard: the journey from electrons to tokens involves layers of artistry, engineering, and science that are "far from deeply understood." Nvidia's role is not just sending a GDS2 file to a foundry; it is designing the full-stack system — chip architecture, packaging, interconnects, networking, software — that makes each generation of compute dramatically more efficient. Jensen describes how Nvidia pushed high-bandwidth memory (HBM) years before the market believed in it, convincing partners like Micron to invest. He frames healthy industry dynamics as demand perpetually exceeding supply, which incentivizes continued innovation across the entire chain. He also warns that doomer-driven regulation could throttle the very progress that makes AI cheaper and more accessible over time. > *In the end, something has to transform electrons to tokens.* ## [16:25] Will TPUs break Nvidia's hold on AI compute? Dwarkesh points out that two of the top three AI models — Claude and Gemini — were trained on Google's TPUs, and asks what that means for Nvidia. Jensen draws a sharp distinction: Nvidia builds accelerated computing, not a tensor processing unit. CUDA powers molecular dynamics, quantum chromodynamics, fluid dynamics, data processing, and robotics — domains no TPU can serve. This breadth of market reach gives Nvidia an R&D flywheel that single-purpose ASICs cannot match. Jensen details how each Nvidia generation achieves massive performance jumps (Hopper to Blackwell: 30–50x) precisely because the architecture co-evolves hardware, numerics, networking, and software stack together. He highlights CUDA's ecosystem lock-in: every major framework (PyTorch, JAX, TensorFlow) is optimized for CUDA, and Nvidia's engineering teams routinely help AI labs extract an additional 2x from their stacks. The chapter also covers Nvidia's investments in OpenAI and Anthropic — Jensen says he invested "as soon as we could have" and wishes he had done it even earlier. > *Nvidia has reinvented the way computing is done, moving from general-purpose computing to accelerated computing.* ## [41:06] Why doesn't Nvidia become a hyperscaler? Dwarkesh presses on why Nvidia, sitting on massive cash reserves and watching AI lab valuations multiply, didn't become a foundation model lab or hyperscaler itself. Jensen explains that Nvidia's role as a neutral platform provider is uniquely valuable — if Nvidia competed with its own customers, the ecosystem trust that took decades to build would collapse. He cites Nvidia's support for smaller players like Nscale as evidence that the platform strategy benefits the entire industry. Jensen draws a historical parallel: when Nvidia started, there were 60 3D graphics companies, and Nvidia survived by committing to a platform that outlasted point solutions. The same logic applies to AI compute. Nvidia aligns supply with demand through deep forecasting and long-term partnerships — some spanning nearly 30 years. The accessibility of Nvidia's infrastructure (from a single rack to datacenter scale) ensures that startups and hyperscalers alike can build on the same platform. > *What that means is, the work that we do with building our computing platform, if we don't do it, I genuinely believe it doesn't get done.* ## [57:36] Should we be selling AI chips to China? The longest chapter opens with Dwarkesh raising Anthropic's Mythos Preview — a model with cyber-offensive capabilities that found thousands of high-severity vulnerabilities, including a 27-year-old bug in OpenBSD. If Chinese entities had access to chips that could train and run such models at scale, is that a national security threat? Jensen responds that Mythos was trained on "fairly mundane capacity" that is already abundantly available in China, making the point that export controls are targeting the wrong layer of the stack. Jensen argues that restricting chip sales to China has three negative effects: it pushes Chinese researchers to develop smarter algorithms with less compute, it hands entire market segments to domestic Chinese chip makers, and it weakens the US chip industry's revenue and ability to invest in the next generation. He contends that the AI application layer — not the chip layer — is where strategic advantage is won, and that the US should compete by building the best applications rather than by throttling hardware supply. The discussion is nuanced, with Jensen acknowledging security concerns but insisting the current policy is counterproductive. > *The best AI researchers in the world, because they're limited in compute, they also come up with extremely smart algorithms.