“No man has the right to be an amateur in the matter of physical training. It is a shame for a man to grow old without seeing the beauty and strength of which his body is capable.” ― Socrates
3.12.1 On noticing that Epigenes, one of his companions, was in poor condition, for a young man, he said: “You look as if you need exercise, Epigenes.”
“Well,” he replied, “I'm not an athlete, Socrates.”
“Just as much as the competitors entered for Olympia,” he retorted. “Or do you count the life and death struggle with their enemies, upon which, it may be, the Athenians will enter, but a small thing?
3.12.2 Why, many, thanks to their bad condition, lose their life in the perils of war or save it disgracefully: many, just for this same cause, are taken prisoners, and then either pass the rest of their days, perhaps, in slavery of the hardest kind, or, after meeting with cruel sufferings and paying, sometimes, more than they have, live on, destitute and in misery. Many, again, by their bodily weakness earn infamy, being thought cowards.
3.12.3 Or do you despise these, the rewards of bad condition, and think that you can easily endure such things? And yet I suppose that what has to be borne by anyone who takes care to keep his body in good condition is far lighter and far pleasanter than these things. Or is it that you think bad condition healthier and generally more serviceable than good, or do you despise the effects of good condition?
3.12.4 And yet the results of physical fitness are the direct opposite of those that follow from unfitness. The fit are healthy and strong; and many, as a consequence, save themselves decorously on the battle-field and escape all the dangers of war; many help friends and do good to their country and for this cause earn gratitude; get great glory and gain very high honours, and for this cause live henceforth a pleasanter and better life, and leave to their children better means of winning a livelihood.
3.12.5 “I tell you, because military training is not publicly recognised by the state, you must not make that an excuse for being a whit less careful in attending to it yourself. For you may rest assured that there is no kind of struggle, apart from war, and no undertaking in which you will be worse off by keeping your body in better fettle. For in everything that men do the body is useful; and in all uses of the body it is of great importance to be in as high a state of physical efficiency as possible.
3.12.6 Why, even in the process of thinking, in which the use of the body seems to be reduced to a minimum, it is matter of common knowledge that grave mistakes may often be traced to bad health. And because the body is in a bad condition, loss of memory, depression, discontent, insanity often assail the mind so violently as to drive whatever knowledge it contains clean out of it.
3.12.7 But a sound and healthy body is a strong protection to a man, and at least there is no danger then of such a calamity happening to him through physical weakness: on the contrary, it is likely that his sound condition will serve to produce effects the opposite of those that arise from bad condition. And surely a man of sense would submit to anything to obtain the effects that are the opposite of those mentioned in my list.
3.12.8 “Besides, it is a disgrace to grow old through sheer carelessness before seeing what manner of man you may become by developing your bodily strength and beauty to their highest limit. But you cannot see that, if you are careless; for it will not come of its own accord.”
From Reddit user Iphikrates:
Sokrates never wrote anything down, so all we know about him is how he is described by others. These accounts offer limited information about his life and don't always agree on his philosophies. Apart from the contemporary parody of Sokrates in Aristophanes' Clouds, we mostly rely on the philosophical dialogues written by two of Sokrates' students, Xenophon and Plato. Whether these authors represented Sokrates' views accurately or merely used him as a mouthpiece for their own ideas is debated. Whether their image of Sokrates as an ugly, poorly dressed, ostentatiously poor old man matched the reality is up for grabs.
So, when we get a quote like this, how can we know whether Sokrates really said it, let along whether he lived by it? Unfortunately, we can't really know for sure. What we can do, though, is work out how likely it is that he held this view, and if so, how likely it is that he held himself to it. To do this, we need to consider the context of the quote.
This context is, in fact, a very short Sokratic dialogue by Xenophon (Memorabilia 3.12). According to the text, Sokrates ran into a young acquaintance of his named Epigenes, who was out of shape; Sokrates told him he ought to go do some exercise. Epigenes replied "I'm not an athlete", at which point Sokrates chewed him out.
The main point of Sokrates' argument, however, is not that men owe it to themselves to train their bodies so they can look their best. The quote you cited (3.12.8) is little more than the cherry on the cake, a closing line meant to convince Epigenes by appealing to his vanity. The entire rest of the argument is that Epigenes owes it to the state to train his body, because otherwise he will be useless in war. Epigenes should think of himself as an athlete, Sokrates argues (3.12.1), because he will have to fight for his city, and the only way to be a good fighter is to get fit.
