Another commission. If it looks familiar, it's because it's the "Alexander the Great kicks even more ass" version of my earlier "Gauls shank Rome' map.
After further delay (I was out of the country visiting my sister, thanks to the financial assistance of my most generous brother), here's the writeup.
In this world Alexander the Great lived longer and put on a solid footing an empire which at its heights extended from central Italy and conquered Carthage in the West to the Punjab in the East. It would clash with the rising Mauryas in India but fail to conquer them, eventual peaceable (mostly) co-existence creating a fairly stable trading region stretching from Bengal to the borders of the Gallic lands. Cultures mingle, ideas spread, and the world advances further and faster than in our world.
Rome ended as a splatted bug on the windshield of Macedonian expansion, but the Celts, a long way from the core of the Empire and not looking appreciably rich in loot, remain unconquered. From the Greeks the Celts would pick up ideas of universal monarchy and imperial administration, while literacy spread further and earlier. The disunity and internecine fighting so typical of the Celtic world OTL would slowly reduce as these ideas were assimilated, with larger and more stable kingdoms establishing themselves in Gaul and Celtic Iberia, with the Avernians being the ones to establish a genuinely unified and lasting All-Gaul state. It would remain so and grow further, albeit with occasional changes of ruling dynasty.
Meanwhile, the Universal Oikumene of the Greeks would, like China, become a cyclical but eternal Empire, with periods of disunity and internal turmoil followed by restoral by new dynasties, from Persia, from Anatolia, most recently from the Turkish steppe. All rulers end up speaking Greek (and Persian, if they’re at all cultured) and pursue the promotion of learning and the arts, the reconquest of lost territories, and the conquest of new ones where possible. For a long time the Celts tended to trail intellectually behind the Oikumene, undergoing periods of native reaction and hostility to Hellenist ideas during the low parts of the Oikumene’s dynastic cycle, but since the latest Oikumene “renaissance” of the 14th century and the discovery of the Americas in the same time frame, the Celtic world has participated fully in this world’s scientific and intellectual flowering, holding up their end of its earlier scientific revolution, and in some ways even surpassing their old teachers.
That the discovery of the Americas was accompanied by the latest unification of the Celtic world under one Empire (Greater Gaul always held together after the Avernians, but the extend of its control varied) was helpful, as was the fact that the Greeks (stuck on the eastern end of the Mediterranean) were poorly placed for Atlantic adventures. In spite of some Oikumene efforts to get there by way of the South Africa (leading to a Celtic cape colony to Conquista-block them) and competitive efforts by the Germanic nations, the Celts would eventually take pretty much all of the more lightly populated parts of the Americas. (Being more tolerant of religious and cultural difference than early modern Europeans, and without the ideological drive for conquest and forced conversion so strong in Spain, the Celts were generally happy to trade with Meso- and Andean-Americans for their silver, coca, and cacao rather than brining Belenus with fire and the sword.)
Today, the world has a roughly tripolar balance. The Rîgion Kelton, the Celtic universal monarchy, is definitely number one. Like the British Empire at its height, it has no permanent allies, only permanent interests, and needs none, having the world’s largest economy by a fair margin. It has been even larger in the past, but has mostly abandoned its empire (mostly of puppets and client states) in Africa as Behavior Not Befitting Us: the measures needed to keep hold of it were just getting a bit embarrassing. The empire is divided into Tirroi (Lands), which are in turn divided into Brogês (roughly Countries, but really meaning provinces ITTL), which are divided into Contrebâ (Cantrevs, essentially counties and major urban areas): sheer geographical spread means it’s a bit more decentralized than our US, but the individual Tirroi aren’t much more autonomous than Canadian provinces.
The Fifth Oikumene is a more compact power, if no more centralized (it's satrapies are actually more autonomous than Celtic Tirroi). Given its poorer resource base, the Fifth Oikumene is now rather behind the Rîgion in the power stakes, something embarrassing to citizens who still are nostalgic for the days when the Celts were those occasionally bothersome western barbarians who nonetheless remained in awe of Hellenic culture. While the Oikumene remains one of the main wellsprings of world culture, it’s days as Top Nation are probably behind them. To maintain a rough balance of power they’ve allied with the loose but extensive Cholan block of nations, those commercial minded south Indians with no fear of maritime bad Karma (Cholans hold that as long as you don’t swim in it, the sea won’t pollute you) having mastered the seas from Madagascar to the Our Timeline Philippines.
The Cholans, in turn, see their Oikumene alliance as a way of boosting their strength vs. the third power. The Chinese, here known as the Wâxiâ Empire, and their small circle of client states, are still over a fifth of humanity, and while they may be the least influential of the three great powers, they are hardly small. (They were readier to modernize, when the time came, than our China. The Chinese generally been more concerned about the outside world and less convinced of their utter supremacy than in our TL: having the Oikumene as an intermittent but usually aggressive neighbor in Central Asia will do that).
There are, of course, other nations outside the tripartite division of the world. Most other nations tend toward neutrality or loose alliances as needed: the sort of harsh ideological divide of our world’s cold war is lacking, and after a somewhat nervous period following the development of nuclear weapons, international tensions have greatly decreased. In fact, tensions are lower right now than they have been in generations (which just leads some people to grumble that means they’re due for some trouble).
