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Tuesday, July 15, 2025
Techcratic
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  • AI
    Artificial Intelligence

    Building End-to-End Data Pipelines: From Data Ingestion to Analysis

    Artificial Intelligence

    How Rapid7 automates vulnerability risk scores with ML pipelines using Amazon SageMaker AI

    Artificial Intelligence

    Build a conversational data assistant, Part 2 – Embedding generative business intelligence with Amazon Q in QuickSight

    Artificial Intelligence

    Enabling Differentially Private Federated Learning for Speech Recognition: Benchmarks, Adaptive Optimizers, and Gradient Clipping

    Artificial Intelligence

    Overcoming Vocabulary Constraints with Pixel-level Fallback

    Artificial Intelligence

    Uphold ethical standards in fashion using multimodal toxicity detection with Amazon Bedrock Guardrails

    Artificial Intelligence

    10 Surprising Things You Can Do with Python’s datetime Module

    Artificial Intelligence

    New capabilities in Amazon SageMaker AI continue to transform how organizations develop AI models

    Artificial Intelligence

    Unlock retail intelligence by transforming data into actionable insights using generative AI with Amazon Q Business

  • Apple

    July 15, 2025 – Apple leadership, Mac growth

    iOS 26 public beta rumored to launch next week

    iOS 26 public beta rumored to launch next week

    Future Apple Watch or iPhone may gain a camera that’s completely hidden when not in use

    Future Apple Watch or iPhone may gain a camera that’s completely hidden when not in use

    iOS 26 gives Apple’s Reminders app a new, faster way to add tasks

    iOS 26 gives Apple’s Reminders app a new, faster way to add tasks

    iPhone 17: Titanium is coming to just one model, and it’s a surprising choice

    iPhone 17: Titanium is coming to just one model, and it’s a surprising choice

    Ultimate Edition’ coming to the Mac on July 17

    Ultimate Edition’ coming to the Mac on July 17

    Samsung reportedly gearing up to produce foldable iPhone displays

    Samsung reportedly gearing up to produce foldable iPhone displays

    How a MacBook with an iPhone chip can redefine Apple’s budget line

    How a MacBook with an iPhone chip can redefine Apple’s budget line

    Apple @ Work Podcast: Fleet launches iOS device management

    Apple @ Work Podcast: WebAI puts LLM power in the hands of your IT team

  • ComputerWorld
    How agentic AI will change IT support roles – Computerworld

    How agentic AI will change IT support roles – Computerworld

    Apple’s done innovating? Be serious – Computerworld

    Apple’s done innovating? Be serious – Computerworld

    For July, a ‘big, broad’ Patch Tuesday release – Computerworld

    For July, a ‘big, broad’ Patch Tuesday release – Computerworld

    AI coding tools can slow down seasoned developers by 19%

    AI coding tools can slow down seasoned developers by 19%

    Will IT turn the AI bot battle into a money maker? (And is that even a good idea?) – Computerworld

    Will IT turn the AI bot battle into a money maker? (And is that even a good idea?) – Computerworld

    Tariff uncertainty hits US PC shipments in Q2 – Computerworld

    Tariff uncertainty hits US PC shipments in Q2 – Computerworld

    The fast way to fix a frozen Start menu or taskbar in Windows – Computerworld

    The fast way to fix a frozen Start menu or taskbar in Windows – Computerworld

    Microsoft’s 19-hour Outlook outage exposes fragility in cloud infrastructure – Computerworld

    Microsoft’s 19-hour Outlook outage exposes fragility in cloud infrastructure – Computerworld

    A magically minimalist Android makeover – Computerworld

    A magically minimalist Android makeover – Computerworld

  • Gaming
    The Nintendo DS had it right all along: Ayaneo launches Flip 1S DS and Flip 1S KB, two new clamshell handheld gaming PCs with prices to make your teeth clench

    The Nintendo DS had it right all along: Ayaneo launches Flip 1S DS and Flip 1S KB, two new clamshell handheld gaming PCs with prices to make your teeth clench

    A Delayed Puzzle – Zelda Breath Of The Wild Walkthrough – Solve Kema Zoos Shrine Puzzle

    A Delayed Puzzle – Zelda Breath Of The Wild Walkthrough – Solve Kema Zoos Shrine Puzzle

    Destiny 2 The Desert Perpetual raid release date and time

    Destiny 2 The Desert Perpetual raid release date and time

    GTA 6 Trailer 2: Release Date Confirmed & Official Screenshots!