* ## [95:06] Why doesn't Nvidia make multiple different chip architectures? Dwarkesh asks whether Nvidia could use older process nodes (like N7) to build cheaper chips and meet demand that leading-edge capacity cannot fill. Jensen explains that modern chip architecture is far more than transistor scale — it involves packaging, stacking, numerics, and system-level co-design. Going backward to an older node would require a separate R&D effort that no company could afford, whereas leaning forward into each new generation compounds improvements. Jensen discusses Nvidia's recent acquisition of Groq and its integration into the CUDA ecosystem, signaling that diverse hardware can plug into the CUDA software stack without requiring separate architectures. He envisions a world of high-ASP tokens where throughput-per-chip matters less than value-per-token. The chapter closes with Jensen emphasizing that CUDA serves far more than AI — structured data processing, scientific computing, and many other workloads depend on it — and that Nvidia's advances democratized deep learning for the entire research community. > *But because of the advances that we made in computing, we democratized deep learning.* ## Entities - **Jensen Huang** (Person): CEO of Nvidia, guest on the episode - **Dwarkesh Patel** (Person): Host of the Dwarkesh Podcast - **CUDA** (Software): Nvidia's parallel computing platform and programming model, the backbone of its software moat - **TSMC** (Organization): Taiwan Semiconductor Manufacturing Company, primary foundry for Nvidia's chips - **Anthropic** (Organization): AI safety company; referenced for Nvidia's investment and for Mythos Preview - **OpenAI** (Organization): AI research company; referenced for Nvidia's investment - **Groq** (Organization): AI chip company recently acquired by Nvidia and folded into CUDA ecosystem - **Blackwell** (Concept): Nvidia's latest GPU architecture, delivering 30–50x improvement over Hopper

Ivanka Trump offers a candid look into her life, from a unique childhood shaped by famous parents and intense media scrutiny to her impactful career in business and public service. She shares lessons learned from her mother, the challenges of building trust, and how pivotal experiences like her parents' divorce and her father's assassination attempt fostered resilience. Trump also discusses her philosophy on intentionality, the power of being underestimated, and her journey of personal growth through motherhood and therapy, culminating in her mission-driven work with Planet Harvest. ## [00:00] Why Trust Doesn’t Come Easy And What That Reveals Ivanka Trump learned early on, particularly during her parents' highly publicized divorce at age nine, to be guarded against insincere relationships due to constant media scrutiny and aggressive paparazzi. Her mother taught her the power of being underestimated and the importance of filtering external "noise" under pressure. While initially developing a strong defense mechanism against trusting others, she has since intentionally cultivated a more trusting approach for deeper connections, accepting the inherent risks. > *my mother taught me that being underestimated is not a bad thing. It's very powerful thing actually [00:22]* > *I've really actually taught myself to be more trusting. [05:48]* ## [03:32] When You Realize You’re Different What Happens Next Ivanka Trump realized her life was atypical from a young age due to constant media attention and public scrutiny, a phenomenon she contrasts with today's amplified social media exposure for children. She notes her parents made efforts to shield her and her siblings from this intense public gaze. She prefers in-depth conversations over frequent interviews. > *I think there was always a lot of media attention and scrutiny. You see it, you experience it very early on. [06:24]* > *not everyone I think the experience our children have where anywhere they go people have a recording device in their hands [06:40]* ## [05:44] What Her Mother Was Really Like Behind Closed Doors Ivanka Trump describes her mother, Ivana, as a disciplined former national skier who instilled the value of sport, leading Ivanka to ballet. She recalls an unusual childhood memory of Michael Jackson attending her Nutcracker performance. Despite these extraordinary experiences, her daily life was grounded by her maternal grandmother, "Bubby," who provided unconditional love and expressed it through cooking. > *my mom um was an incredible skier... she really believed in the importance of of sport for cultivating discipline [07:07]* > *My grandmother... really raised us... she taught me um a type of unconditional love and tenderness [08:44]* ## [11:47] The Key Difference That Shaped Who She Became Ivanka Trump's upbringing was profoundly shaped by both her nurturing grandmother, "Bubby," who provided unconditional love and daily care, and her mother, Ivana, who served as a trailblazing role model. Ivana exemplified strength, ambition, and resilience, demonstrating how to pursue professional goals while being a loving mother. Ivanka clarifies that despite her parents' busy careers, they were present and made her feel like a priority, with her grandmother filling the traditional caregiving role. > *My mother was an