Bartimaeus often boasts about his previous epic feats. Ran with buffalo fathers, rebuilt walls of Karnak, Prague et cetera. How many of these boasts do we have evidence for?
Bartimaeus has a definite tendency towards self-aggrandizement. As such, we can consider what he says to be entirely confirmed only when shown in the text, or when confirmed by other witnesses to these events, or when Bartimaeus mentions it to them and they do not contest it. Since most of these events happened hundreds or thousands of years prior to the events of the books, the only remaining witnesses are other spirits. Bartimaeus has claimed hundreds of feats and associations throughout the series, and only a few of these can be confirmed.
"I have spoken with Solomon and Ptolemy, and hunted down the Sea Peoples in the company of kings."
—The Golem's Eye
In Ptolemy's Gate, we see Bartimaeus interacting with Ptolemy.
The boy lowered his gaze to the impassive doppelganger watching him across the moonlit room. I gave a mock salute. Ptolemy brushed the dark hair from his eyes and bowed.
"Thank you, Rekhyt," he said.
Indeed. he more than knew Ptolemy: Ptolemy was one of the few magicians who did not try to enslave Bartimaeus, and consequently one of the few he genuinely respected (as illustrated by the previous quote). They were good friends for several years.
"I have spoken with Solomon—"
"Oh, please!" The afrit made a dismissive gesture. "Haven't we all? Let's face it, he got around."
—The Golem's Eye
You might say that Bartimaeus knew Solomon. He spoke with him, stole his Ring, and otherwise irritated him.
“Now,” King Solomon said, “to my judgment. Bartimaeus of Uruk, you first of all. Your crimes are legion. You have caused the deaths of dozens of my spirits, you have spread chaos and disaster across Jerusalem. It was by your advice and through your actions that this girl was able to get access to the Ring. Not only that, you have at all times displayed extraordinary insolence toward my royal person. Your hippo guise—”
“No, no, that was perfectly coincidental! It looks nothing like your wife!”
—The Ring of Solomon
Built the walls of a number of cities
"I have rebuilt the walls of Uruk, Karnak, and Prague—"
—The Golem's Eye
This was not contradicted by Queezle, who knew him well. She also added that he had built the walls of Jericho.
The young man smirked. "Prague? What, these ones here? The ones it took Gladstone five minutes to break down? Sure you didn't work on Jericho, too?"
"Yes, he did," Queezle put in. "One of his first jobs. He keeps quiet about it, but—"
—The Golem's Eye
Our first introduction to Bartimaeus:
"I am Bartimaeus! I am Sakhr al-Jinni, N'gorso the Mighty and the Serpent of Silver Plumes! I have rebuilt the walls of Uruk, Karnak and Prague. I have spoken with Solomon. I have run with the buffalo fathers of the plains. I have watched over Old Zimbabwe till the stones fell and the jackals fed on its people. I am Bartimaeus! I recognise no master. So I charge you in your turn, boy. Who are you to summon me?"
Impressive stuff, eh? All true as well, which gives it more power. And I wasn't just doing it to sound big. I rather hoped the kid would be blustered by it into telling me his name in return, which would give me something to go on when his back was turned.
-- The Amulet of Samarkand, Chapter 1
He claims that this is all true, but we can't necessarily take him at his word since he's known to be an unreliable narrator at times. So let's go through his claims:
I am Bartimaeus! I am Sakhr al-Jinni, N'gorso the Mighty and the Serpent of Silver Plumes!
True. These are just names; not much of a boast there.
I have rebuilt the walls of Uruk, Karnak and Prague.
Probably true. He repeats this claim so often over the course of the series that you would've expected someone to pick him up on it at some point if it were a lie.
I have spoken with Solomon.
True. In fact, as we find out in The Ring of Solomon, he has done rather more than just spoken with Solomon - he held, for a while, a position that perhaps no other spirit ever did. (Spoilers!)
I have run with the buffalo fathers of the plains.
Unknown. As far as I recall, he never elaborates on this. Probably true though - when you get right down to it, it doesn't sound like a particularly impressive feat, so if he'd wanted to make something up, he probably would have chosen something more grandiose.
I have watched over Old Zimbabwe till the stones fell and the jackals fed on its people.
Unknown. Probably true though, since again it doesn't sound like much of a feat, to sit and watch over a city.
The very last boast we hear from Bartimaeus, as he taunts Nouda during the final stages of book 3:
"Nouda! It is I, Bartimaeus, Sakhr al-Jinni, N'gorso the Mighty and the Serpent of Silver Plumes! I have fought a thousand battles and won them all! I have destroyed far greater entities than you! Ramuthra fled before my majesty. Tchue cowered in a crack in the earth. Hoepo the Thunder Snake ingested his own tail and so swallowed himself rather than taste my fury! So then, I challenge you now. Come face me!"
-- Ptolemy's Gate, Chapter 38
Most of these claims are rather more embellished, and at best a grotesquely twisted version of the truth.
I have fought a thousand battles and won them all!
