How did the Upanishad Rishis solved the ‘Problem of One and Many? I will elaborate this after explaining why there are no definable objects in the world.
All Object Names Are Merely Conventional 
Let us take an example of Tomato. Tomato from it’s initial small size, will gradually grow, and after a few weeks, will become big. During this course of time, it’s properties will change; it will turn from green color to red, and then finally, it will rot.
So, here, we can say that tomato passes through many stages. In each stage, it acquires different properties, nature and taste. Yet, ironically, we continue to call that object as ‘Tomato’. In other words, we give a fixed Name to every objects in the world, even though those objects change their properties and nature, continuously!
What does this indicate?
The implication is very clear – All the names of objects (in the world) are merely conventional. That is, object names do not reflect any of the qualities or essence of that particular object. It is just a set of alphabetic characters to denote that object. A name denotes all of the different states of a particular object.
There Are No Objects In The Experiential World. Why?
‘Many’ are, actually, just different stages of object’s existence. That is, the corresponding names, associated with different stages/phases of objects are merely conventional, not actual. Every stage is unstable, and therefore, in the next moment ‘current stage’ will become another stage. It is not these undefinable and unstable stages, that are getting changed in the next second. Each unstable stage is a mere link of a lengthy chain of continuous flux/change. A stage is a state of an object at a particular time. In summary, these changes/stages make it totally impossible to define or describe any object in the experiential world, in a satisfactory manner. i.e., All definitions about worldly objects are temporal. So what conclusion can be derived from the above mentioned facts? The Conclusion is obvious – THERE ARE NO DEFINABLE OBJECTS IN THE EXPERIENTIAL WORLD!
Upcoming Article -> If there are no definable objects in the experiential world, and what we see are the different stages of unending changes, then what is that which undergo change ?
Featured Image Credit -> https://amiracarluccio.com/2018/03/03/zen-stories-there-is-no-objective-world/
 “O Good looking one, as by knowing a lump of gold all things made of gold become known: all transformation has speech as its basis, and it is name only. Gold as such is the reality”
— Chandogya Upanishad, Sankara Bhashyam. Page 410. (Tran: Swami Gambhirananda, Advaita Ashrama).