    GTA 6 Trailer 2: Release Date Confirmed & Official Screenshots!

    As if being worth $4 trillion isn’t enough, Nvidia claims the US government says it can start selling AI GPUs to China again

    As if being worth $4 trillion isn’t enough, Nvidia claims the US government says it can start selling AI GPUs to China again

    GOW  Ragnarok Valhalla (DLC) Gameplay/Walkthrough – No Commentary –  Part 7 (1080p 60fps on Ultra)

    GOW Ragnarok Valhalla (DLC) Gameplay/Walkthrough – No Commentary – Part 7 (1080p 60fps on Ultra)

    US Defense Department awards $200 million contract to Elon Musk’s Grok aka ‘MechaHitler’ and is looking forward to deploying it ‘in our warfighting domain’

    US Defense Department awards $200 million contract to Elon Musk’s Grok aka ‘MechaHitler’ and is looking forward to deploying it ‘in our warfighting domain’

    Why God Of War Ragnarok Will Be One Of THE BEST Games Of 2022 | God Of War Ragnarok Review Roundup

    Why God Of War Ragnarok Will Be One Of THE BEST Games Of 2022 | God Of War Ragnarok Review Roundup

    If you’re on the latest Windows 11 Insider build you might have to uninstall your Xbox controller driver to get it to play nicely

    If you’re on the latest Windows 11 Insider build you might have to uninstall your Xbox controller driver to get it to play nicely

  • Retro Rewind
    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 57 April 1994

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: Computer Gaming World Magazine Issue 73 December 1998

    Retro Rewind: Computer Gaming World Magazine Issue 73 December 1998

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

  • Tech Art
    Virtual Reality is Not What You Think

    Virtual Reality is Not What You Think

    MAJU TALK EPISODE # 2   I  Media and Art Industry Role in Pakistan

    MAJU TALK EPISODE # 2 I Media and Art Industry Role in Pakistan

    Draw A Lotus Flower in Ms Paint | Kamal Kaa Phool Ms Paint Me Kaise Bnaye

    Draw A Lotus Flower in Ms Paint | Kamal Kaa Phool Ms Paint Me Kaise Bnaye

    INSIDE Mirror Mirror: ArtScience Museum's NEW interactive exhibition

    INSIDE Mirror Mirror: ArtScience Museum's NEW interactive exhibition

    Woman Having a Hard Time: Falon Stutzman @ Megan Mulrooney Gallery, Los Angeles

    Woman Having a Hard Time: Falon Stutzman @ Megan Mulrooney Gallery, Los Angeles

    Creating a 3D VENOM Sculpture in Zbrush | Timelapse

    Creating a 3D VENOM Sculpture in Zbrush | Timelapse

    Alicja Kwade: Geologies of the Impossible

    Alicja Kwade: Geologies of the Impossible

    [SWTT] Generative Art NFT Tutorial

    [SWTT] Generative Art NFT Tutorial

    Using Unreal Engine 4 for CONCEPT ART – Full Process Video | From Zero to Concept Art

    Using Unreal Engine 4 for CONCEPT ART – Full Process Video | From Zero to Concept Art

  • Tech Deals
    LEGO Star Wars: The Force Awakens – Xbox 360 Standard Edition

    LEGO Star Wars: The Force Awakens – Xbox 360 Standard Edition

    Western Digital 10TB WD Purple Surveillance Internal Hard Drive HDD – SATA 6 Gb/s, 256…

    Western Digital 10TB WD Purple Surveillance Internal Hard Drive HDD – SATA 6 Gb/s, 256…

    NexStar 6G, 2.5” SATA III to USB 3.2 Gen1 External SSD/HDD Enclosure, ID: Black

    NexStar 6G, 2.5” SATA III to USB 3.2 Gen1 External SSD/HDD Enclosure, ID: Black

    Toshiba Canvio Basics 4TB Portable External Hard Drive USB 3.0, Black – HDTB540XK3CA

    Toshiba Canvio Basics 4TB Portable External Hard Drive USB 3.0, Black – HDTB540XK3CA

    Vansuny 64GB Type C Flash Drive 2 in 1 OTG USB 3.0 + USB C Memory Stick with Keychain…

