{"id": 1380499163708846082, "geo": null, "lang": "en", "text": "Brilliant! Looks like @_KartikMenon rediscovered a proof for a version of Ramanujan Nested Log-Trigonometric Integr\u2026 https://t.co/ccaId0amxW", "user": {"id": 381289719, "url": "http://www.realworldrisk.com", "lang": null, "name": "Nassim Nicholas Taleb", "id_str": "381289719", "location": null, "verified": true, "following": null, "protected": false, "time_zone": null, "created_at": "Wed Sep 28 02:19:07 +0000 2011", "utc_offset": null, "description": "Flaneur: probability (philosophy, mathematics), probability (real life),  Phoenician wine, deadlifts & dead languages\nGreco-Levantine\n#RWRI\nUber rating ~4.9", "geo_enabled": false, "screen_name": "nntaleb", "listed_count": 9964, "friends_count": 1156, "is_translator": false, "notifications": null, "statuses_count": 31419, "default_profile": false, "followers_count": 721224, "translator_type": "none", "favourites_count": 50051, "profile_image_url": "http://pbs.twimg.com/profile_images/1200820286964346880/Zz6YSFus_normal.jpg", "profile_banner_url": "https://pbs.twimg.com/profile_banners/381289719/1402489958", "profile_link_color": "0084B4", "profile_text_color": "333333", "follow_request_sent": null, "contributors_enabled": false, "default_profile_image": false, "profile_background_tile": false, "profile_image_url_https": "https://pbs.twimg.com/profile_images/1200820286964346880/Zz6YSFus_normal.jpg", "profile_background_color": "C0DEED", "profile_sidebar_fill_color": "DDEEF6", "profile_background_image_url": "http://abs.twimg.com/images/themes/theme1/bg.png", "profile_sidebar_border_color": "FFFFFF", "profile_use_background_image": false, "profile_background_image_url_https": "https://abs.twimg.com/images/themes/theme1/bg.png"}, "place": null, "id_str": "1380499163708846082", "source": "<a href=\"https://mobile.twitter.com\" rel=\"nofollow\">Twitter Web App</a>", "entities": {"urls": [{"url": "https://t.co/ccaId0amxW", "indices": [117, 140], "display_url": "twitter.com/i/web/status/1\u2026", "expanded_url": "https://twitter.com/i/web/status/1380499163708846082"}], "symbols": [], "hashtags": [], "user_mentions": [{"id": 1263291588161294336, "name": "Kartik Menon", "id_str": "1263291588161294336", "indices": [22, 35], "screen_name": "_KartikMenon"}]}, "favorited": false, "retweeted": false, "truncated": true, "created_at": "Fri Apr 09 12:33:43 +0000 2021", "coordinates": null, "quote_count": 0, "reply_count": 0, "contributors": null, "filter_level": "low", "timestamp_ms": "1617971623719", "retweet_count": 0, "extended_tweet": {"entities": {"urls": [], "media": [{"id": 1380495954458124289, "url": "https://t.co/CRIfJ7UxIF", "type": "photo", "sizes": {"large": {"h": 1006, "w": 1482, "resize": "fit"}, "small": {"h": 462, "w": 680, "resize": "fit"}, "thumb": {"h": 150, "w": 150, "resize": "crop"}, "medium": {"h": 815, "w": 1200, "resize": "fit"}}, "id_str": "1380495954458124289", "indices": [280, 303], "media_url": "http://pbs.twimg.com/media/EyiBwaNXIAEUTVB.jpg", "display_url": "pic.twitter.com/CRIfJ7UxIF", "expanded_url": "https://twitter.com/nntaleb/status/1380499163708846082/photo/1", "media_url_https": "https://pbs.twimg.com/media/EyiBwaNXIAEUTVB.jpg"}, {"id": 1380498410374098948, "url": "https://t.co/CRIfJ7UxIF", "type": "photo", "sizes": {"large": {"h": 334, "w": 1246, "resize": "fit"}, "small": {"h": 182, "w": 680, "resize": "fit"}, "thumb": {"h": 150, "w": 150, "resize": "crop"}, "medium": {"h": 322, "w": 1200, "resize": "fit"}}, "id_str": "1380498410374098948", "indices": [280, 303], "media_url": "http://pbs.twimg.com/media/EyiD_XNW8AQGYvq.jpg", "display_url": "pic.twitter.com/CRIfJ7UxIF", "expanded_url": "https://twitter.com/nntaleb/status/1380499163708846082/photo/1", "media_url_https": "https://pbs.twimg.com/media/EyiD_XNW8AQGYvq.jpg"}], "symbols": [], "hashtags": [], "user_mentions": [{"id": 1263291588161294336, "name": "Kartik Menon", "id_str": "1263291588161294336", "indices": [22, 35], "screen_name": "_KartikMenon"}]}, "full_text": "Brilliant! Looks like @_KartikMenon rediscovered a proof for a version of Ramanujan Nested Log-Trigonometric Integrals (partial nesting).\nSee (second screenshot) two major tricks with cos(t)=sqrt(\\frac{log(cos x)^2)}{...}_ and  cos(t/n)= sqrt(\\frac{1}{2}+\\frac{1}{2}..... cos(t). https://t.co/CRIfJ7UxIF", "extended_entities": {"media": [{"id": 1380495954458124289, "url": "https://t.co/CRIfJ7UxIF", "type": "photo", "sizes": {"large": {"h": 1006, "w": 1482, "resize": "fit"}, "small": {"h": 462, "w": 680, "resize": "fit"}, "thumb": {"h": 150, "w": 150, "resize": "crop"}, "medium": {"h": 815, "w": 1200, "resize": "fit"}}, "id_str": "1380495954458124289", "indices": [280, 303], "media_url": "http://pbs.twimg.com/media/EyiBwaNXIAEUTVB.jpg", "display_url": "pic.twitter.com/CRIfJ7UxIF", "expanded_url": "https://twitter.com/nntaleb/status/1380499163708846082/photo/1", "media_url_https": "https://pbs.twimg.com/media/EyiBwaNXIAEUTVB.jpg"}, {"id": 1380498410374098948, "url": "https://t.co/CRIfJ7UxIF", "type": "photo", "sizes": {"large": {"h": 334, "w": 1246, "resize": "fit"}, "small": {"h": 182, "w": 680, "resize": "fit"}, "thumb": {"h": 150, "w": 150, "resize": "crop"}, "medium": {"h": 322, "w": 1200, "resize": "fit"}}, "id_str": "1380498410374098948", "indices": [280, 303], "media_url": "http://pbs.twimg.com/media/EyiD_XNW8AQGYvq.jpg", "display_url": "pic.twitter.com/CRIfJ7UxIF", "expanded_url": "https://twitter.com/nntaleb/status/1380499163708846082/photo/1", "media_url_https": "https://pbs.twimg.com/media/EyiD_XNW8AQGYvq.jpg"}]}, "display_text_range": [0, 279]}, "favorite_count": 0, "is_quote_status": false, "display_text_range": [0, 140], "possibly_sensitive": false, "in_reply_to_user_id": 381289719, "in_reply_to_status_id": 1380265306883559426, "in_reply_to_screen_name": "nntaleb", "in_reply_to_user_id_str": "381289719", "in_reply_to_status_id_str": "1380265306883559426"}