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The phrase 'our first discovery' is correct and usable in written English.
You can use the phrase when referring to the first instance of a particular insight or discovery made by yourself or a group. For example: "Our first discovery was that the region had an abundance of natural resources."
Exact(7)
Our first discovery came the following afternoon at Lewis and Clark State Park at Blue Lake, Iowa, about 400 miles from St . Louis
Since our first discovery of a CD4-mimic, NBD-556, which targets the Phe43 cavity of HIV-1 gp120, we and other groups made considerable progress in designing new CD4-mimics with viral entry-antagonist property.
"This is our first discovery of a group of Rohingya which suggests that smuggling in this region might have increased in recent years," police captain Somporn Thongcheen told Reuters.
In the first edition of Science and Health (1875), she wrote that she had "made our first discovery that science mentally applied would heal the sick" in 1864, while she was seeing Quimby, and in 1883 told the Boston Post that she had "laid the foundations of mental healing" in 1853, when she was practising homeopathy.
Our first discovery, as indicated by the relatively low (30.2%) response, was that physicians did not want to respond to our questionnaire.
A detailed discussion of why our false negative rate is lower and our first discovery of function rate is higher than past studies as well as other technical details of improving results from RNAi screens can be found elsewhere [ 43].
Similar(53)
Our second discovery was Skrinkle Haven, a beach that is only accessible via its neighbouring cove, Church Doors, and then by a mysterious clamber through a narrow sea cave.
Perhaps that first discovery of our adult selves lives on inside everything that follows, like a time capsule buried somewhere at the core of what we make of the rest of our lives.
To our knowledge, this is the first discovery of multiple group I introns in a single chromosomal gene of a bacterium (multiple group I introns are also present in at least one phage gene [ 24] and one prophage gene [ 25]).
Since the first discovery of miRNAs, our understanding of biogenesis and regulation has exponentially grown.
Our second major discovery was that there were patterns of Internet usage that were statistically high among participants with depressive symptoms compared with those without symptoms.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com