    Vansuny 64GB Type C Flash Drive 2 in 1 OTG USB 3.0 + USB C Memory Stick with Keychain…

    SABRENT USB C to USB C Charging Cable with Smart Display, 2M/6.6FT Long, E-Marker Chip,…

    SABRENT USB C to USB C Charging Cable with Smart Display, 2M/6.6FT Long, E-Marker Chip,…

    XTRONS for Fiat 500 (2007-2015) Touch Screen Radio, 7 Inch Android 13 Car Stereo for…

    XTRONS for Fiat 500 (2007-2015) Touch Screen Radio, 7 Inch Android 13 Car Stereo for…

    XTRONS Single Din Car Stereo for Fiat 500, Android 13 Octa Core 4GB RAM 64GB ROM Car…

    XTRONS Single Din Car Stereo for Fiat 500, Android 13 Octa Core 4GB RAM 64GB ROM Car…

    Pioneer DJ HDJ-CUE1 On-ear DJ Headphones – Black

    Pioneer DJ HDJ-CUE1 On-ear DJ Headphones – Black

  • Techs Got To Eat
    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Oreo Mug Cake: 2-Minute Cookie & Cake Combo!

    Oreo Mug Cake: 2-Minute Cookie & Cake Combo!

  • Tesla

    Tesla’s long-time head of sales in North America is out

    RYANSTAR RACING Black Car Door Handles Compatible with Tesla Cybertruck 2023 2024 2025 4…

    RYANSTAR RACING Black Car Door Handles Compatible with Tesla Cybertruck 2023 2024 2025 4…

    Tesla finally launches in India, but at a price that doesn’t make sense

    Tesla finally launches in India, but at a price that doesn’t make sense

    Cyber Hooks Heavy Duty Steel L Track Cleat Hooks – 4PCS Set, OEM Style Compatible with…

    Cyber Hooks Heavy Duty Steel L Track Cleat Hooks – 4PCS Set, OEM Style Compatible with…

    Rear Center Console Organizer for Tesla Cybertruck Trash Can with Anti-Slip Lid Cover…

    Rear Center Console Organizer for Tesla Cybertruck Trash Can with Anti-Slip Lid Cover…

    2025 Upgraded J1772 & CCS to Tesla Cybertruck Adapter Fast Charging Adapter Compatible…

    2025 Upgraded J1772 & CCS to Tesla Cybertruck Adapter Fast Charging Adapter Compatible…

    Truck Cover Custom Fit for Tesla Cybertruck, Waterproof All Weather Lightweight Pickup…

    Truck Cover Custom Fit for Tesla Cybertruck, Waterproof All Weather Lightweight Pickup…

    Inflatable Truck Bed Air Mattress for Tesla Cybertruck 2024 2025 Accessories Thicken Air…

    Inflatable Truck Bed Air Mattress for Tesla Cybertruck 2024 2025 Accessories Thicken Air…

    REDTIGER 4K Dash Cam Front, ADAS, Built-in WiFi GPS, Mini Hidden Dash Camera for Cars…

    REDTIGER 4K Dash Cam Front, ADAS, Built-in WiFi GPS, Mini Hidden Dash Camera for Cars…

  • UFO
    New York Eye & Ear Control

    New York Eye & Ear Control

    Drones with Camera for Adults 6K Foldable Headless Drone with Obstacle Avoidance Function Optical Flow Positioning Gesture Photography with Storage Bag 2 Battery

    Drones with Camera for Adults 6K Foldable Headless Drone with Obstacle Avoidance Function Optical Flow Positioning Gesture Photography with Storage Bag 2 Battery

    Women’S Sarong Coverups Beach Bathing Suit Wrap Skirt Sheer Bikini Wraps Chiffon Cover Ups For Swimwear

    Women’S Sarong Coverups Beach Bathing Suit Wrap Skirt Sheer Bikini Wraps Chiffon Cover Ups For Swimwear

    JWST's Mind Blowing Exoplanet Discovery!  #space #spaceexploration #exoplanets #nasa #fyp #shorts

    JWST's Mind Blowing Exoplanet Discovery! #space #spaceexploration #exoplanets #nasa #fyp #shorts

    Space Theme Birthday Candle, Shiny Astronaut Number Candle Spaceship Outer Space Cake Topper Perfect Universe Rocket Spacecraft Cake Decorations and Party Favors(Number 1)