Sokrates admits, as many modern scholars do, that "the city does not publicly train for war" (3.12.5). There was no group drill or military exercise for the Athenian hoplite militia. To make up for this shortcoming, Sokrates says, individual men like Epigenes ought to do all they can to make sure they are at least individually as fit as they can be, so that they won't let their community down or get a reputation for cowardice. All the other benefits of physical fitness listed by Sokrates (3.12.6-8) are just a bonus.
This argument ties into two strands of Classical Greek thought. The first and older of the two is the ideal that the elite, having the leisure to do whatever they want, ought to use their time to be the best possible people. They should sharpen their minds to become better shepherds to their fellow man, and improve their bodies so they will be better protectors of their community. These ideals have their most competitive product in the Games held throughout the Greek world, with the Olympics being the most famous. In their desire to be the best at paramilitary activities like javelin throwing, wrestling or running in armour, athletes at the Olympics were simply taking an old leisure-class ideal to an extreme.
In practice, however, most of the rich couldn't be bothered. Having a perfect physique took a lot of hard work that could also be spent hunting or drinking or reading or sleeping with prostitutes. Many among the elite fell short of their ideal of being kaloikagathoi, the beautiful and good, who earned their high status by being literally better than others. Both Xenophon and Plato complain about the "fat rich men" who live their lives in the shade and aren't worth much when called upon to fight for their city. Instead of exemplars for the common folk, they are the subject of derision - the pasty white, flabby, gormless rich who wouldn't know which end of a spear to stick in the bad guys. This is why Sokrates in this dialogue (3.12.2) stresses that Epigenes ought to train so that people won't think he's a coward.
The second strand is the notion that Greek armies really ought to do more training. All sources suggest that they generally received none, and Xenophon and Plato in particular are extremely vocal in their disappointment about this. Both advocate more comprehensive state-funded training programmes. Both also advocate similar methods to be used by armies on campaign. In Xenophon's case, this probably derives from his own experience as a mercenary and his observations when he was living with the Spartans. For Plato, however, it simply fits into the general philosophical trend of the later 5th and particularly the 4th century, to regard all areas of expertise as teachable, including martial prowess. In this new way of thinking, armies didn't just fight with innate skill or courage, but could be taught to fight better. They needed to be trained, both in collective drill and mock combat, and in weapon proficiency. Since no Greek state went very far in bringing this into practice even in the later 4th century BC, Xenophon and Plato could do nothing but describe the superior condition and military abilities of those who did train (the Spartans, and the Guardians of Plato's ideal city-state, respectively), and encourage individual members of the leisure class to do themselves and the state a favour by setting the right example. This is what Sokrates is made to say (3.12.5):
I tell you, just because the city does not publicly train for war, you must not make that an excuse for being any less careful in attending to it yourself.
With this context in mind, is it likely that Sokrates held these views and practiced what he preached? As a contemporary of the sophists, who were the first to argue that anything could be taught, it is possible that Sokrates already believed in the merits of military training. However, the frustrations of Xenophon and Plato, and their hammering on about training as a result, belongs to the 4th century BC. The specific reference to a lack of proper state-funded training, and the complaint about rich citizens who choose to be weak and lazy, shows that Xenophon is using Sokrates here as an authoritative mouthpiece for his solutions to problems he saw in his own time. There is little to suggest that there was a debate on the merits of military training in Sokrates' day, so it's not very likely that Xenophon was representing the actual words of Sokrates.
As to whether Sokrates himself was in shape, there isn't much to go on. Xenophon insists that he was fond of dancing, which may have kept him spritely even in old age - but dancing is often promoted as another way to stay fit and agile for battle. Perhaps this is yet another intrusion of Xenophon's own obsession with the need to prepare for war.
We do know from Xenophon and Plato that Sokrates - being a member of the leisure class himself - saw extensive military service. He served at the siege of Potidaia (432-430 BC), at Delion (424 BC) and at Amphipolis (422 BC), earning a reputation for level-headedness, courage, and indifference to hardship. But there is nothing to suggest that he was fit. The army certainly wouldn't have trained him, since, as noted above, Greek armies didn't train. Some armies held athletic competitions while on campaign, to improve the overall fitness of the troops by invoking their competitive instincts, but there's no evidence that the Athenians at Potidaia did this. No part of Sokrates' typical description suggests he was muscled; instead, he is described as lean and ugly and dirty. His hardiness on campaign wasn't meant to show his embodiment of the old leisure-class ideal of the perfect man, but to prove his credentials as a perfect philosopher: putting mind above matter, he had become completely indifferent to the sufferings of his body, allowing it to go without warmth or food at will. It seems highly unlikely that such a man, if Sokrates was really like this, could have maintained a perfect physique.