Thursday, December 25, 2025

Quotes of G.H. Hardy

 GHH was a leading mathematician of his time.

 “I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, 'Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.”

 “In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.”

 “It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.”

 “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

 “Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”

 “No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.”

 “The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”

 “The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness.”

Progress in Alzheimer's

 From Science Daily.

 Here is the link.

 https://www.sciencedaily.com/releases/2025/12/251224032354.htm

Sunday, December 07, 2025

Wednesday, December 03, 2025

The Three O’Clock Patient

 Mark Litwin, MD, at JAMA.

 Internally, I rolled my eyes when I read the 3:00 pm listing on my clinic schedule, “37-year old male for second opinion, metastatic penile cancer,” suppressing my frustration that the call center staff had mistakenly scheduled this man to see me, a surgeon, when he obviously should have been directed to medical oncology. This would take most of an hour, and surely there was nothing I could offer him.

 Sunset would bring Yom Kippur, and I wanted to get to temple on time for the holiest of all evenings on the Jewish calendar. On this holiday, we contemplate and atone for our sins and we—Jewish people believe—are inscribed in the so-called Book of Life for a new year of good health. The solemn, 25-hour observance is among our most sacred, and I didn’t want to be late.

 Reading the extensive medical history, I grew restless. Diagnosed 2 years earlier during circumcision for a suspicious lesion and advised to undergo a potentially curative operation, he was lost to follow-up, instead seeking alternative care in Mexico. But when the primary tumor began growing, he had returned to the US a few months ago and was found to have metastatic lymph nodes in his groins and abdomen. First-line chemotherapy at an out-of-state medical center had failed to slow the growth of the tumor, which had now spread to his bones and was causing substantial pain. He had then transferred his care to a nearby cancer center where he had undergone placement of a peripherally inserted central catheter line for extended antibiotic treatment of infections at the site of the tumor and was scheduled to begin second-line chemotherapy 2 days later. What could I possibly do? I straightened my white coat, scraped the depths of my training, and steeled myself as I entered the examination room.

 He slouched in a wheelchair, wizened from the cancer and bald from chemotherapy, a large gold crucifix hanging from a chain around his neck, attentive wife at his side. A brief physical examination confirmed the worst: large mass where the tumor had started, bilateral inguinal masses where cancer-filled lymph nodes pushed through paper-thin skin, bitter smell permeating the room. He stared up at me for salvation.

 We exchanged introductions. “I’ve reviewed your records so I know the basics of what you have been through, but tell me how I can help,” I began. He glanced over at his wife, as I’ve seen male patients often do, to recount his story. She finished her summary with a plea, “We just need to know if we are doing the right thing, we just want him to get better, to be cured.” Full stop. He did not need my surgical care. He did not need care from our medical oncologist. What he needed was caring.

 “The doctors you are seeing are planning the same treatment you would receive here. The other medical center is one of the top places for cancer. I can reassure you that they are prescribing the best medicines for what you have. That will give you the best chance.” I knew the prognosis was dismal, but I sensed that they did not. Someone needed to level with them yet, apparently, no one had.

 “What you have is very serious,” I struggled to find the right words. “It’s very serious and, very serious and,” my voice cracking as I repeated myself. I paused to collect my thoughts. “Even with the best treatment, even with the best treatment, you, you might not make it,” I stumbled. “What you have is very serious.” I felt my words opening a previously unaccessed channel, as tears began to stream down both their cheeks. “Do you have kids?” I inquired. Yes, 2 children, ages 12 and 13 years. “Talk to them, spend time with them, take pictures with them,” I offered. Silence.

 As a left-brained medical scientist, I don’t generally bring up religion with patients. But I had reached the limit of my healing capacity, so I took a cue from the patient himself. “You believe in God?” I asked. They nodded. “Well, God may soon be calling you to be with Him. You may pass away from this. We pray for the best, but sometimes God has other plans for us.” They nodded and cried. My words felt as unfamiliar as they did natural and in a strange way even comforting. Tissues are always plentiful in my office, and the patient and his wife used their share. But they left the office with a bit of calm that replaced a bit of angst.

 As evening fell and Yom Kippur began, I slouched in my pew, unable to shake the memory of the 3:00 pm patient and his wife. A cello whispered the haunting opening melody of the Kol Nidre prayer and I wondered, had I helped him or was I feeling overly self-satisfied. Throughout the evening and next day of prayerful meditation, I kept thinking about whether he would be inscribed in the Book.

 The progressive Yom Kippur liturgy typically concludes with swelling music, poignant entreaties, a crescendo of chants, and the exalted final blows of the shofar. Weakened from a day of fasting, we imagine the gates of heaven closing, our fates sealed. Did I squeak through? Did he?

 It is ironic in the modern era of extraordinary technology, genetic targeting, and innovations unimaginable a generation ago that when science fails us, we reach for philosophy, for the humanities, and for religion even. Yet therein lies our strength as clinicians. Our uniquely human ability to connect empowers us to provide caring in our care, as Francis Peabody wrote a century ago,1 to help heal when we cannot cure.

 Two days after Yom Kippur, we read a passage from Deuteronomy that tells us to circumcise our hearts to open them to others. Trimming away the excess trappings of our profession brings us closer to patients and to each other. The work of the head and the hands is consummated by the work of the heart.