    Space Theme Birthday Candle, Shiny Astronaut Number Candle Spaceship Outer Space Cake Topper Perfect Universe Rocket Spacecraft Cake Decorations and Party Favors(Number 1)

    The Dark Truth About 23andMe

    The Dark Truth About 23andMe

    Spacecraft Dashboard Gaming Mouse Pad Large Mouse Pad Office Desk Accessories XL Desk Mat 31.5×11.8×0.12 inch Blue Large Desk Pad Keyboard Pad (Console)

    Spacecraft Dashboard Gaming Mouse Pad Large Mouse Pad Office Desk Accessories XL Desk Mat 31.5×11.8×0.12 inch Blue Large Desk Pad Keyboard Pad (Console)

    How Much Does it Cost to Launch a Satellite? #shorts

    How Much Does it Cost to Launch a Satellite? #shorts

    Top Secret UFO Sightings #joerogan #podcast #aliens

    Top Secret UFO Sightings #joerogan #podcast #aliens

  • AI
    Artificial Intelligence

    Building End-to-End Data Pipelines: From Data Ingestion to Analysis

    Artificial Intelligence

    How Rapid7 automates vulnerability risk scores with ML pipelines using Amazon SageMaker AI

    Artificial Intelligence

    Build a conversational data assistant, Part 2 – Embedding generative business intelligence with Amazon Q in QuickSight

    Artificial Intelligence

    Enabling Differentially Private Federated Learning for Speech Recognition: Benchmarks, Adaptive Optimizers, and Gradient Clipping

    Artificial Intelligence

    Overcoming Vocabulary Constraints with Pixel-level Fallback

    Artificial Intelligence

    Uphold ethical standards in fashion using multimodal toxicity detection with Amazon Bedrock Guardrails

    Artificial Intelligence

    10 Surprising Things You Can Do with Python’s datetime Module

    Artificial Intelligence

    New capabilities in Amazon SageMaker AI continue to transform how organizations develop AI models

    Artificial Intelligence

    Unlock retail intelligence by transforming data into actionable insights using generative AI with Amazon Q Business

  • Apple

    July 15, 2025 – Apple leadership, Mac growth

    iOS 26 public beta rumored to launch next week

    iOS 26 public beta rumored to launch next week

    Future Apple Watch or iPhone may gain a camera that’s completely hidden when not in use

    Future Apple Watch or iPhone may gain a camera that’s completely hidden when not in use

    iOS 26 gives Apple’s Reminders app a new, faster way to add tasks

    iOS 26 gives Apple’s Reminders app a new, faster way to add tasks

    iPhone 17: Titanium is coming to just one model, and it’s a surprising choice

    iPhone 17: Titanium is coming to just one model, and it’s a surprising choice

    Ultimate Edition’ coming to the Mac on July 17

    Ultimate Edition’ coming to the Mac on July 17

    Samsung reportedly gearing up to produce foldable iPhone displays

    Samsung reportedly gearing up to produce foldable iPhone displays

    How a MacBook with an iPhone chip can redefine Apple’s budget line

    How a MacBook with an iPhone chip can redefine Apple’s budget line

    Apple @ Work Podcast: Fleet launches iOS device management

    Apple @ Work Podcast: WebAI puts LLM power in the hands of your IT team

  • ComputerWorld
    How agentic AI will change IT support roles – Computerworld

    How agentic AI will change IT support roles – Computerworld

    Apple’s done innovating? Be serious – Computerworld

    Apple’s done innovating? Be serious – Computerworld

    For July, a ‘big, broad’ Patch Tuesday release – Computerworld

    For July, a ‘big, broad’ Patch Tuesday release – Computerworld

    AI coding tools can slow down seasoned developers by 19%

    AI coding tools can slow down seasoned developers by 19%

    Will IT turn the AI bot battle into a money maker? (And is that even a good idea?) – Computerworld

    Will IT turn the AI bot battle into a money maker? (And is that even a good idea?) – Computerworld

    Tariff uncertainty hits US PC shipments in Q2 – Computerworld

    Tariff uncertainty hits US PC shipments in Q2 – Computerworld

    The fast way to fix a frozen Start menu or taskbar in Windows – Computerworld

    The fast way to fix a frozen Start menu or taskbar in Windows – Computerworld

    Microsoft’s 19-hour Outlook outage exposes fragility in cloud infrastructure – Computerworld