incredible trailblazer... an amazing example for me of strength and resilience and glamour and determination and ambition. [11:57]* > *There was never a doubt in my mind that I was his top priority and that he was available to me. [14:42]* ## [15:43] What Donald And Ivana Trump’s Divorce Really Meant For Her Donald and Ivana Trump's highly publicized divorce, which Ivanka learned about from a newspaper at age nine, profoundly impacted her. She recalls feeling scared by the intense media scrutiny and experiencing the normal fears of a child during parental separation. This challenging period, which garnered more headlines than the O.J. Simpson trial, fostered a unique bond among her and her siblings. Later in life, after her mother's passing, Ivanka gained a deeper understanding of Ivana's complex character, shaped by her upbringing in communist Czechoslovakia, wishing she had asked more questions while her mother was alive. > *this divorce apparently garnered more headlines than the OJ Simpson trial. [20:04]* > *the positive for me and my siblings were we really like bonded in a different type of way because we were going through it together. [23:21]* ## [18:27] The Reality Of Being Trump’s Daughter What People Get Wrong Being Donald Trump's daughter meant navigating intense public scrutiny from a young age, particularly during her parents' divorce, which taught her a necessary caution about trust. She has since learned to "find the signal in the noise" and avoid engaging in combative social media, prioritizing inner peace. Ivanka notes her parents' deep authenticity, and while she approaches communication more delicately, she maintains a strong sense of self, guided by Stoic philosophy, to live authentically and resist external pressures. > *If I didn't have that lesson, I don't know that I'd be tough. It taught me not to trust anybody. [18:53]* > *I don't punch back because I don't... believe in sort of spending my time and focus like being combative like jumping into that particular arena and like the nasty swirl of social media. [26:19]* ## [23:36] How Do You Find Yourself Surrounded By Power And Fame Surrounded by power and fame, Ivanka Trump found her sense of self through intentional personal growth and the transformative experience of motherhood, which "cracked her open" and deepened her capacity for love. She emphasizes the critical importance of self-awareness to resist external pressures and define oneself, rather than letting "the mob win." She applies this philosophy to her parenting, fostering individuality in her children, and credits her own parents for allowing respectful dissent, enabling her to be true to herself. > *If you don't know who you are the mob wins. [29:55]* > *They created an environment where like disscent was okay. [32:44]* ## [30:57] Why Being Underestimated Became Her Biggest Advantage Ivanka Trump learned from her mother that being underestimated can be a powerful advantage. In her early real estate career, she was often misjudged as both the child of successful parents and a young woman in a male-dominated industry. She harnessed this perception, using it as motivation to work harder and be overprepared, ultimately leveraging it to her benefit against those who underestimated her. > *my mother taught me that being underestimated is not a bad thing. It's very powerful thing actually [00:22]* > *I harnessed that like sort of fear, that sentiment and I used it to sort of propel me. [35:06]* ## [32:59] What She Actually Looks For When Hiring And Why It Matters When hiring, Ivanka Trump prioritizes individuals with a strong sense of self, agency, good judgment, and "street smarts," as these innate qualities are difficult to teach. She emphasizes the importance of working with "good people" whom she trusts and respects, considering these attributes fundamental to successful work relationships and overall team dynamics. > *It's very hard to teach people, you know, you could have a brilliant person, but if they don't have like good judgment or if they're not like a self-starter, it's very hard to give them that. [38:15]* > *I don't want to work with people I don't enjoy that I don't think are like good people because I don't want to spend my time with somebody who I don't trust or who I don't respect. [39:00]* ## [37:49] Why She Walked Away From Fashion For Government Despite a prestigious job offer from Anna Wintour at Vogue upon graduating from Wharton, Ivanka Trump pursued her lifelong passion for real estate. She later built a successful fashion brand, Ivanka Trump.com, which grew to nearly $800 million in annual sales. However, she made the deliberate decision to shut down this thriving business to comply with government ethics rules when she accepted her father's request to serve in his administration. She viewed this opportunity as an undeniable privilege and duty to her country, despite the significant personal and professional