Ms Mathur noticed the similarities after moving to BBC Radio Wales
"We tend to pronounce everything - all the consonants, all the vowels."
'Apu from the Simpsons holidaying in Swansea' or Pete Postlethwaite?
Remarkably, no-one has yet done a direct proper comparative study between the two languages to found out why this is so, says Ms Mathur.
"What I'm hoping is that if amateurs like myself - who have indulged in doing a little bit of research here and there - come forward, we can actually do proper research with professional linguists," she told BBC World Service's Everywoman programme.
Ms Mathur explained that when she moved to Wales, everyone instantly assumed she was Welsh from her accent.
"I would just answer the phone, and they would say 'oh hello, which part of Wales are you from?'," she said.
We tend to pronounce everything - all the consonants, all the vowels
Sonia Mathur "I would explain that I'm not from Wales at all - I'm from India.
"It was just hilarious each time this conversation happened."
Her interest aroused, Ms Mathur spoke to a number of other people whose first language is Hindi.
One Hindi doctor in north Wales told her that when he answered the phone, people hearing his accent would begin talking to him in Welsh.
"I thought maybe it isn't a coincidence, and if I dig deeper I might find something more," Ms Mathur said.
Particular similarities between the accents are the way that both place emphasis on the last part of word, and an elongated way of speaking that pronounces all the letters of a word.
"We tend to pronounce everything - all the consonants, all the vowels," Ms Mathur said.
"For example, if you were to pronounce 'predominantly', it would sound really similar in both because the 'r' is rolled, there is an emphasis on the 'd', and all the letters that are used to make the word can be heard.
"It's just fascinating that these things happen between people who come from such varied backgrounds."
The similarities have sometimes proved particularly tricky for actors - Pete Postlethwaite, playing an Asian criminal in the 1995 film The Usual Suspects, had his accent described by Empire magazine as "Apu from the Simpsons holidaying in Swansea".
But not only the two languages' accents share notable common features - their vocabularies do too.
'Apu from the Simpsons holidaying in Swansea' or Pete Postlethwaite? Ms Mathur's own research on basic words, such as the numbers one to 10, found that many were similar - "seven", for example, is "saith" in Welsh, "saat" in Hindi.
"These kind of things really struck me," she said.
"When I reached number nine they were exactly the same - it's 'naw' - and I thought there had to be more to it than sheer coincidence."
She later spoke to professor Colin Williams of Cardiff University's School Of Welsh, who specialises in comparative languages.
He suggested that the similarities are because they come from the same mother language - the proto-European language.
"It was basically the mother language to Celtic, Latin, and Sanskrit," Ms Mathur added.
"So basically that's where this link originates from."
Yes, Welsh and Hindi are related languages, going back 4000 years plus. But at that separation, sound similarities are probably coincidence.