    Microsoft’s 19-hour Outlook outage exposes fragility in cloud infrastructure – Computerworld

    A magically minimalist Android makeover – Computerworld

    A magically minimalist Android makeover – Computerworld

  • Gaming
    The Nintendo DS had it right all along: Ayaneo launches Flip 1S DS and Flip 1S KB, two new clamshell handheld gaming PCs with prices to make your teeth clench

    The Nintendo DS had it right all along: Ayaneo launches Flip 1S DS and Flip 1S KB, two new clamshell handheld gaming PCs with prices to make your teeth clench

    A Delayed Puzzle – Zelda Breath Of The Wild Walkthrough – Solve Kema Zoos Shrine Puzzle

    A Delayed Puzzle – Zelda Breath Of The Wild Walkthrough – Solve Kema Zoos Shrine Puzzle

    Destiny 2 The Desert Perpetual raid release date and time

    Destiny 2 The Desert Perpetual raid release date and time

    GTA 6 Trailer 2: Release Date Confirmed & Official Screenshots!

    GTA 6 Trailer 2: Release Date Confirmed & Official Screenshots!

    As if being worth $4 trillion isn’t enough, Nvidia claims the US government says it can start selling AI GPUs to China again

    As if being worth $4 trillion isn’t enough, Nvidia claims the US government says it can start selling AI GPUs to China again

    GOW  Ragnarok Valhalla (DLC) Gameplay/Walkthrough – No Commentary –  Part 7 (1080p 60fps on Ultra)

    GOW Ragnarok Valhalla (DLC) Gameplay/Walkthrough – No Commentary – Part 7 (1080p 60fps on Ultra)

    US Defense Department awards $200 million contract to Elon Musk’s Grok aka ‘MechaHitler’ and is looking forward to deploying it ‘in our warfighting domain’

    US Defense Department awards $200 million contract to Elon Musk’s Grok aka ‘MechaHitler’ and is looking forward to deploying it ‘in our warfighting domain’

    Why God Of War Ragnarok Will Be One Of THE BEST Games Of 2022 | God Of War Ragnarok Review Roundup

    Why God Of War Ragnarok Will Be One Of THE BEST Games Of 2022 | God Of War Ragnarok Review Roundup

    If you’re on the latest Windows 11 Insider build you might have to uninstall your Xbox controller driver to get it to play nicely

    If you’re on the latest Windows 11 Insider build you might have to uninstall your Xbox controller driver to get it to play nicely

  • Retro Rewind
    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 57 April 1994

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: Computer Gaming World Magazine Issue 73 December 1998

    Retro Rewind: Computer Gaming World Magazine Issue 73 December 1998

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

  • Tech Art
    Virtual Reality is Not What You Think

    Virtual Reality is Not What You Think

    MAJU TALK EPISODE # 2   I  Media and Art Industry Role in Pakistan

    MAJU TALK EPISODE # 2 I Media and Art Industry Role in Pakistan

    Draw A Lotus Flower in Ms Paint | Kamal Kaa Phool Ms Paint Me Kaise Bnaye

    Draw A Lotus Flower in Ms Paint | Kamal Kaa Phool Ms Paint Me Kaise Bnaye

    INSIDE Mirror Mirror: ArtScience Museum's NEW interactive exhibition

    INSIDE Mirror Mirror: ArtScience Museum's NEW interactive exhibition

    Woman Having a Hard Time: Falon Stutzman @ Megan Mulrooney Gallery, Los Angeles

    Woman Having a Hard Time: Falon Stutzman @ Megan Mulrooney Gallery, Los Angeles

    Creating a 3D VENOM Sculpture in Zbrush | Timelapse

    Creating a 3D VENOM Sculpture in Zbrush | Timelapse

    Alicja Kwade: Geologies of the Impossible

    Alicja Kwade: Geologies of the Impossible

    [SWTT] Generative Art NFT Tutorial

    [SWTT] Generative Art NFT Tutorial

    Using Unreal Engine 4 for CONCEPT ART – Full Process Video | From Zero to Concept Art

    Using Unreal Engine 4 for CONCEPT ART – Full Process Video | From Zero to Concept Art