False. Whether or not he's won a thousand battles in his life is unknown, but he certainly hasn't won all the battles he's fought, and likely not even the last thousand. For instance, in the Battle of Prague he was rather ignominiously defeated, as we saw in the prologue to The Golem's Eye.
I have destroyed far greater entities than you!
Unknown. I'm tempted to say 'false', since Bartimaeus is only a mid-level djinni and Nouda a spirit vastly more powerful than even a marid. But then, Bartimaeus did defeat Jabor (a powerful djinni), Honorius (an afrit), and, in The Ring of Solomon, even a marid. He does have the potential to defeat much more powerful spirits, by his trademark guile and trickery.
Ramuthra fled before my majesty.
False. Ramuthra, the spirit summoned at the end of book 1, was defeated and sent back to the Other Place by a joint effort of which Bartimaeus was part, but "fled before my majesty" is a blatant lie.
Tchue cowered in a crack in the earth. Hoepo the Thunder Snake ingested his own tail and so swallowed himself rather than taste my fury!
Unknown. But given the rest of Bartimaeus's rant here, I suspect false.
Now I've been through some of Bartimaeus's most notorious and oft-repeated boasts. I'm not terribly inclined to do a DVK and go through every single statement Bartimaeus ever made in all three or four books to verify its veracity or otherwise; but if anybody else wants to do so, I'll certainly award them a bounty for the effort.
The Amulet of Samarkand
On Simon Lovelace's defence nexus:
"Not bad but I could handle it."
True - He dug under it on the way in and tore through it on exit.
On Lovelace's imp:
"I could squash it without a second thought."
True - They never fight but Bartimaeus beats a lot of imps so it seems likely.
On triloids (Lovelace's guards):
"Thus does superior intelligence win over brute strength."
False - The triloid has actually outsmarted him (with Farqual's help) by leading him to Faqual.
To Kitty Jones
"You don't really know who I am, do you?", "A magician would know better than to trifle with one such as me.", "I'm toying with you.", "I have many abilities at my command."
False - Bartimaeus freely admits this is "empty bluster".
A footnote on talking to Djinn:
"Strictly advisable when dealing with subtle, intelligent entities such as myself."
True - His intelligence is his main trait.
On swinging through a door using spider webs:
"It was a great stunt"
Probably true - We have no reason to disbelieve it.
At this point we have the first (I think) name drop of Ptolemy.
"Ptolemy was about fourteen when I knew him best."
True - He did know Ptolemy very well as seen in Ptolemy's Gate.
When asking an imp about Lovelace's servants:
"I don't mean squirts like you, but potent ones like me."
True-ish- He is more powerful than the imp but he is less powerful than Lovelace's servants Farqual and Jabba.
On how intelligent he is compared to humans:
"My mind works on several levels."
True - He is seen multi-tasking several times in the books.
On Uttuku and his prowess killing them:
"I first fought these at the battle of Al-Arish."
True - Batuk calls him "The destroyer of my people" giving some credit to his claims of defeating many utukku.
More name drops now:
I, Bartimaeus, who spoke with Solomon and Hiawatha"
Not sure - The Solomon bit is true the Hiawatha bit I don't think is ever repeated but it seems possible so I would be tempted to say true.
On serving in Pharaoh Tuthmosis's army:
A motley group of higher Djinn of which surely the most notable was...No, modesty prevents me from continuing."
Probably false - It seems likely he served in the army as most Djinn serve in many armies and he is shown to serve in Egypt. I doubt he was their most notable Djinn as his tactic in the battle of Prague seemed to be to allow others to take the brunt if the enemy.
On the rescue and flight from Jabba:
"That dramatic rescue I pulled off"
True - They succeed in not only escaping but also temporarily slowing Jabba.
Threatening Nathaniel's scurrying imp:
"I pick my teeth with imps his size"
False - We never see him eat an imp or kill one if he doesn't have to. He even let Nittles go despite having trapped him.
Next Bartimaeus boasts of his exploits in Prague:
"A Czech magician, who shall remain nameless, charged me to steal certain documents."
Probably true - He was one of Prague's most powerful spirits in the later days of the war and was given various important charges.
On his essence and position among sprits levels of power:
"When you're pretty darn perfect to start with"
False - He has many flaws including boastfulness.
Talking about his construction experience:
"When you've helped construct some of the world's most majestic buildings, and in some instances given some pretty useful tips to the architects concerned"
Exaggeration - He has done a lot of building work, including things like Solomon's Temple, but we never see him giving out any architectural tips and he mainly seems to so building not planning.
On his lizard form:
"All things considered, it was another perfect choice of form."
True - In this situation a camouflaged, climbing lizard was a good choice.
On stealing the Amulet:
"My fine trick"
True - It was a very clever idea which worked to get the Amulet.
On his escape from the Tower of London:
"The swashbuckling djinn I who had lately escaped from the government prison."
Exaggeration - While he did escape it was not down to his power but from Farqual and Jabba's assistance.
So in the Amulet of Samarkand Bartimaeus is mostly truthful with some exaggeration although he does occasionally lie.