In the Americas, after threading the eye of a demographic needle (Celts were cleaner than OTL European colonizers, but still brought diseases) the major native American civilizations have revived and even (in the case of the Maya and the Naua) expanded, but remain like OTL Mexico somewhat in the shade of their giant neighbor. Actually muscular enough to historically have made the Celts sweat at times, the Thiudiski Rike is an economic and technological powerhouse, if on a smaller scale than the Big Three, a (looser) union of Germanic powers threatened by the unification of the Celts and their total victory in the colonial sweepstakes. (Also includes Balts and Finns, Germanized to some extent). The Slavic state of Venedska is just happy to have avoided becoming an Oikumene client state, while historically most African states have _been_ someone’s client states at one time or another. Greco-Punic-Berber Kharkhedon is another proudly successful second-rank power, while some Africans see the possibility of unifying to become a new global power center, if the great powers allow it – pity that Kongo, the West Africans, and the East African Uwere Oikumene all disagree rather strongly on the details.
Then there are some states which just exist as neutralized buffer states, such as formerly much fought over south Italy, and those products of clever Wâxiân diplomacy masquerading as concern for small nations, Odul and Kurika (Our Mongolia, roughly), which prevent a long border with the Oikumene to the north. (Böd, OTOH, is more beloved by the northern Indians than by Wâxiâ ).
Religiously this world is lacking the great monotheistic religions of OTL, Christianity never having arisen and Zoroastrianism having remained a mostly regional faith. There still are Jews, mostly in the Oikumene, but they’re a not particularly large group, a minority even in their traditional homeland (south Arabia, Mesopotamia and Khemi/Egypt are the main centers of Jewish population outside Palestine). Various forms of systematized polytheism are the most common form of faith in this world, although some have emphasized one deity or another to the extent of becoming “near monotheist.” Buddhism is a bit less widespread and successful in this world (well, compared OTL before the commies, anyway) while traditional belief-systems and religious cults of all sorts flourish, the latter proliferating wildly in this TL’s equivalent of the Internet Era. Of late, as technology of all sorts races ahead and the notion of possible physical immortality in this world starts looking like less of a pipe dream, religious devotion has been flagging. The importance of religious ritual and practice in everyday life and custom militates against a “Godless” society, but a fashionable skepticism akin to that of the old Roman and Greek elites is widespread, along with a certain malaise which helps keep new cults pop up regularly.
There remain places where belief in the Gods is still pushed hard – the Pukina Priesthood has modernized to the extent where they hold that all 100 billion * 100 billion stars in the universe are manifestations of the Sun God, but you should really avoid going around broadcasting that you don’t see how the Sun can also be a Jaguar during the High Holy Days.
Technologically this world is rather more advanced than our own. Planetary standards of living are very high, and even the poorest nations are pretty well off by our standards (not that they don’t feel poor, since that stuff is always relative.) Energy is cheap, clean and reliable, nanotech is widely used in manufacturing and medicine, and cancers of any type are straightforwardly curable. Quantum computing exists (which causes all sorts of headaches for computer security), and strong AI is theoretically possible but so heavily regulated that there is very little actual work being done (there have been cases where AI in development have gone alarmingly strange, and none of the major government wants any of that crap taking place again under insecure circumstances. Fortunately, the human brain isn’t nearly as hackable as a lot of Singularitarians think it is).
Biotech is also advanced, although again there is a lot of government control, compounded by a reverence for nature strongly held by Celts and East Asians alike, and in the case of humans a strong cultural belief in the beauty and dignity of the “normal” human body among both Greeks and Celts: this is also reflected in mores about cybernetic implants and enhancements, which are generally carefully disguised to be as invisible as possible. There are of course exceptions: in some African nations and among some Native American groups, the Maya in particular, are quite fond of visible cybernetic enhancements, and some worry about where the Cholan fad for imitating their Gods (blue skin is in, as are cybernetic extra arms) may go.
In any event, human biotech modification has mostly gone towards eliminating genetic damage and defects, and to minor enhancements of things like disease resistance, heat tolerance, memory, etc. Really serious modifications that could create a physical “superman” or substantially change the nature of the human mind are currently off the table. There is a heated debate going on in Wâxiân circles as to where curing mental illness ends and eliminating normal eccentricity or orneriness begins.
Weapons tech includes railguns portable and orbital, particle beams, high power lasers, gas tight “Starship Troopers” (the book) type power armor with chameleon capacity, and an endless variety of smart drones just a bit short of true AI (and carefully managed to stay that way). Due to the currently peaceful conditions on Earth, military budgets aren’t too high, but there’s an element of national prestige in having the shiniest toys, so R & D budgets remain substantial.
Interplanetary travel has been in existence for quite a while: not only have all the Great Powers but most of the middling powers as well have space programs. Every planet  out to Makemake has been reached, if only for bragging rights, and there are a few colonies on Mars, quite a few on the Moon, and a crapload of space habitats in various Earth orbits.
New theories in physics promise the possibility of actual FTL travel (there is some uncertainty as to whether you stay inside the same universe while you do it, though) and researchers enthusiastic about soon getting to the stars having been shocked and in some cases dismayed by a spin-off of their work: a method to open gates to parallel worlds. While an actual starship is some ways away, it’s possible right now to just walk into an alternate universe, and cautious exploration is beginning. Some fear that funding for the FTL program will be cut: why spend all that money to go to (probably) uninhabitable solar systems when there are an infinite number of habitable worlds just waiting to be visited – and a lot of them even have clean bathrooms already!
 In this world, dwarf planet is just a sub-category of planet, and there they count hundreds of them out in the Kupier belt. Fortunately, schoolchildren are not required to memorize them.