  • Tech Deals
    LEGO Star Wars: The Force Awakens – Xbox 360 Standard Edition

    LEGO Star Wars: The Force Awakens – Xbox 360 Standard Edition

    Western Digital 10TB WD Purple Surveillance Internal Hard Drive HDD – SATA 6 Gb/s, 256…

    Western Digital 10TB WD Purple Surveillance Internal Hard Drive HDD – SATA 6 Gb/s, 256…

    NexStar 6G, 2.5” SATA III to USB 3.2 Gen1 External SSD/HDD Enclosure, ID: Black

    NexStar 6G, 2.5” SATA III to USB 3.2 Gen1 External SSD/HDD Enclosure, ID: Black

    Toshiba Canvio Basics 4TB Portable External Hard Drive USB 3.0, Black – HDTB540XK3CA

    Toshiba Canvio Basics 4TB Portable External Hard Drive USB 3.0, Black – HDTB540XK3CA

    Vansuny 64GB Type C Flash Drive 2 in 1 OTG USB 3.0 + USB C Memory Stick with Keychain…

    Vansuny 64GB Type C Flash Drive 2 in 1 OTG USB 3.0 + USB C Memory Stick with Keychain…

    SABRENT USB C to USB C Charging Cable with Smart Display, 2M/6.6FT Long, E-Marker Chip,…

    SABRENT USB C to USB C Charging Cable with Smart Display, 2M/6.6FT Long, E-Marker Chip,…

    XTRONS for Fiat 500 (2007-2015) Touch Screen Radio, 7 Inch Android 13 Car Stereo for…

    XTRONS for Fiat 500 (2007-2015) Touch Screen Radio, 7 Inch Android 13 Car Stereo for…

    XTRONS Single Din Car Stereo for Fiat 500, Android 13 Octa Core 4GB RAM 64GB ROM Car…

    XTRONS Single Din Car Stereo for Fiat 500, Android 13 Octa Core 4GB RAM 64GB ROM Car…

    Pioneer DJ HDJ-CUE1 On-ear DJ Headphones – Black

    Pioneer DJ HDJ-CUE1 On-ear DJ Headphones – Black

  • Techs Got To Eat
    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Oreo Mug Cake: 2-Minute Cookie & Cake Combo!

    Oreo Mug Cake: 2-Minute Cookie & Cake Combo!

  • Tesla

    Tesla’s long-time head of sales in North America is out

    RYANSTAR RACING Black Car Door Handles Compatible with Tesla Cybertruck 2023 2024 2025 4…

    RYANSTAR RACING Black Car Door Handles Compatible with Tesla Cybertruck 2023 2024 2025 4…

    Tesla finally launches in India, but at a price that doesn’t make sense

    Tesla finally launches in India, but at a price that doesn’t make sense

    Cyber Hooks Heavy Duty Steel L Track Cleat Hooks – 4PCS Set, OEM Style Compatible with…

    Cyber Hooks Heavy Duty Steel L Track Cleat Hooks – 4PCS Set, OEM Style Compatible with…

    Rear Center Console Organizer for Tesla Cybertruck Trash Can with Anti-Slip Lid Cover…

    Rear Center Console Organizer for Tesla Cybertruck Trash Can with Anti-Slip Lid Cover…

    2025 Upgraded J1772 & CCS to Tesla Cybertruck Adapter Fast Charging Adapter Compatible…

    2025 Upgraded J1772 & CCS to Tesla Cybertruck Adapter Fast Charging Adapter Compatible…

    Truck Cover Custom Fit for Tesla Cybertruck, Waterproof All Weather Lightweight Pickup…

    Truck Cover Custom Fit for Tesla Cybertruck, Waterproof All Weather Lightweight Pickup…

    Inflatable Truck Bed Air Mattress for Tesla Cybertruck 2024 2025 Accessories Thicken Air…

    Inflatable Truck Bed Air Mattress for Tesla Cybertruck 2024 2025 Accessories Thicken Air…

    REDTIGER 4K Dash Cam Front, ADAS, Built-in WiFi GPS, Mini Hidden Dash Camera for Cars…

    REDTIGER 4K Dash Cam Front, ADAS, Built-in WiFi GPS, Mini Hidden Dash Camera for Cars…

  • UFO
    New York Eye & Ear Control

    New York Eye & Ear Control

    Drones with Camera for Adults 6K Foldable Headless Drone with Obstacle Avoidance Function Optical Flow Positioning Gesture Photography with Storage Bag 2 Battery