sacrifices. > *We were doing close to $800 million in sales annually when I shut it down when I went into government. [42:30]* > *I feel incredibly privileged that he gave us the opportunity to serve a country we love so much. [43:30]* ## [41:06] What Really Happened When Trump Decided To Run Donald Trump's decision to run for president in 2015 was announced at a family meeting in Bedminster, surprising Ivanka with its swiftness, despite his long-standing, though unarticulated, political ambitions since the 1980s. She recalls a childhood panic at 16, fearing he would run, only to be reassured otherwise. His entry into presidential politics was a "radical adjustment" for the family, profoundly expanding Ivanka's worldview beyond her New York City "bubble" and initiating an "extraordinary ride" into public service. > *I do remember once thinking it was real. I was 16 and I was at boarding school and I called him up... 'This is going to ruin my life.' [51:48]* > *his campaign like ripped it open for me and that I realized like the bubble that I was in [48:02]* ## [46:23] Trump Running For President What Changed Everything Donald Trump's decision to run for president fundamentally changed everything for Ivanka, marking a "radical adjustment" for the entire family. His unconventional entry into politics, bypassing traditional career paths, was like "drinking water from a fire hose." The campaign shattered Ivanka's perceived "bubble" in New York City, profoundly expanding her worldview and leading her to embrace the privilege of serving her country. > *It was drinking water from a fire hose for all of us. [47:08]* > *his campaign like ripped it open for me and that I realized like the bubble that I was in [48:02]* ## [48:52] Ads This segment features an advertisement for Shopify, an e-commerce platform that simplifies building online stores, selling on social media, and managing operations with AI tools. It also promotes Pipe Drive, an intelligent CRM used by the host, highlighting its visual pipeline dashboard for clear sales process visibility. > *Shopify, makes it easy to get started because you can build your store, sell on socials, take payments, use AI tools, and manage everything all in one place. [49:22]* > *Pipe Drive is an easy to use intelligent CRM... it makes your sales process visible through one dashboard. [50:17]* ## [51:04] Did She Ever Think Her Father Would Actually Do It While Donald Trump had considered running for president since the 1980s, Ivanka states this ambition was not explicitly discussed during her childhood. She vividly recalls a moment at 16 when she panicked, believing her father was running, only to be reassured it wasn't happening. She notes his consistent viewpoints on issues like trade policy remained unchanged over decades. > *I do remember once thinking it was real. I was 16 and I was at boarding school and I called him up... 'This is going to ruin my life.' [51:48]* > *his viewpoint remained consistent over time and remains consistent to this day on exactly that about trade policy [52:35]* ## [54:26] Was Leaving The White House A Relief Or Something Else Leaving the White House was not a relief in the sense of regret, as Ivanka Trump feels she "left it all on the field" and is proud of her accomplishments during her four years of public service. She views the opportunity to serve as an "amazing privilege" but has no desire to return to politics, prioritizing her children and unwilling to let them pay the price of further public life. She is content with her contributions and feels her father now has a strong team to support him. > *I left it all on the field, you know? I I don't look back and say... I don't have regrets. [53:33]* > *My first responsibility is to be their mom. [56:49]* ## [58:08] Was Anyone Truly Prepared For Life Inside The White House Ivanka Trump admits that nothing truly prepares an individual for the intense experience of high-level politics and life inside the White House. She observed that power, much like wealth, tends to amplify people's inherent traits. Her interactions with global leaders, from monarchs to elected officials, demystified them, revealing that at their core, they are "just people" with ordinary struggles, which ultimately dispelled any intimidation she might have felt. > *There's nothing that trains you for the experience. [58:26]* > *You realize at the end of the day like people are people. [59:03]* ## [59:44] What The Assassination Attempt Changed Forever The assassination attempt on her father in July 2024 radically changed Ivanka Trump's life, intensifying security concerns and necessitating US Secret Service protection. Witnessing the event in real-time with her children, her immediate reaction was to shield them, though she had an intuitive sense her father would be fine. This harrowing experience, alongside other family health scares, reinforced her belief in the preciousness of life