How is taste of chemical compounds determined?
When a compound is synthesised or isolated, it needs to be characterised. This characterisation serves to determine whether something has been synthesised/isolated before and as a template for later generations to compare their synthesised/isolated compounds to the one you have.

Nowadays, one reports NMR and mass spectrometry data; for chiral compounds specific rotation is measured. Sometimes, elemental analysis is included. Depending on the journal’s requirement you might also need to measure IR and/or melting points. Furthermore, you typically describe your compound (is it a yellow oil or white needle-like crystals?) although the description is considered secondary and the NMR/mass data is what you look at for matches.

In the old days, these analytical methods were not available. Instead, analyses would rely heavily on what a compound looks like and how it behaves. Thus, it was attempted to generate various crystalline forms and reactions with various standard reagents were investigated. Additionally, melting points were measured and chemists used all available senses to characterise. Thus, when the paper says that boron phosphate is a white, odourless and tasteless compound, the chemist in question not only sniffed the flask but also put a bit on his tongue to assess taste.

The problem with this approach is that you have no idea whether something is toxic/harmful or not. As there are many mechanisms by which a compound can interfere with the tightly controlled reactions in our body and cells or the macromolecular structures therein, many (if not most) compounds will be harmful in at least one way. While the common approach was to taste as little as possible, the risk remains as sometimes the $\mathrm{LD_{50}}$ is in the $\pu{\mu g/kg}$ range so even the smallest sample could kill you (although compounds that toxic are thankfully rare). Furthermore, a lot of compounds are able to induce DNA mutations which likely led to increased cancer rates and an overall lower life expectancy for chemists.

This is, quite obviously, unacceptable from a workplace safety point of view. Thus, tasting chemicals was prohibited practically everywhere. Furthermore, to prevent accidental contamination or confusion of glasses, not even the consumption of food and drink is permitted in most laboratories. Therefore, for anything that has been synthesised or isolated for the first time after these measures were in effect, we typically do not know taste any more. In fact, unless we are certain that we have evidence a compound is harmless, it is to be treated as highly toxic in the lab with all according security measures.

A compound’s odour is a slightly different story. It is said that the chemist working ideally will never get a wiff of their compounds because they will make sure that none access the common lab air. In practice, that is practically unattainable especially since lab scales are often in the middle of the room and most solids are in glass bottles that need to be opened fully to take out a sample. Thus, it is unavoidable that chemists pick up the smell of a number of (typically particularly volatile or particularly odourous) compounds. Systematic odour examinations are no longer performed but where the odour is characteristic, it is sometimes included in a compound’s characterisation (e.g. ‘sulphurous odour’). Some chemists take this a step further: a former colleague once sniffed at the flask of another former colleague and exclaimed ‘it smells like your product’, explaining that tertiary alcohols apparantly have a distinctive odour.