    Drones with Camera for Adults 6K Foldable Headless Drone with Obstacle Avoidance Function Optical Flow Positioning Gesture Photography with Storage Bag 2 Battery

    Women’S Sarong Coverups Beach Bathing Suit Wrap Skirt Sheer Bikini Wraps Chiffon Cover Ups For Swimwear

    Women’S Sarong Coverups Beach Bathing Suit Wrap Skirt Sheer Bikini Wraps Chiffon Cover Ups For Swimwear

    JWST's Mind Blowing Exoplanet Discovery!  #space #spaceexploration #exoplanets #nasa #fyp #shorts

    JWST's Mind Blowing Exoplanet Discovery! #space #spaceexploration #exoplanets #nasa #fyp #shorts

    Space Theme Birthday Candle, Shiny Astronaut Number Candle Spaceship Outer Space Cake Topper Perfect Universe Rocket Spacecraft Cake Decorations and Party Favors(Number 1)

    Space Theme Birthday Candle, Shiny Astronaut Number Candle Spaceship Outer Space Cake Topper Perfect Universe Rocket Spacecraft Cake Decorations and Party Favors(Number 1)

    The Dark Truth About 23andMe

    The Dark Truth About 23andMe

    Spacecraft Dashboard Gaming Mouse Pad Large Mouse Pad Office Desk Accessories XL Desk Mat 31.5×11.8×0.12 inch Blue Large Desk Pad Keyboard Pad (Console)

    Spacecraft Dashboard Gaming Mouse Pad Large Mouse Pad Office Desk Accessories XL Desk Mat 31.5×11.8×0.12 inch Blue Large Desk Pad Keyboard Pad (Console)

    How Much Does it Cost to Launch a Satellite? #shorts

    How Much Does it Cost to Launch a Satellite? #shorts

    Top Secret UFO Sightings #joerogan #podcast #aliens

    Top Secret UFO Sightings #joerogan #podcast #aliens

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Techcratic
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Home Hacker News

A tool to verify estimates, II: a flexible proof assistant

Hacker News by Hacker News
May 14, 2025
in Hacker News
Reading Time: 11 mins read
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2025-05-10 06:41:00
terrytao.wordpress.com

In a recent post, I talked about a proof of concept tool to verify estimates automatically. Since that post, I have overhauled the tool twice: first to turn it into a rudimentary proof assistant that could also handle some propositional logic; and second into a much more flexible proof assistant (deliberately designed to mimic the Lean proof assistant in several key aspects) that is also powered by the extensive Python package sympy for symbolic algebra, following the feedback from previous commenters. This I think is now a stable framework with which one can extend the tool much further; my initial aim was just to automate (or semi-automate) the proving of asymptotic estimates involving scalar functions, but in principle one could keep adding tactics, new sympy types, and lemmas to the tool to handle a very broad range of other mathematical tasks as well.

The current version of the proof assistant can be found here. (As with my previous coding, I ended up relying heavily on large language model assistance to understand some of the finer points of Python and sympy, with the autocomplete feature of Github Copilot being particularly useful.) While the tool can support fully automated proofs, I have decided to focus more for now on semi-automated interactive proofs, where the human user supplies high-level “tactics” that the proof assistant then performs the necessary calculations for, until the proof is completed.

It’s easiest to explain how the proof assistant works with examples. Right now I have implemented the assistant to work inside the interactive mode of Python, in which one enters Python commands one at a time. (Readers from my generation may be familiar with text adventure games, which have a broadly similar interface.) I would be interested developing at some point a graphical user interface for the tool, but for prototype purposes, the Python interactive version suffices. (One can also run the proof assistant within a Python script, of course.)

After downloading the relevant files, one can launch the proof assistant inside Python by typing from main import * and then loading one of the pre-made exercises. Here is one such exercise:

>>> from main import *
>>> p = linarith_exercise()
Starting proof.  Current proof state:
x: pos_real
y: pos_real
z: pos_real
h1: x 

This is the proof assistant’s formalization of the following problem: If x,y,z are positive reals such that x < 2y and y < 3z+1, prove that x < 7z+2.

The way the proof assistant works is that one directs the assistant to use various “tactics” to simplify the problem until it is solved. In this case, the problem can be solved by linear arithmetic, as formalized by the Linarith() tactic:

>>> p.use(Linarith())
Goal solved by linear arithmetic!
Proof complete!