and her commitment to choosing positivity and valuing every moment, despite the troubling correlation between public service and violence. > *My first reaction was to turn them away. [62:02]* > *In life, you have a choice only in how you respond. And I choose to see the positive outcome. [66:05]* ## [1:07:20] What Life Looks Like After Stepping Away From Politics After stepping away from politics in 2022, Ivanka Trump's life now prioritizes her young children and private family life, as she found the "dark world" of politics at odds with her nature. She navigates public criticism using the "eagle and crow" metaphor, choosing to rise above negativity rather than engage. This period of intense public scrutiny, including her father's near-death experience, has been a "medicine" for personal growth, teaching her to seek inner peace and harmony within her control, and to focus on gratitude for life's blessings. > *Politics is a pretty dark world. There's a lot of darkness, a lot of negativity, and it's just really at odds with what feels good to me as a human being. [67:45]* > *The eagle's response to this... isn't to like twist and turn and knock the crow off or um defend itself... It's just to fly up. [69:28]* ## [1:11:04] Ads This chapter represents a brief advertisement break within the podcast. ## [1:14:24] How Therapy Changed The Way She Sees Everything Ivanka Trump began adult therapy, viewing it as an "internal inventory" tool, driven by her "growth-oriented mindset" and a desire to process significant life events. Key catalysts included her husband Jared's second thyroid cancer diagnosis, her departure from Washington, and her mother's unexpected passing. Therapy helped her nurture herself and process emotions rather than compartmentalizing, ultimately changing her perspective on self-understanding and moving forward. > *I have like a very growthoriented mindset... I'm always looking to learn about myself and about the world [74:35]* > *Jared um was diagnosed with thyroid cancer for a second time. Um and uh and then my mother passed [75:59]* ## [1:20:28] The Loss Of Her Mother And What It Taught Her Ivanka Trump reflects on the sudden and tragic death of her mother, Ivana Trump, in 2022, highlighting the unique impact of an unexpected parental loss. She committed to a proper grieving process, confronting discomfort and processing her feelings. As a parent, she now aims to expose her children to her mother's positive qualities while consciously avoiding passing on her challenges, gaining a clearer adult perspective of her mother's life. > *She lived a good life though. [81:07]* > *I really took the time to think about her not through the eyes of the child who idolized her fully but through the eyes of an adult who saw her clearly. [83:15]* ## [1:26:28] The 3 Rules She Believes Define Success And Happiness Ivanka Trump believes that true success and happiness are defined by three key principles, particularly for entrepreneurship, which she would share with her daughter, Arabella. First, one must genuinely love what they do, as passion is essential for dedication. Second, authenticity is paramount; being oneself and blazing one's own path is crucial, as imitation leads to losing. Third, and most fundamentally, one must cultivate self-belief before the world believes in them, as this is the starting point for any achievement. She also notes that traditional "work-life balance" is elusive, instead striving for alignment with priorities. > *I have never seen someone at the peak of their game who doesn't absolutely love what they do. [92:46]* > *you're going to have to believe in yourself before the world believes in you. [94:48]* ## [1:28:37] What Planet Harvest Is And Why It Could Matter More Than You Think Planet Harvest is Ivanka Trump's mission-driven venture aimed at reducing food waste and supporting American farmers. The initiative was inspired during the COVID-19 pandemic when she observed vast amounts of perishable produce being discarded due to supply chain issues. Planet Harvest addresses the ongoing problem of perfectly good food being rejected by retailers for not meeting strict cosmetic standards, thereby providing incremental revenue for farmers and benefiting the environment. > *Planet Harvest was born... ensuring that when people needed food, the food in the fields wasn't going to waste by being tilled under as we saw in the early days of the pandemic. [89:18]* > *400 million pounds of strawberries every year get left in the fields... Not because they're imperfect. They're just don't meet a really rigid cosmetic specification. [90:57]* ## Entities - **Ivanka Trump** (Person): Daughter of Donald and Ivana Trump, businesswoman, and former government official. - **The Diary Of A CEO** (Organization): The podcast hosting the interview. - **Donald Trump** (Person): Ivanka Trump's father, former President of the United States. - **Ivana Trump** (Person): Ivanka