If instead one wanted a bit more detail on how the linear arithmetic worked, one could have run this tactic instead with a verbose flag:

>>> p.use(Linarith(verbose=true))
Checking feasibility of the following inequalities:
1*z > 0
1*x + -7*z >= 2
1*y + -3*z  0
1*x > 0
1*x + -2*y  0 multiplied by 1/4
1*x + -7*z >= 2 multiplied by 1/4
1*y + -3*z 

Sometimes, the proof involves case splitting, and then the final proof has the structure of a tree. Here is one example, where the task is to show that the hypotheses (x>-1) \wedge (x<1) and (y>-2) \wedge (y<2) imply (x+y>-3) \wedge (x+y<3):

>>> from main import *
>>> p = split_exercise()
Starting proof.  Current proof state:
x: real
y: real
h1: (x > -1) & (x  -2) & (y  -3) & (x + y >> p.use(SplitHyp("h1"))
Decomposing h1: (x > -1) & (x  -1, x >> p.use(SplitHyp("h2"))
Decomposing h2: (y > -2) & (y  -2, y >> p.use(SplitGoal())
Split into conjunctions: x + y > -3, x + y >> p.use(Linarith())
Goal solved by linear arithmetic!
1 goal remaining.
>>> p.use(Linarith())
Goal solved by linear arithmetic!
Proof complete!
>>> print(p.proof())
example (x: real) (y: real) (h1: (x > -1) & (x  -2) & (y  -3) & (x + y 

Here at the end we gave a “pseudo-Lean” description of the proof in terms of the three tactics used: a tactic cases h1 to case split on the hypothesis h1, followed by two applications of the simp_all tactic to simplify in each of the two cases.

The tool supports asymptotic estimation. I found a way to implement the order of magnitude formalism from the previous post within sympy. It turns out that sympy, in some sense, already natively implements nonstandard analysis: its symbolic variables have an is_number flag which basically corresponds to the concept of a “standard” number in nonstandard analysis. For instance, the sympy version S(3) of the number 3 has S(3).is_number == True and so is standard, whereas an integer variable n = Symbol("n", integer=true) has n.is_number == False and so is nonstandard. Within sympy, I was able to construct orders of magnitude Theta(X) of various (positive) expressions X, with the property that Theta(n)=Theta(1) if n is a standard number, and use this concept to then define asymptotic estimates such as X \lesssim Y (implemented as lesssim(X,Y)). One can then apply a logarithmic form of linear arithmetic to then automatically verify some asymptotic estimates. Here is a simple example, in which one is given a positive integer N and positive reals x,y such that x \leq 2N^2 and y < 3N, and the task is to conclude that xy \lesssim N^4:

>>> p = loglinarith_exercise()
Starting proof.  Current proof state:
N: pos_int
x: pos_real
y: pos_real
h1: x >> p.use(LogLinarith(verbose=True))
Checking feasibility of the following inequalities:
Theta(N)**1 >= Theta(1)
Theta(x)**1 * Theta(N)**-2  Theta(1)
Infeasible by multiplying the following:
Theta(N)**1 >= Theta(1) raised to power 1
Theta(x)**1 * Theta(N)**-2  Theta(1) raised to power 1
Proof complete!

The logarithmic linear programming solver can also handle lower order terms, by a rather brute force branching method:

>>> p = loglinarith_hard_exercise()
Starting proof.  Current proof state:
N: pos_int
x: pos_real
y: pos_real
h1: x >> p.use(LogLinarith())
Goal solved by log-linear arithmetic!
Proof complete!

I plan to start developing tools for estimating function space norms of symbolic functions, for instance creating tactics to deploy lemmas such as Holder’s inequality and the Sobolev embedding inequality. It looks like the sympy framework is flexible enough to allow for creating further object classes for these sorts of objects. (Right now, I only have one proof-of-concept lemma to illustrate the framework, the arithmetic mean-geometric mean lemma.)

I am satisfied enough with the basic framework of this proof assistant that I would be open to further suggestions or contributions of new features, for instance by introducing new data types, lemmas, and tactics, or by contributing example problems that ought to be easily solvable by such an assistant, but are currently beyond its ability, for instance due to the lack of appropriate tactics and lemmas.

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