Trump's mother, former skier for Czechoslovakia. - **Michael Jackson** (Person): Famous American singer, songwriter, and dancer. - **O.J. Simpson** (Person): Former American football player, broadcaster, actor, and convicted felon. - **Marcus Aurelius** (Person): Roman emperor and Stoic philosopher. - **Shopify** (Organization): E-commerce platform for building online stores. - **Pipe Drive** (Organization): Intelligent CRM (Customer Relationship Management) software. - **Anna Wintour** (Person): Editor-in-chief of Vogue. - **Vogue** (Organization): Fashion and lifestyle magazine. - **Wharton School of Business** (Organization): Business school at the University of Pennsylvania. - **Office of Government Ethics** (Organization): U.S. government agency responsible for preventing conflicts of interest. - **Jared Kushner** (Person): Ivanka Trump's husband, who also served in government. - **US Secret Service** (Organization): Government agency responsible for protecting Ivanka Trump and her family. - **Planet Harvest** (Organization): A business co-founded by Ivanka Trump focused on reducing food waste and supporting farmers. - **Arabella** (Person): Ivanka Trump's oldest daughter. - **Stoicism** (Philosophy): An ancient Greek school of philosophy. - **Buddhism** (Philosophy): An Eastern philosophy. - **Daoism** (Philosophy): An Eastern philosophy. - **Czechoslovakia** (Location): A former country in Central Europe. - **New York City** (Location): Major city in the United States. - **Bedminster, New Jersey** (Location): Location where Ivanka Trump was when she learned of the assassination attempt on her father. - **Child Tax Credit** (Policy): US tax credit for families with children. - **Great American Outdoors Act** (Policy): Legislation supported by Ivanka Trump. - **Human Trafficking Legislation** (Policy): Legislation Ivanka Trump worked on during her public service. - **Vocational Education and Skills Training** (Initiative): Programs promoted by Ivanka Trump to skill and reskill American workers. - **Meditations** (Book): A series of personal writings by Marcus Aurelius.

Terence Tao discusses the evolving role of AI in mathematics, asserting that while AI will automate many routine tasks, it will not fully replace human mathematicians but rather shift their focus to new frontiers. He emphasizes the future of human-AI collaboration and the unpredictable nature of AI's long-term impact on scientific discovery. ## [00:10] AI's Current Role in Frontier Math Terence Tao explains that AI is already performing 'frontier math' that humans cannot, though it's a different kind of frontier. He likens this to how calculators expanded mathematical capabilities in the past, handling tasks beyond human capacity but in a specialized way. > *in some ways they're already doing frontier math that is super intelligent that humans can't do but it's a different frontier from what we're used to.* ## [00:52] AI as an Automation Tool, Not a Replacement Tao predicts that within a decade, AI will handle many routine tasks currently performed by mathematicians, allowing humans to focus on more complex, important problems. He draws parallels to historical shifts where tools like computers automated tasks previously done by human 'computers' or how genome sequencing became automated, yet fields like genetics continued to evolve to new scales. > *within a decade a lot of things that mathematicians currently do... can be done by AI. But we will find that that actually wasn't the most important part of what we do.* ## [02:46] The Future of Human-AI Collaboration in Math Dwarkesh Patel asks about AI autonomously solving Millennium Prize Problems. Terence Tao believes that 'hybrid human plus AIs' will dominate mathematics for much longer, as current AI lacks all the necessary ingredients for a complete replacement of intellectual tasks, functioning more as a complementary tool. > *I do believe that that hybrid human plus AIs will will dominate mathematics for a lot longer.* ## [03:43] Unpredictable Impact on Scientific Discovery Tao acknowledges that while AI will accelerate science and new discoveries, there's also a possibility it could inhibit certain types of progress by 'destroying serendipity.' He concludes that the future impact of AI on scientific discovery is highly unpredictable. > *it's possible that also by somehow destroying serendipity, we we actually inhibit certain types of progress.* ## Entities - **Terence Tao** (Person): Guest speaker, a prominent mathematician. - **Dwarkesh Patel** (Person): Host of the podcast. - **AI** (Concept): Artificial Intelligence, discussed in its role in mathematics and scientific discovery. - **Mathematica / Wolfram Alpha** (Software): Computational tools mentioned as examples of automation in mathematics. - **Millennium Prize Problems** (Concept): Seven unsolved problems in mathematics for which a $1 million prize is offered for each solution.